Nektar++
CoupledLinearNS.cpp
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3 // File CoupledLinearNS.cpp
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9 // Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
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30 //
31 // Description: Coupled Solver for the Linearised Incompressible
32 // Navier Stokes equations
33 ///////////////////////////////////////////////////////////////////////////////
34 
35 #include <boost/algorithm/string.hpp>
36 
37 #include <IncNavierStokesSolver/EquationSystems/CoupledLinearNS.h>
38 #include <LibUtilities/BasicUtils/Timer.h>
39 #include <LocalRegions/MatrixKey.h>
40 #include <MultiRegions/ContField.h>
41 #include <MultiRegions/GlobalLinSysDirectStaticCond.h>
42 
43 using namespace std;
44 
45 namespace Nektar
46 {
47 
48 string CoupledLinearNS::className =
49  SolverUtils::GetEquationSystemFactory().RegisterCreatorFunction(
50  "CoupledLinearisedNS", CoupledLinearNS::create);
51 
52 /**
53  * @class CoupledLinearNS
54  *
55  * Set up expansion field for velocity and pressure, the local to
56  * global mapping arrays and the basic memory definitions for
57  * coupled matrix system
58  */
59 CoupledLinearNS::CoupledLinearNS(
60  const LibUtilities::SessionReaderSharedPtr &pSession,
61  const SpatialDomains::MeshGraphSharedPtr &pGraph)
62  : UnsteadySystem(pSession, pGraph), IncNavierStokes(pSession, pGraph),
63  m_zeroMode(false)
64 {
65 }
66 
67 void CoupledLinearNS::v_InitObject(bool DeclareField)
68 {
69  IncNavierStokes::v_InitObject(DeclareField);
70 
71  int i;
72  int expdim = m_graph->GetMeshDimension();
73 
74  // Get Expansion list for orthogonal expansion at p-2
75  const SpatialDomains::ExpansionInfoMap &pressure_exp =
76  GenPressureExp(m_graph->GetExpansionInfo("u"));
77 
78  m_nConvectiveFields = m_fields.size();
79  if (boost::iequals(
80  m_boundaryConditions->GetVariable(m_nConvectiveFields - 1), "p"))
81  {
82  ASSERTL0(false, "Last field is defined as pressure but this is not "
83  "suitable for this solver, please remove this field as "
84  "it is implicitly defined");
85  }
86  // Decide how to declare explist for pressure.
87  if (expdim == 2)
88  {
89  int nz;
90 
91  if (m_HomogeneousType == eHomogeneous1D)
92  {
93  ASSERTL0(m_fields.size() > 2, "Expect to have three at least three "
94  "components of velocity variables");
95  LibUtilities::BasisKey Homo1DKey =
96  m_fields[0]->GetHomogeneousBasis()->GetBasisKey();
97 
98  m_pressure = MemoryManager<MultiRegions::ExpList3DHomogeneous1D>::
99  AllocateSharedPtr(m_session, Homo1DKey, m_LhomZ, m_useFFT,
100  m_homogen_dealiasing, pressure_exp);
101 
102  ASSERTL1(m_npointsZ % 2 == 0,
103  "Non binary number of planes have been specified");
104  nz = m_npointsZ / 2;
105  }
106  else
107  {
108  m_pressure =
109  MemoryManager<MultiRegions::ExpList>::AllocateSharedPtr(
110  m_session, pressure_exp);
111  nz = 1;
112  }
113 
114  Array<OneD, MultiRegions::ExpListSharedPtr> velocity(m_velocity.size());
115  for (i = 0; i < m_velocity.size(); ++i)
116  {
117  velocity[i] = m_fields[m_velocity[i]];
118  }
119 
120  // Set up Array of mappings
121  m_locToGloMap = Array<OneD, CoupledLocalToGlobalC0ContMapSharedPtr>(nz);
122 
123  if (m_singleMode)
124  {
125 
126  ASSERTL0(nz <= 2,
127  "For single mode calculation can only have nz <= 2");
128  if (m_session->DefinesSolverInfo("BetaZero"))
129  {
130  m_zeroMode = true;
131  }
132  int nz_loc = 2;
133  m_locToGloMap[0] =
134  MemoryManager<CoupledLocalToGlobalC0ContMap>::AllocateSharedPtr(
135  m_session, m_graph, m_boundaryConditions, velocity,
136  m_pressure, nz_loc, m_zeroMode);
137  }
138  else
139  {
140  // base mode
141  int nz_loc = 1;
142  m_locToGloMap[0] =
143  MemoryManager<CoupledLocalToGlobalC0ContMap>::AllocateSharedPtr(
144  m_session, m_graph, m_boundaryConditions, velocity,
145  m_pressure, nz_loc);
146 
147  if (nz > 1)
148  {
149  nz_loc = 2;
150  // Assume all higher modes have the same boundary conditions and
151  // re-use mapping
152  m_locToGloMap[1] =
153  MemoryManager<CoupledLocalToGlobalC0ContMap>::
154  AllocateSharedPtr(
155  m_session, m_graph, m_boundaryConditions, velocity,
156  m_pressure->GetPlane(2), nz_loc, false);
157  // Note high order modes cannot be singular
158  for (i = 2; i < nz; ++i)
159  {
160  m_locToGloMap[i] = m_locToGloMap[1];
161  }
162  }
163  }
164  }
165  else if (expdim == 3)
166  {
167  // m_pressure =
168  // MemoryManager<MultiRegions::ExpList3D>::AllocateSharedPtr(pressure_exp);
169  ASSERTL0(false, "Setup mapping aray");
170  }
171  else
172  {
173  ASSERTL0(false, "Exp dimension not recognised");
174  }
175 
176  // creation of the extrapolation object
177  if (m_equationType == eUnsteadyNavierStokes)
178  {
179  std::string vExtrapolation = "Standard";
180 
181  if (m_session->DefinesSolverInfo("Extrapolation"))
182  {
183  vExtrapolation = m_session->GetSolverInfo("Extrapolation");
184  }
185 
186  m_extrapolation = GetExtrapolateFactory().CreateInstance(
187  vExtrapolation, m_session, m_fields, m_pressure, m_velocity,
188  m_advObject);
189  }
190 }
191 
192 /**
193  * Set up a coupled linearised Naviers-Stokes solve. Primarily a
194  * wrapper fuction around the full mode by mode version of
195  * SetUpCoupledMatrix.
196  *
197  */
198 void CoupledLinearNS::SetUpCoupledMatrix(
199  const NekDouble lambda, const Array<OneD, Array<OneD, NekDouble>> &Advfield,
200  bool IsLinearNSEquation)
201 {
202 
203  int nz;
204  if (m_singleMode)
205  {
206 
207  NekDouble lambda_imag;
208 
209  // load imaginary component of any potential shift
210  // Probably should be called from DriverArpack but not yet
211  // clear how to do this
212  m_session->LoadParameter("imagShift", lambda_imag,
213  NekConstants::kNekUnsetDouble);
214  nz = 1;
215  m_mat = Array<OneD, CoupledSolverMatrices>(nz);
216 
217  ASSERTL1(m_npointsZ <= 2, "Only expected a maxmimum of two planes in "
218  "single mode linear NS solver");
219 
220  if (m_zeroMode)
221  {
222  SetUpCoupledMatrix(lambda, Advfield, IsLinearNSEquation, 0,
223  m_mat[0], m_locToGloMap[0], lambda_imag);
224  }
225  else
226  {
227  NekDouble beta = 2 * M_PI / m_LhomZ;
228  NekDouble lam = lambda + m_kinvis * beta * beta;
229 
230  SetUpCoupledMatrix(lam, Advfield, IsLinearNSEquation, 1, m_mat[0],
231  m_locToGloMap[0], lambda_imag);
232  }
233  }
234  else
235  {
236  int n;
237  if (m_npointsZ > 1)
238  {
239  nz = m_npointsZ / 2;
240  }
241  else
242  {
243  nz = 1;
244  }
245 
246  m_mat = Array<OneD, CoupledSolverMatrices>(nz);
247 
248  // mean mode or 2D mode.
249  SetUpCoupledMatrix(lambda, Advfield, IsLinearNSEquation, 0, m_mat[0],
250  m_locToGloMap[0]);
251 
252  for (n = 1; n < nz; ++n)
253  {
254  NekDouble beta = 2 * M_PI * n / m_LhomZ;
255 
256  NekDouble lam = lambda + m_kinvis * beta * beta;
257 
258  SetUpCoupledMatrix(lam, Advfield, IsLinearNSEquation, n, m_mat[n],
259  m_locToGloMap[n]);
260  }
261  }
262 }
263 
264 /**
265  * Set up a coupled linearised Naviers-Stokes solve in the
266  * following manner:
267  *
268  * Consider the linearised Navier-Stokes element matrix denoted as
269  *
270  * \f[ \left [ \begin{array}{ccc} A
271  * & -D_{bnd}^T & B\\ -D_{bnd}& 0 & -D_{int}\\ \tilde{B}^T &
272  * -D_{int}^T & C \end{array} \right ] \left [ \begin{array}{c} {\bf
273  * v}_{bnd} \\ p\\ {\bf v}_{int} \end{array} \right ] = \left [
274  * \begin{array}{c} {\bf f}_{bnd} \\ 0\\ {\bf f}_{int} \end{array}
275  * \right ] \f]
276  *
277  * where \f${\bf v}_{bnd}, {\bf f}_{bnd}\f$ denote the degrees of
278  * freedom of the elemental velocities on the boundary of the
279  * element, \f${\bf v}_{int}, {\bf f}_{int}\f$ denote the degrees
280  * of freedom of the elemental velocities on the interior of the
281  * element and \f$p\f$ is the piecewise continuous pressure. The
282  * matrices have the interpretation
283  *
284  * \f[ A[n,m] = (\nabla \phi^b_n, \nu \nabla
285  * \phi^b_m) + (\phi^b_n,{\bf U \cdot \nabla} \phi^b_m) +
286  * (\phi^b_n \nabla^T {\bf U} \phi^b_m), \f]
287  *
288  * \f[ B[n,m] = (\nabla \phi^b_n, \nu \nabla \phi^i_m) +
289  * (\phi^b_n,{\bf U \cdot \nabla} \phi^i_m) + (\phi^b_n \nabla^T
290  * {\bf U} \phi^i_m),\f]
291  *
292  * \f[\tilde{B}^T[n,m] = (\nabla \phi^i_n, \nu \nabla \phi^b_m) +
293  * (\phi^i_n,{\bf U \cdot \nabla} \phi^b_m) + (\phi^i_n \nabla^T
294  * {\bf U} \phi^b_m) \f]
295  *
296  * \f[ C[n,m] = (\nabla \phi^i_n, \nu \nabla
297  * \phi^i_m) + (\phi^i_n,{\bf U \cdot \nabla} \phi^i_m) +
298  * (\phi^i_n \nabla^T {\bf U} \phi^i_m),\f]
299  *
300  * \f[ D_{bnd}[n,m] = (\psi_m,\nabla \phi^b),\f]
301  *
302  * \f[ D_{int}[n,m] = (\psi_m,\nabla \phi^i) \f]
303  *
304  * where \f$\psi\f$ is the space of pressures typically at order
305  * \f$P-2\f$ and \f$\phi\f$ is the velocity vector space of
306  * polynomial order \f$P\f$. (Note the above definitions for the
307  * transpose terms shoudl be interpreted with care since we have
308  * used a tensor differential for the \f$\nabla^T \f$ terms)
309  *
310  * Note \f$B = \tilde{B}^T\f$ if just considering the stokes
311  * operator and then \f$C\f$ is also symmetric. Also note that
312  * \f$A,B\f$ and \f$C\f$ are block diagonal in the Oseen equation
313  * when \f$\nabla^T {\bf U}\f$ are zero.
314  *
315  * Since \f$C\f$ is invertible we can premultiply the governing
316  * elemental equation by the following matrix:
317  *
318  * \f[ \left [ \begin{array}{ccc} I & 0 &
319  * -BC^{-1}\\ 0& I & D_{int}C^{-1}\\ 0 & 0 & I \end{array}
320  * \right ] \left \{ \left [ \begin{array}{ccc} A & -D_{bnd}^T &
321  * B\\ -D_{bnd}& 0 & -D_{int}\\ \tilde{B}^T & -D_{int}^T & C
322  * \end{array} \right ] \left [ \begin{array}{c} {\bf v}_{bnd} \\
323  * p\\ {\bf v_{int}} \end{array} \right ] = \left [
324  * \begin{array}{c} {\bf f}_{bnd} \\ 0\\ {\bf f_{int}} \end{array}
325  * \right ] \right \} \f]
326  *
327  * which if we multiply out the matrix equation we obtain
328  *
329  * \f[ \left [ \begin{array}{ccc} A - B
330  * C^{-1}\tilde{B}^T & -D_{bnd}^T +B C^{-1} D_{int}^T& 0\\
331  * -D_{bnd}+D_{int} C^{-1} \tilde{B}^T & -D_{int} C^{-1}
332  * D_{int}^T & 0\\ \tilde{B}^T & -D_{int}^T & C \end{array} \right ]
333  * \left [ \begin{array}{c} {\bf v}_{bnd} \\ p\\ {\bf v_{int}}
334  * \end{array} \right ] = \left [ \begin{array}{c} {\bf f}_{bnd}
335  * -B C^{-1} {\bf f}_{int}\\ f_p = D_{int} C^{-1} {\bf
336  * f}_{int}\\ {\bf f_{int}} \end{array} \right ] \f]
337  *
338  * In the above equation the \f${\bf v}_{int}\f$ degrees of freedom
339  * are decoupled and so we need to solve for the \f${\bf v}_{bnd},
340  * p\f$ degrees of freedom. The final step is to perform a second
341  * level of static condensation but where we will lump the mean
342  * pressure mode (or a pressure degree of freedom containing a
343  * mean component) with the velocity boundary degrees of
344  * freedom. To do we define \f${\bf b} = [{\bf v}_{bnd}, p_0]\f$ where
345  * \f$p_0\f$ is the mean pressure mode and \f$\hat{p}\f$ to be the
346  * remainder of the pressure space. We now repartition the top \f$2
347  * \times 2\f$ block of matrices of previous matrix equation as
348  *
349  * \f[ \left [ \begin{array}{cc} \hat{A} & \hat{B}\\ \hat{C} &
350  * \hat{D} \end{array} \right ] \left [ \begin{array}{c} {\bf b}
351  * \\ \hat{p} \end{array} \right ] = \left [ \begin{array}{c}
352  * \hat{\bf f}_{bnd} \\ \hat{f}_p \end{array} \right ]
353  * \label{eqn.linNS_fac2} \f]
354  *
355  * where
356  *
357  * \f[ \hat{A}_{ij} = \left [ \begin{array}{cc} A - B
358  * C^{-1}\tilde{B}^T & [-D_{bnd}^T +B C^{-1} D_{int}^T]_{i0}\\
359  * {[}-D_{bnd}+D_{int} C^{-1} \tilde{B}^T]_{0j} & -[D_{int}
360  * C^{-1} D_{int}^T ]_{00} \end{array} \right ] \f]
361  *
362  * \f[ \hat{B}_{ij} = \left [ \begin{array}{c} [-D_{bnd}^T +B
363  * C^{-1} D_{int}^T]_{i,j+1} \\ {[} -D_{int} C^{-1} D^T_{int}
364  * ]_{0j}\end{array} \right ] \f]
365  *
366  * \f[ \hat{C}_{ij} = \left [\begin{array}{cc} -D_{bnd} +
367  * D_{int} C^{-1} \tilde{B}^T, & {[} -D_{int} C^{-1} D^T_{int}
368  * ]_{i+1,0}\end{array} \right ] \f]
369  *
370  * \f[ \hat{D}_{ij} = \left [\begin{array}{c} {[} -D_{int}
371  * C^{-1} D^T_{int} ]_{i+1,j+1}\end{array} \right ] \f]
372  *
373  * and
374  *
375  * \f[ fh\_{bnd} = \left [ \begin{array}{c} {\bf
376  * f}_{bnd} -B C^{-1} {\bf f}_{int}\\ {[}D_{int} C^{-1} {\bf
377  * f}_{int}]_0 \end{array}\right ] \hspace{1cm} [fh\_p_{i} =
378  * \left [ \begin{array}{c} {[}D_{int} C^{-1} {\bf f}_{iint}]_{i+1}
379  * \end{array}\right ] \f]
380  *
381  * Since the \f$\hat{D}\f$ is decoupled and invertible we can now
382  * statically condense the previous matrix equationto decouple
383  * \f${\bf b}\f$ from \f$\hat{p}\f$ by solving the following system
384  *
385  * \f[ \left [ \begin{array}{cc} \hat{A} - \hat{B} \hat{D}^{-1}
386  * \hat{C} & 0 \\ \hat{C} & \hat{D} \end{array} \right ] \left
387  * [ \begin{array}{c} {\bf b} \\ \hat{p} \end{array} \right ] =
388  * \left [ \begin{array}{c} \hat{\bf f}_{bnd} - \hat{B}
389  * \hat{D}^{-1} \hat{f}_p\\ \hat{f}_p \end{array} \right ] \f]
390  *
391  * The matrix \f$\hat{A} - \hat{B} \hat{D}^{-1} \hat{C}\f$ has
392  * to be globally assembled and solved iteratively or
393  * directly. One we obtain the solution to \f${\bf b}\f$ we can use
394  * the second row of equation fourth matrix equation to solve for
395  * \f$\hat{p}\f$ and finally the last row of equation second
396  * matrix equation to solve for \f${\bf v}_{int}\f$.
397  *
398  */
399 
400 void CoupledLinearNS::SetUpCoupledMatrix(
401  const NekDouble lambda, const Array<OneD, Array<OneD, NekDouble>> &Advfield,
402  bool IsLinearNSEquation, const int HomogeneousMode,
403  CoupledSolverMatrices &mat,
404  CoupledLocalToGlobalC0ContMapSharedPtr &locToGloMap,
405  const NekDouble lambda_imag)
406 {
407  int n, i, j, k;
408  int nel = m_fields[m_velocity[0]]->GetNumElmts();
409  int nvel = m_velocity.size();
410 
411  // if Advfield is defined can assume it is an Oseen or LinearNS equation
412  bool AddAdvectionTerms =
413  (Advfield == NullNekDoubleArrayOfArray) ? false : true;
414  // bool AddAdvectionTerms = true; // Temporary debugging trip
415 
416  // call velocity space Static condensation and fill block
417  // matrices. Need to set this up differently for Oseen and
418  // Lin NS. Ideally should make block diagonal for Stokes and
419  // Oseen problems.
420  DNekScalMatSharedPtr loc_mat;
421  StdRegions::StdExpansionSharedPtr locExp;
422  NekDouble one = 1.0;
423  int nint, nbndry;
424  int rows, cols;
425  NekDouble zero = 0.0;
426  Array<OneD, unsigned int> bmap, imap;
427 
428  Array<OneD, unsigned int> nsize_bndry(nel);
429  Array<OneD, unsigned int> nsize_bndry_p1(nel);
430  Array<OneD, unsigned int> nsize_int(nel);
431  Array<OneD, unsigned int> nsize_p(nel);
432  Array<OneD, unsigned int> nsize_p_m1(nel);
433 
434  int nz_loc;
435 
436  if (HomogeneousMode) // Homogeneous mode flag
437  {
438  nz_loc = 2;
439  }
440  else
441  {
442  if (m_singleMode)
443  {
444  nz_loc = 2;
445  }
446  else
447  {
448  nz_loc = 1;
449  }
450  }
451 
452  // Set up block matrix sizes -
453  for (n = 0; n < nel; ++n)
454  {
455  nsize_bndry[n] = nvel *
456  m_fields[m_velocity[0]]->GetExp(n)->NumBndryCoeffs() *
457  nz_loc;
458  nsize_bndry_p1[n] = nsize_bndry[n] + nz_loc;
459  nsize_int[n] =
460  (nvel * m_fields[m_velocity[0]]->GetExp(n)->GetNcoeffs() * nz_loc -
461  nsize_bndry[n]);
462  nsize_p[n] = m_pressure->GetExp(n)->GetNcoeffs() * nz_loc;
463  nsize_p_m1[n] = nsize_p[n] - nz_loc;
464  }
465 
466  MatrixStorage blkmatStorage = eDIAGONAL;
467  DNekScalBlkMatSharedPtr pAh =
468  MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
469  nsize_bndry_p1, nsize_bndry_p1, blkmatStorage);
470  mat.m_BCinv = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
471  nsize_bndry, nsize_int, blkmatStorage);
472  mat.m_Btilde = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
473  nsize_bndry, nsize_int, blkmatStorage);
474  mat.m_Cinv = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
475  nsize_int, nsize_int, blkmatStorage);
476 
477  mat.m_D_bnd = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
478  nsize_p, nsize_bndry, blkmatStorage);
479 
480  mat.m_D_int = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
481  nsize_p, nsize_int, blkmatStorage);
482 
483  // Final level static condensation matrices.
484  DNekScalBlkMatSharedPtr pBh =
485  MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
486  nsize_bndry_p1, nsize_p_m1, blkmatStorage);
487  DNekScalBlkMatSharedPtr pCh =
488  MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
489  nsize_p_m1, nsize_bndry_p1, blkmatStorage);
490  DNekScalBlkMatSharedPtr pDh =
491  MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(nsize_p_m1, nsize_p_m1,
492  blkmatStorage);
493 
494  LibUtilities::Timer timer;
495  timer.Start();
496 
497  for (n = 0; n < nel; ++n)
498  {
499  nbndry = nsize_bndry[n];
500  nint = nsize_int[n];
501  k = nsize_bndry_p1[n];
502  DNekMatSharedPtr Ah =
503  MemoryManager<DNekMat>::AllocateSharedPtr(k, k, zero);
504  Array<OneD, NekDouble> Ah_data = Ah->GetPtr();
505  int AhRows = k;
506  DNekMatSharedPtr B =
507  MemoryManager<DNekMat>::AllocateSharedPtr(nbndry, nint, zero);
508  Array<OneD, NekDouble> B_data = B->GetPtr();
509  DNekMatSharedPtr C =
510  MemoryManager<DNekMat>::AllocateSharedPtr(nbndry, nint, zero);
511  Array<OneD, NekDouble> C_data = C->GetPtr();
512  DNekMatSharedPtr D =
513  MemoryManager<DNekMat>::AllocateSharedPtr(nint, nint, zero);
514  Array<OneD, NekDouble> D_data = D->GetPtr();
515 
516  DNekMatSharedPtr Dbnd = MemoryManager<DNekMat>::AllocateSharedPtr(
517  nsize_p[n], nsize_bndry[n], zero);
518  DNekMatSharedPtr Dint = MemoryManager<DNekMat>::AllocateSharedPtr(
519  nsize_p[n], nsize_int[n], zero);
520 
521  locExp = m_fields[m_velocity[0]]->GetExp(n);
522  locExp->GetBoundaryMap(bmap);
523  locExp->GetInteriorMap(imap);
524  StdRegions::ConstFactorMap factors;
525  factors[StdRegions::eFactorLambda] = lambda / m_kinvis;
526  LocalRegions::MatrixKey helmkey(
527  StdRegions::eHelmholtz, locExp->DetShapeType(), *locExp, factors);
528 
529  int ncoeffs = m_fields[m_velocity[0]]->GetExp(n)->GetNcoeffs();
530  int nphys = m_fields[m_velocity[0]]->GetExp(n)->GetTotPoints();
531  int nbmap = bmap.size();
532  int nimap = imap.size();
533 
534  Array<OneD, NekDouble> coeffs(ncoeffs);
535  Array<OneD, NekDouble> phys(nphys);
536  int psize = m_pressure->GetExp(n)->GetNcoeffs();
537  int pqsize = m_pressure->GetExp(n)->GetTotPoints();
538 
539  Array<OneD, NekDouble> deriv(pqsize);
540  Array<OneD, NekDouble> pcoeffs(psize);
541 
542  if (AddAdvectionTerms == false) // use static condensed managed matrices
543  {
544  // construct velocity matrices using statically
545  // condensed elemental matrices and then construct
546  // pressure matrix systems
547  DNekScalBlkMatSharedPtr CondMat;
548  CondMat = locExp->GetLocStaticCondMatrix(helmkey);
549 
550  for (k = 0; k < nvel * nz_loc; ++k)
551  {
552  DNekScalMat &SubBlock = *CondMat->GetBlock(0, 0);
553  rows = SubBlock.GetRows();
554  cols = SubBlock.GetColumns();
555  for (i = 0; i < rows; ++i)
556  {
557  for (j = 0; j < cols; ++j)
558  {
559  (*Ah)(i + k * rows, j + k * cols) =
560  m_kinvis * SubBlock(i, j);
561  }
562  }
563  }
564 
565  for (k = 0; k < nvel * nz_loc; ++k)
566  {
567  DNekScalMat &SubBlock = *CondMat->GetBlock(0, 1);
568  DNekScalMat &SubBlock1 = *CondMat->GetBlock(1, 0);
569  rows = SubBlock.GetRows();
570  cols = SubBlock.GetColumns();
571  for (i = 0; i < rows; ++i)
572  {
573  for (j = 0; j < cols; ++j)
574  {
575  (*B)(i + k * rows, j + k * cols) = SubBlock(i, j);
576  (*C)(i + k * rows, j + k * cols) =
577  m_kinvis * SubBlock1(j, i);
578  }
579  }
580  }
581 
582  for (k = 0; k < nvel * nz_loc; ++k)
583  {
584  DNekScalMat &SubBlock = *CondMat->GetBlock(1, 1);
585  NekDouble inv_kinvis = 1.0 / m_kinvis;
586  rows = SubBlock.GetRows();
587  cols = SubBlock.GetColumns();
588  for (i = 0; i < rows; ++i)
589  {
590  for (j = 0; j < cols; ++j)
591  {
592  (*D)(i + k * rows, j + k * cols) =
593  inv_kinvis * SubBlock(i, j);
594  }
595  }
596  }
597 
598  // Loop over pressure space and construct boundary block matrices.
599  for (i = 0; i < bmap.size(); ++i)
600  {
601  // Fill element with mode
602  Vmath::Zero(ncoeffs, coeffs, 1);
603  coeffs[bmap[i]] = 1.0;
604  m_fields[m_velocity[0]]->GetExp(n)->BwdTrans(coeffs, phys);
605 
606  // Differentiation & Inner product wrt base.
607  for (j = 0; j < nvel; ++j)
608  {
609  if ((nz_loc == 2) && (j == 2)) // handle d/dz derivative
610  {
611  NekDouble beta = -2 * M_PI * HomogeneousMode / m_LhomZ;
612 
613  Vmath::Smul(
614  m_fields[m_velocity[0]]->GetExp(n)->GetTotPoints(),
615  beta, phys, 1, deriv, 1);
616 
617  m_pressure->GetExp(n)->IProductWRTBase(deriv, pcoeffs);
618 
619  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
620  Dbnd->GetRawPtr() +
621  ((nz_loc * j + 1) * bmap.size() + i) *
622  nsize_p[n],
623  1);
624 
625  Vmath::Neg(psize, pcoeffs, 1);
626  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
627  Dbnd->GetRawPtr() +
628  ((nz_loc * j) * bmap.size() + i) *
629  nsize_p[n] +
630  psize,
631  1);
632  }
633  else
634  {
635  if (j < 2) // required for mean mode of homogeneous
636  // expansion
637  {
638  locExp->PhysDeriv(MultiRegions::DirCartesianMap[j],
639  phys, deriv);
640  m_pressure->GetExp(n)->IProductWRTBase(deriv,
641  pcoeffs);
642  // copy into column major storage.
643  for (k = 0; k < nz_loc; ++k)
644  {
645  Blas::Dcopy(
646  psize, &(pcoeffs)[0], 1,
647  Dbnd->GetRawPtr() +
648  ((nz_loc * j + k) * bmap.size() + i) *
649  nsize_p[n] +
650  k * psize,
651  1);
652  }
653  }
654  }
655  }
656  }
657 
658  for (i = 0; i < imap.size(); ++i)
659  {
660  // Fill element with mode
661  Vmath::Zero(ncoeffs, coeffs, 1);
662  coeffs[imap[i]] = 1.0;
663  m_fields[m_velocity[0]]->GetExp(n)->BwdTrans(coeffs, phys);
664 
665  // Differentiation & Inner product wrt base.
666  for (j = 0; j < nvel; ++j)
667  {
668  if ((nz_loc == 2) && (j == 2)) // handle d/dz derivative
669  {
670  NekDouble beta = -2 * M_PI * HomogeneousMode / m_LhomZ;
671 
672  Vmath::Smul(
673  m_fields[m_velocity[0]]->GetExp(n)->GetTotPoints(),
674  beta, phys, 1, deriv, 1);
675 
676  m_pressure->GetExp(n)->IProductWRTBase(deriv, pcoeffs);
677 
678  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
679  Dint->GetRawPtr() +
680  ((nz_loc * j + 1) * imap.size() + i) *
681  nsize_p[n],
682  1);
683 
684  Vmath::Neg(psize, pcoeffs, 1);
685  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
686  Dint->GetRawPtr() +
687  ((nz_loc * j) * imap.size() + i) *
688  nsize_p[n] +
689  psize,
690  1);
691  }
692  else
693  {
694  if (j < 2) // required for mean mode of homogeneous
695  // expansion
696  {
697  // m_fields[m_velocity[0]]->GetExp(n)->PhysDeriv(j,phys,
698  // deriv);
699  locExp->PhysDeriv(MultiRegions::DirCartesianMap[j],
700  phys, deriv);
701 
702  m_pressure->GetExp(n)->IProductWRTBase(deriv,
703  pcoeffs);
704 
705  // copy into column major storage.
706  for (k = 0; k < nz_loc; ++k)
707  {
708  Blas::Dcopy(
709  psize, &(pcoeffs)[0], 1,
710  Dint->GetRawPtr() +
711  ((nz_loc * j + k) * imap.size() + i) *
712  nsize_p[n] +
713  k * psize,
714  1);
715  }
716  }
717  }
718  }
719  }
720  }
721  else
722  {
723  // construct velocity matrices and pressure systems at
724  // the same time resusing differential of velocity
725  // space
726 
727  DNekScalMat &HelmMat =
728  *(locExp->as<LocalRegions::Expansion>()->GetLocMatrix(helmkey));
729  DNekScalMatSharedPtr MassMat;
730 
731  Array<OneD, const NekDouble> HelmMat_data =
732  HelmMat.GetOwnedMatrix()->GetPtr();
733  NekDouble HelmMatScale = HelmMat.Scale();
734  int HelmMatRows = HelmMat.GetRows();
735 
736  if ((lambda_imag != NekConstants::kNekUnsetDouble) && (nz_loc == 2))
737  {
738  LocalRegions::MatrixKey masskey(
739  StdRegions::eMass, locExp->DetShapeType(), *locExp);
740  MassMat = locExp->as<LocalRegions::Expansion>()->GetLocMatrix(
741  masskey);
742  }
743 
744  Array<OneD, NekDouble> Advtmp;
745  Array<OneD, Array<OneD, NekDouble>> AdvDeriv(nvel * nvel);
746  // Use ExpList phys array for temporaary storage
747  Array<OneD, NekDouble> tmpphys = m_fields[0]->UpdatePhys();
748  int phys_offset = m_fields[m_velocity[0]]->GetPhys_Offset(n);
749  int nv;
750  int npoints = locExp->GetTotPoints();
751 
752  // Calculate derivative of base flow
753  if (IsLinearNSEquation)
754  {
755  int nv1;
756  int cnt = 0;
757  AdvDeriv[0] = Array<OneD, NekDouble>(nvel * nvel * npoints);
758  for (nv = 0; nv < nvel; ++nv)
759  {
760  for (nv1 = 0; nv1 < nvel; ++nv1)
761  {
762  if (cnt < nvel * nvel - 1)
763  {
764  AdvDeriv[cnt + 1] = AdvDeriv[cnt] + npoints;
765  ++cnt;
766  }
767 
768  if ((nv1 == 2) && (m_HomogeneousType == eHomogeneous1D))
769  {
770  Vmath::Zero(npoints, AdvDeriv[nv * nvel + nv1],
771  1); // dU/dz = 0
772  }
773  else
774  {
775  locExp->PhysDeriv(
776  MultiRegions::DirCartesianMap[nv1],
777  Advfield[nv] + phys_offset,
778  AdvDeriv[nv * nvel + nv1]);
779  }
780  }
781  }
782  }
783 
784  for (i = 0; i < nbmap; ++i)
785  {
786 
787  // Fill element with mode
788  Vmath::Zero(ncoeffs, coeffs, 1);
789  coeffs[bmap[i]] = 1.0;
790  locExp->BwdTrans(coeffs, phys);
791 
792  for (k = 0; k < nvel * nz_loc; ++k)
793  {
794  for (j = 0; j < nbmap; ++j)
795  {
796  // Ah_data[i+k*nbmap +
797  // (j+k*nbmap)*AhRows] +=
798  // m_kinvis*HelmMat(bmap[i],bmap[j]);
799  Ah_data[i + k * nbmap + (j + k * nbmap) * AhRows] +=
800  m_kinvis * HelmMatScale *
801  HelmMat_data[bmap[i] + HelmMatRows * bmap[j]];
802  }
803 
804  for (j = 0; j < nimap; ++j)
805  {
806  B_data[i + k * nbmap + (j + k * nimap) * nbndry] +=
807  m_kinvis * HelmMatScale *
808  HelmMat_data[bmap[i] + HelmMatRows * imap[j]];
809  }
810  }
811 
812  if ((lambda_imag != NekConstants::kNekUnsetDouble) &&
813  (nz_loc == 2))
814  {
815  for (k = 0; k < nvel; ++k)
816  {
817  for (j = 0; j < nbmap; ++j)
818  {
819  Ah_data[i + 2 * k * nbmap +
820  (j + (2 * k + 1) * nbmap) * AhRows] -=
821  lambda_imag * (*MassMat)(bmap[i], bmap[j]);
822  }
823 
824  for (j = 0; j < nbmap; ++j)
825  {
826  Ah_data[i + (2 * k + 1) * nbmap +
827  (j + 2 * k * nbmap) * AhRows] +=
828  lambda_imag * (*MassMat)(bmap[i], bmap[j]);
829  }
830 
831  for (j = 0; j < nimap; ++j)
832  {
833  B_data[i + 2 * k * nbmap +
834  (j + (2 * k + 1) * nimap) * nbndry] -=
835  lambda_imag * (*MassMat)(bmap[i], imap[j]);
836  }
837 
838  for (j = 0; j < nimap; ++j)
839  {
840  B_data[i + (2 * k + 1) * nbmap +
841  (j + 2 * k * nimap) * nbndry] +=
842  lambda_imag * (*MassMat)(bmap[i], imap[j]);
843  }
844  }
845  }
846 
847  for (k = 0; k < nvel; ++k)
848  {
849  if ((nz_loc == 2) && (k == 2)) // handle d/dz derivative
850  {
851  NekDouble beta = -2 * M_PI * HomogeneousMode / m_LhomZ;
852 
853  // Real Component
854  Vmath::Smul(npoints, beta, phys, 1, deriv, 1);
855 
856  m_pressure->GetExp(n)->IProductWRTBase(deriv, pcoeffs);
857  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
858  Dbnd->GetRawPtr() +
859  ((nz_loc * k + 1) * bmap.size() + i) *
860  nsize_p[n],
861  1);
862 
863  // Imaginary Component
864  Vmath::Neg(psize, pcoeffs, 1);
865  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
866  Dbnd->GetRawPtr() +
867  ((nz_loc * k) * bmap.size() + i) *
868  nsize_p[n] +
869  psize,
870  1);
871 
872  // now do advection terms
873  Vmath::Vmul(npoints, Advtmp = Advfield[k] + phys_offset,
874  1, deriv, 1, tmpphys, 1);
875 
876  locExp->IProductWRTBase(tmpphys, coeffs);
877 
878  // real contribution
879  for (nv = 0; nv < nvel; ++nv)
880  {
881  for (j = 0; j < nbmap; ++j)
882  {
883  Ah_data[j + 2 * nv * nbmap +
884  (i + (2 * nv + 1) * nbmap) * AhRows] +=
885  coeffs[bmap[j]];
886  }
887 
888  for (j = 0; j < nimap; ++j)
889  {
890  C_data[i + (2 * nv + 1) * nbmap +
891  (j + 2 * nv * nimap) * nbndry] +=
892  coeffs[imap[j]];
893  }
894  }
895 
896  Vmath::Neg(ncoeffs, coeffs, 1);
897  // imaginary contribution
898  for (nv = 0; nv < nvel; ++nv)
899  {
900  for (j = 0; j < nbmap; ++j)
901  {
902  Ah_data[j + (2 * nv + 1) * nbmap +
903  (i + 2 * nv * nbmap) * AhRows] +=
904  coeffs[bmap[j]];
905  }
906 
907  for (j = 0; j < nimap; ++j)
908  {
909  C_data[i + 2 * nv * nbmap +
910  (j + (2 * nv + 1) * nimap) * nbndry] +=
911  coeffs[imap[j]];
912  }
913  }
914  }
915  else
916  {
917  if (k < 2)
918  {
919  locExp->PhysDeriv(MultiRegions::DirCartesianMap[k],
920  phys, deriv);
921  Vmath::Vmul(npoints,
922  Advtmp = Advfield[k] + phys_offset, 1,
923  deriv, 1, tmpphys, 1);
924  locExp->IProductWRTBase(tmpphys, coeffs);
925 
926  for (nv = 0; nv < nvel * nz_loc; ++nv)
927  {
928  for (j = 0; j < nbmap; ++j)
929  {
930  Ah_data[j + nv * nbmap +
931  (i + nv * nbmap) * AhRows] +=
932  coeffs[bmap[j]];
933  }
934 
935  for (j = 0; j < nimap; ++j)
936  {
937  C_data[i + nv * nbmap +
938  (j + nv * nimap) * nbndry] +=
939  coeffs[imap[j]];
940  }
941  }
942 
943  // copy into column major storage.
944  m_pressure->GetExp(n)->IProductWRTBase(deriv,
945  pcoeffs);
946  for (j = 0; j < nz_loc; ++j)
947  {
948  Blas::Dcopy(
949  psize, &(pcoeffs)[0], 1,
950  Dbnd->GetRawPtr() +
951  ((nz_loc * k + j) * bmap.size() + i) *
952  nsize_p[n] +
953  j * psize,
954  1);
955  }
956  }
957  }
958 
959  if (IsLinearNSEquation)
960  {
961  for (nv = 0; nv < nvel; ++nv)
962  {
963  // u' . Grad U terms
964  Vmath::Vmul(npoints, phys, 1,
965  AdvDeriv[k * nvel + nv], 1, tmpphys, 1);
966  locExp->IProductWRTBase(tmpphys, coeffs);
967 
968  for (int n1 = 0; n1 < nz_loc; ++n1)
969  {
970  for (j = 0; j < nbmap; ++j)
971  {
972  Ah_data[j + (k * nz_loc + n1) * nbmap +
973  (i + (nv * nz_loc + n1) * nbmap) *
974  AhRows] += coeffs[bmap[j]];
975  }
976 
977  for (j = 0; j < nimap; ++j)
978  {
979  C_data[i + (nv * nz_loc + n1) * nbmap +
980  (j + (k * nz_loc + n1) * nimap) *
981  nbndry] += coeffs[imap[j]];
982  }
983  }
984  }
985  }
986  }
987  }
988 
989  for (i = 0; i < nimap; ++i)
990  {
991  // Fill element with mode
992  Vmath::Zero(ncoeffs, coeffs, 1);
993  coeffs[imap[i]] = 1.0;
994  locExp->BwdTrans(coeffs, phys);
995 
996  for (k = 0; k < nvel * nz_loc; ++k)
997  {
998  for (j = 0; j < nbmap; ++j) // C set up as transpose
999  {
1000  C_data[j + k * nbmap + (i + k * nimap) * nbndry] +=
1001  m_kinvis * HelmMatScale *
1002  HelmMat_data[imap[i] + HelmMatRows * bmap[j]];
1003  }
1004 
1005  for (j = 0; j < nimap; ++j)
1006  {
1007  D_data[i + k * nimap + (j + k * nimap) * nint] +=
1008  m_kinvis * HelmMatScale *
1009  HelmMat_data[imap[i] + HelmMatRows * imap[j]];
1010  }
1011  }
1012 
1013  if ((lambda_imag != NekConstants::kNekUnsetDouble) &&
1014  (nz_loc == 2))
1015  {
1016  for (k = 0; k < nvel; ++k)
1017  {
1018  for (j = 0; j < nbmap; ++j) // C set up as transpose
1019  {
1020  C_data[j + 2 * k * nbmap +
1021  (i + (2 * k + 1) * nimap) * nbndry] +=
1022  lambda_imag * (*MassMat)(bmap[j], imap[i]);
1023  }
1024 
1025  for (j = 0; j < nbmap; ++j) // C set up as transpose
1026  {
1027  C_data[j + (2 * k + 1) * nbmap +
1028  (i + 2 * k * nimap) * nbndry] -=
1029  lambda_imag * (*MassMat)(bmap[j], imap[i]);
1030  }
1031 
1032  for (j = 0; j < nimap; ++j)
1033  {
1034  D_data[i + 2 * k * nimap +
1035  (j + (2 * k + 1) * nimap) * nint] -=
1036  lambda_imag * (*MassMat)(imap[i], imap[j]);
1037  }
1038 
1039  for (j = 0; j < nimap; ++j)
1040  {
1041  D_data[i + (2 * k + 1) * nimap +
1042  (j + 2 * k * nimap) * nint] +=
1043  lambda_imag * (*MassMat)(imap[i], imap[j]);
1044  }
1045  }
1046  }
1047 
1048  for (k = 0; k < nvel; ++k)
1049  {
1050  if ((nz_loc == 2) && (k == 2)) // handle d/dz derivative
1051  {
1052  NekDouble beta = -2 * M_PI * HomogeneousMode / m_LhomZ;
1053 
1054  // Real Component
1055  Vmath::Smul(npoints, beta, phys, 1, deriv, 1);
1056  m_pressure->GetExp(n)->IProductWRTBase(deriv, pcoeffs);
1057  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
1058  Dint->GetRawPtr() +
1059  ((nz_loc * k + 1) * imap.size() + i) *
1060  nsize_p[n],
1061  1);
1062  // Imaginary Component
1063  Vmath::Neg(psize, pcoeffs, 1);
1064  Blas::Dcopy(psize, &(pcoeffs)[0], 1,
1065  Dint->GetRawPtr() +
1066  ((nz_loc * k) * imap.size() + i) *
1067  nsize_p[n] +
1068  psize,
1069  1);
1070 
1071  // Advfield[k] *d/dx_k to all velocity
1072  // components on diagonal
1073  Vmath::Vmul(npoints, Advtmp = Advfield[k] + phys_offset,
1074  1, deriv, 1, tmpphys, 1);
1075  locExp->IProductWRTBase(tmpphys, coeffs);
1076 
1077  // Real Components
1078  for (nv = 0; nv < nvel; ++nv)
1079  {
1080  for (j = 0; j < nbmap; ++j)
1081  {
1082  B_data[j + 2 * nv * nbmap +
1083  (i + (2 * nv + 1) * nimap) * nbndry] +=
1084  coeffs[bmap[j]];
1085  }
1086 
1087  for (j = 0; j < nimap; ++j)
1088  {
1089  D_data[j + 2 * nv * nimap +
1090  (i + (2 * nv + 1) * nimap) * nint] +=
1091  coeffs[imap[j]];
1092  }
1093  }
1094  Vmath::Neg(ncoeffs, coeffs, 1);
1095  // Imaginary
1096  for (nv = 0; nv < nvel; ++nv)
1097  {
1098  for (j = 0; j < nbmap; ++j)
1099  {
1100  B_data[j + (2 * nv + 1) * nbmap +
1101  (i + 2 * nv * nimap) * nbndry] +=
1102  coeffs[bmap[j]];
1103  }
1104 
1105  for (j = 0; j < nimap; ++j)
1106  {
1107  D_data[j + (2 * nv + 1) * nimap +
1108  (i + 2 * nv * nimap) * nint] +=
1109  coeffs[imap[j]];
1110  }
1111  }
1112  }
1113  else
1114  {
1115  if (k < 2)
1116  {
1117  // Differentiation & Inner product wrt base.
1118  // locExp->PhysDeriv(k,phys, deriv);
1119  locExp->PhysDeriv(MultiRegions::DirCartesianMap[k],
1120  phys, deriv);
1121  Vmath::Vmul(npoints,
1122  Advtmp = Advfield[k] + phys_offset, 1,
1123  deriv, 1, tmpphys, 1);
1124  locExp->IProductWRTBase(tmpphys, coeffs);
1125 
1126  for (nv = 0; nv < nvel * nz_loc; ++nv)
1127  {
1128  for (j = 0; j < nbmap; ++j)
1129  {
1130  B_data[j + nv * nbmap +
1131  (i + nv * nimap) * nbndry] +=
1132  coeffs[bmap[j]];
1133  }
1134 
1135  for (j = 0; j < nimap; ++j)
1136  {
1137  D_data[j + nv * nimap +
1138  (i + nv * nimap) * nint] +=
1139  coeffs[imap[j]];
1140  }
1141  }
1142  // copy into column major storage.
1143  m_pressure->GetExp(n)->IProductWRTBase(deriv,
1144  pcoeffs);
1145  for (j = 0; j < nz_loc; ++j)
1146  {
1147  Blas::Dcopy(
1148  psize, &(pcoeffs)[0], 1,
1149  Dint->GetRawPtr() +
1150  ((nz_loc * k + j) * imap.size() + i) *
1151  nsize_p[n] +
1152  j * psize,
1153  1);
1154  }
1155  }
1156  }
1157 
1158  if (IsLinearNSEquation)
1159  {
1160  int n1;
1161  for (nv = 0; nv < nvel; ++nv)
1162  {
1163  // u'.Grad U terms
1164  Vmath::Vmul(npoints, phys, 1,
1165  AdvDeriv[k * nvel + nv], 1, tmpphys, 1);
1166  locExp->IProductWRTBase(tmpphys, coeffs);
1167 
1168  for (n1 = 0; n1 < nz_loc; ++n1)
1169  {
1170  for (j = 0; j < nbmap; ++j)
1171  {
1172  B_data[j + (k * nz_loc + n1) * nbmap +
1173  (i + (nv * nz_loc + n1) * nimap) *
1174  nbndry] += coeffs[bmap[j]];
1175  }
1176 
1177  for (j = 0; j < nimap; ++j)
1178  {
1179  D_data[j + (k * nz_loc + n1) * nimap +
1180  (i + (nv * nz_loc + n1) * nimap) *
1181  nint] += coeffs[imap[j]];
1182  }
1183  }
1184  }
1185  }
1186  }
1187  }
1188 
1189  D->Invert();
1190  (*B) = (*B) * (*D);
1191 
1192  // perform (*Ah) = (*Ah) - (*B)*(*C) but since size of
1193  // Ah is larger than (*B)*(*C) easier to call blas
1194  // directly
1195  Blas::Dgemm('N', 'T', B->GetRows(), C->GetRows(), B->GetColumns(),
1196  -1.0, B->GetRawPtr(), B->GetRows(), C->GetRawPtr(),
1197  C->GetRows(), 1.0, Ah->GetRawPtr(), Ah->GetRows());
1198  }
1199 
1200  mat.m_BCinv->SetBlock(
1201  n, n,
1202  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, B));
1203  mat.m_Btilde->SetBlock(
1204  n, n,
1205  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, C));
1206  mat.m_Cinv->SetBlock(
1207  n, n,
1208  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, D));
1209  mat.m_D_bnd->SetBlock(
1210  n, n,
1211  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, Dbnd));
1212  mat.m_D_int->SetBlock(
1213  n, n,
1214  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, Dint));
1215 
1216  // Do matrix manipulations and get final set of block matries
1217  // reset boundary to put mean mode into boundary system.
1218 
1219  DNekMatSharedPtr Cinv, BCinv, Btilde;
1220  DNekMat DintCinvDTint, BCinvDTint_m_DTbnd, DintCinvBTtilde_m_Dbnd;
1221 
1222  Cinv = D;
1223  BCinv = B;
1224  Btilde = C;
1225 
1226  DintCinvDTint = (*Dint) * (*Cinv) * Transpose(*Dint);
1227  BCinvDTint_m_DTbnd = (*BCinv) * Transpose(*Dint) - Transpose(*Dbnd);
1228 
1229  // This could be transpose of BCinvDint in some cases
1230  DintCinvBTtilde_m_Dbnd =
1231  (*Dint) * (*Cinv) * Transpose(*Btilde) - (*Dbnd);
1232 
1233  // Set up final set of matrices.
1234  DNekMatSharedPtr Bh = MemoryManager<DNekMat>::AllocateSharedPtr(
1235  nsize_bndry_p1[n], nsize_p_m1[n], zero);
1236  DNekMatSharedPtr Ch = MemoryManager<DNekMat>::AllocateSharedPtr(
1237  nsize_p_m1[n], nsize_bndry_p1[n], zero);
1238  DNekMatSharedPtr Dh = MemoryManager<DNekMat>::AllocateSharedPtr(
1239  nsize_p_m1[n], nsize_p_m1[n], zero);
1240  Array<OneD, NekDouble> Dh_data = Dh->GetPtr();
1241 
1242  // Copy matrices into final structures.
1243  int n1, n2;
1244  for (n1 = 0; n1 < nz_loc; ++n1)
1245  {
1246  for (i = 0; i < psize - 1; ++i)
1247  {
1248  for (n2 = 0; n2 < nz_loc; ++n2)
1249  {
1250  for (j = 0; j < psize - 1; ++j)
1251  {
1252  //(*Dh)(i+n1*(psize-1),j+n2*(psize-1)) =
1253  //-DintCinvDTint(i+1+n1*psize,j+1+n2*psize);
1254  Dh_data[(i + n1 * (psize - 1)) +
1255  (j + n2 * (psize - 1)) * Dh->GetRows()] =
1256  -DintCinvDTint(i + 1 + n1 * psize,
1257  j + 1 + n2 * psize);
1258  }
1259  }
1260  }
1261  }
1262 
1263  for (n1 = 0; n1 < nz_loc; ++n1)
1264  {
1265  for (i = 0; i < nsize_bndry_p1[n] - nz_loc; ++i)
1266  {
1267  (*Ah)(i, nsize_bndry_p1[n] - nz_loc + n1) =
1268  BCinvDTint_m_DTbnd(i, n1 * psize);
1269  (*Ah)(nsize_bndry_p1[n] - nz_loc + n1, i) =
1270  DintCinvBTtilde_m_Dbnd(n1 * psize, i);
1271  }
1272  }
1273 
1274  for (n1 = 0; n1 < nz_loc; ++n1)
1275  {
1276  for (n2 = 0; n2 < nz_loc; ++n2)
1277  {
1278  (*Ah)(nsize_bndry_p1[n] - nz_loc + n1,
1279  nsize_bndry_p1[n] - nz_loc + n2) =
1280  -DintCinvDTint(n1 * psize, n2 * psize);
1281  }
1282  }
1283 
1284  for (n1 = 0; n1 < nz_loc; ++n1)
1285  {
1286  for (j = 0; j < psize - 1; ++j)
1287  {
1288  for (i = 0; i < nsize_bndry_p1[n] - nz_loc; ++i)
1289  {
1290  (*Bh)(i, j + n1 * (psize - 1)) =
1291  BCinvDTint_m_DTbnd(i, j + 1 + n1 * psize);
1292  (*Ch)(j + n1 * (psize - 1), i) =
1293  DintCinvBTtilde_m_Dbnd(j + 1 + n1 * psize, i);
1294  }
1295  }
1296  }
1297 
1298  for (n1 = 0; n1 < nz_loc; ++n1)
1299  {
1300  for (n2 = 0; n2 < nz_loc; ++n2)
1301  {
1302  for (j = 0; j < psize - 1; ++j)
1303  {
1304  (*Bh)(nsize_bndry_p1[n] - nz_loc + n1,
1305  j + n2 * (psize - 1)) =
1306  -DintCinvDTint(n1 * psize, j + 1 + n2 * psize);
1307  (*Ch)(j + n2 * (psize - 1),
1308  nsize_bndry_p1[n] - nz_loc + n1) =
1309  -DintCinvDTint(j + 1 + n2 * psize, n1 * psize);
1310  }
1311  }
1312  }
1313 
1314  // Do static condensation
1315  Dh->Invert();
1316  (*Bh) = (*Bh) * (*Dh);
1317  //(*Ah) = (*Ah) - (*Bh)*(*Ch);
1318  Blas::Dgemm('N', 'N', Bh->GetRows(), Ch->GetColumns(), Bh->GetColumns(),
1319  -1.0, Bh->GetRawPtr(), Bh->GetRows(), Ch->GetRawPtr(),
1320  Ch->GetRows(), 1.0, Ah->GetRawPtr(), Ah->GetRows());
1321 
1322  // Set matrices for later inversion. Probably do not need to be
1323  // attached to class
1324  pAh->SetBlock(
1325  n, n,
1326  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, Ah));
1327  pBh->SetBlock(
1328  n, n,
1329  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, Bh));
1330  pCh->SetBlock(
1331  n, n,
1332  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, Ch));
1333  pDh->SetBlock(
1334  n, n,
1335  loc_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, Dh));
1336  }
1337  timer.Stop();
1338  cout << "Matrix Setup Costs: " << timer.TimePerTest(1) << endl;
1339 
1340  timer.Start();
1341  // Set up global coupled boundary solver.
1342  // This is a key to define the solution matrix type
1343  // currently we are giving it a argument of eLInearAdvectionReaction
1344  // since this then makes the matrix storage of type eFull
1345  MultiRegions::GlobalLinSysKey key(StdRegions::eLinearAdvectionReaction,
1346  locToGloMap);
1347  mat.m_CoupledBndSys =
1348  MemoryManager<MultiRegions::GlobalLinSysDirectStaticCond>::
1349  AllocateSharedPtr(key, m_fields[0], pAh, pBh, pCh, pDh,
1350  locToGloMap);
1351  mat.m_CoupledBndSys->Initialise(locToGloMap);
1352 }
1353 
1354 void CoupledLinearNS::v_GenerateSummary(SolverUtils::SummaryList &s)
1355 {
1356  SolverUtils::AddSummaryItem(s, "Solver Type", "Coupled Linearised NS");
1357 }
1358 
1359 void CoupledLinearNS::v_DoInitialise(void)
1360 {
1361  switch (m_equationType)
1362  {
1363  case eUnsteadyStokes:
1364  case eUnsteadyNavierStokes:
1365  {
1366  // LibUtilities::TimeIntegrationMethod intMethod;
1367  // std::string TimeIntStr =
1368  // m_session->GetSolverInfo("TIMEINTEGRATIONMETHOD");
1369  // int i;
1370  // for(i = 0; i < (int)
1371  // LibUtilities::SIZE_TimeIntegrationMethod; ++i)
1372  // {
1373  // if(boost::iequals(LibUtilities::TimeIntegrationMethodMap[i],TimeIntStr))
1374  // {
1375  // intMethod =
1376  // (LibUtilities::TimeIntegrationMethod)i;
1377  // break;
1378  // }
1379  // }
1380  //
1381  // ASSERTL0(i != (int)
1382  // LibUtilities::SIZE_TimeIntegrationMethod, "Invalid
1383  // time integration type.");
1384  //
1385  // m_integrationScheme =
1386  // LibUtilities::GetTimeIntegrationWrapperFactory().CreateInstance(LibUtilities::TimeIntegrationMethodMap[intMethod]);
1387 
1388  // Could defind this from IncNavierStokes class?
1389  m_ode.DefineOdeRhs(&CoupledLinearNS::EvaluateAdvection, this);
1390 
1391  m_ode.DefineImplicitSolve(
1392  &CoupledLinearNS::SolveUnsteadyStokesSystem, this);
1393 
1394  // Set initial condition using time t=0
1395 
1396  SetInitialConditions(0.0);
1397  }
1398  case eSteadyStokes:
1399  SetUpCoupledMatrix(0.0);
1400  break;
1401  case eSteadyOseen:
1402  {
1403  Array<OneD, Array<OneD, NekDouble>> AdvField(m_velocity.size());
1404  for (int i = 0; i < m_velocity.size(); ++i)
1405  {
1406  AdvField[i] = Array<OneD, NekDouble>(
1407  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1408  }
1409 
1410  ASSERTL0(m_session->DefinesFunction("AdvectionVelocity"),
1411  "Advection Velocity section must be defined in "
1412  "session file.");
1413 
1414  std::vector<std::string> fieldStr;
1415  for (int i = 0; i < m_velocity.size(); ++i)
1416  {
1417  fieldStr.push_back(
1418  m_boundaryConditions->GetVariable(m_velocity[i]));
1419  }
1420  GetFunction("AdvectionVelocity")->Evaluate(fieldStr, AdvField);
1421 
1422  SetUpCoupledMatrix(0.0, AdvField, false);
1423  }
1424  break;
1425  case eSteadyNavierStokes:
1426  {
1427  m_session->LoadParameter("KinvisMin", m_kinvisMin);
1428  m_session->LoadParameter("KinvisPercentage", m_KinvisPercentage);
1429  m_session->LoadParameter("Tolerence", m_tol);
1430  m_session->LoadParameter("MaxIteration", m_maxIt);
1431  m_session->LoadParameter("MatrixSetUpStep", m_MatrixSetUpStep);
1432  m_session->LoadParameter("Restart", m_Restart);
1433 
1434  DefineForcingTerm();
1435 
1436  if (m_Restart == 1)
1437  {
1438  ASSERTL0(m_session->DefinesFunction("Restart"),
1439  "Restart section must be defined in session file.");
1440 
1441  Array<OneD, Array<OneD, NekDouble>> Restart(m_velocity.size());
1442  for (int i = 0; i < m_velocity.size(); ++i)
1443  {
1444  Restart[i] = Array<OneD, NekDouble>(
1445  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1446  }
1447  std::vector<std::string> fieldStr;
1448  for (int i = 0; i < m_velocity.size(); ++i)
1449  {
1450  fieldStr.push_back(
1451  m_boundaryConditions->GetVariable(m_velocity[i]));
1452  }
1453  GetFunction("Restart")->Evaluate(fieldStr, Restart);
1454 
1455  for (int i = 0; i < m_velocity.size(); ++i)
1456  {
1457  m_fields[m_velocity[i]]->FwdTransLocalElmt(
1458  Restart[i], m_fields[m_velocity[i]]->UpdateCoeffs());
1459  }
1460  cout << "Saving the RESTART file for m_kinvis = " << m_kinvis
1461  << " (<=> Re = " << 1 / m_kinvis << ")" << endl;
1462  }
1463  else // We solve the Stokes Problem
1464  {
1465 
1466  SetUpCoupledMatrix(0.0);
1467  m_initialStep = true;
1468  m_counter = 1;
1469  // SolveLinearNS(m_ForcingTerm_Coeffs);
1470  Solve();
1471  m_initialStep = false;
1472  cout << "Saving the Stokes Flow for m_kinvis = " << m_kinvis
1473  << " (<=> Re = " << 1 / m_kinvis << ")" << endl;
1474  }
1475  }
1476  break;
1477  case eSteadyLinearisedNS:
1478  {
1479  SetInitialConditions(0.0);
1480 
1481  Array<OneD, Array<OneD, NekDouble>> AdvField(m_velocity.size());
1482  for (int i = 0; i < m_velocity.size(); ++i)
1483  {
1484  AdvField[i] = Array<OneD, NekDouble>(
1485  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1486  }
1487 
1488  ASSERTL0(m_session->DefinesFunction("AdvectionVelocity"),
1489  "Advection Velocity section must be defined in "
1490  "session file.");
1491 
1492  std::vector<std::string> fieldStr;
1493  for (int i = 0; i < m_velocity.size(); ++i)
1494  {
1495  fieldStr.push_back(
1496  m_boundaryConditions->GetVariable(m_velocity[i]));
1497  }
1498  GetFunction("AdvectionVelocity")->Evaluate(fieldStr, AdvField);
1499 
1500  SetUpCoupledMatrix(m_lambda, AdvField, true);
1501  }
1502  break;
1503  case eNoEquationType:
1504  default:
1505  ASSERTL0(false,
1506  "Unknown or undefined equation type for CoupledLinearNS");
1507  }
1508 }
1509 
1510 void CoupledLinearNS::EvaluateAdvection(
1511  const Array<OneD, const Array<OneD, NekDouble>> &inarray,
1512  Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
1513 {
1514  // evaluate convection terms
1515  EvaluateAdvectionTerms(inarray, outarray, time);
1516 
1517  for (auto &x : m_forcing)
1518  {
1519  x->Apply(m_fields, outarray, outarray, time);
1520  }
1521 }
1522 
1523 void CoupledLinearNS::SolveUnsteadyStokesSystem(
1524  const Array<OneD, const Array<OneD, NekDouble>> &inarray,
1525  Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time,
1526  const NekDouble aii_Dt)
1527 {
1528  int i;
1529  Array<OneD, Array<OneD, NekDouble>> F(m_nConvectiveFields);
1530  NekDouble lambda = 1.0 / aii_Dt;
1531  static NekDouble lambda_store;
1532  Array<OneD, Array<OneD, NekDouble>> forcing(m_velocity.size());
1533  // Matrix solution
1534  if (fabs(lambda_store - lambda) > 1e-10)
1535  {
1536  SetUpCoupledMatrix(lambda);
1537  lambda_store = lambda;
1538  }
1539 
1540  // Forcing for advection solve
1541  for (i = 0; i < m_velocity.size(); ++i)
1542  {
1543  bool waveSpace = m_fields[m_velocity[i]]->GetWaveSpace();
1544  m_fields[m_velocity[i]]->SetWaveSpace(true);
1545  m_fields[m_velocity[i]]->IProductWRTBase(
1546  inarray[i], m_fields[m_velocity[i]]->UpdateCoeffs());
1547  m_fields[m_velocity[i]]->SetWaveSpace(waveSpace);
1548  Vmath::Smul(m_fields[m_velocity[i]]->GetNcoeffs(), lambda,
1549  m_fields[m_velocity[i]]->GetCoeffs(), 1,
1550  m_fields[m_velocity[i]]->UpdateCoeffs(), 1);
1551  forcing[i] = m_fields[m_velocity[i]]->GetCoeffs();
1552  }
1553 
1554  SolveLinearNS(forcing);
1555 
1556  for (i = 0; i < m_velocity.size(); ++i)
1557  {
1558  m_fields[m_velocity[i]]->BwdTrans(m_fields[m_velocity[i]]->GetCoeffs(),
1559  outarray[i]);
1560  }
1561 }
1562 
1563 void CoupledLinearNS::v_TransCoeffToPhys(void)
1564 {
1565  int nfields = m_fields.size();
1566  for (int k = 0; k < nfields; ++k)
1567  {
1568  // Backward Transformation in physical space for time evolution
1569  m_fields[k]->BwdTrans(m_fields[k]->GetCoeffs(),
1570  m_fields[k]->UpdatePhys());
1571  }
1572 }
1573 
1574 void CoupledLinearNS::v_TransPhysToCoeff(void)
1575 {
1576  int nfields = m_fields.size();
1577  for (int k = 0; k < nfields; ++k)
1578  {
1579  // Forward Transformation in physical space for time evolution
1580  m_fields[k]->FwdTransLocalElmt(m_fields[k]->GetPhys(),
1581  m_fields[k]->UpdateCoeffs());
1582  }
1583 }
1584 
1585 void CoupledLinearNS::v_DoSolve(void)
1586 {
1587  switch (m_equationType)
1588  {
1589  case eUnsteadyStokes:
1590  case eUnsteadyNavierStokes:
1591  // AdvanceInTime(m_steps);
1592  UnsteadySystem::v_DoSolve();
1593  break;
1594  case eSteadyStokes:
1595  case eSteadyOseen:
1596  case eSteadyLinearisedNS:
1597  {
1598  Solve();
1599  break;
1600  }
1601  case eSteadyNavierStokes:
1602  {
1603  LibUtilities::Timer Generaltimer;
1604  Generaltimer.Start();
1605 
1606  int Check(0);
1607 
1608  // Saving the init datas
1609  Checkpoint_Output(Check);
1610  Check++;
1611 
1612  cout << "We execute INITIALLY SolveSteadyNavierStokes for m_kinvis "
1613  "= "
1614  << m_kinvis << " (<=> Re = " << 1 / m_kinvis << ")" << endl;
1615  SolveSteadyNavierStokes();
1616 
1617  while (m_kinvis > m_kinvisMin)
1618  {
1619  if (Check == 1)
1620  {
1621  cout << "We execute SolveSteadyNavierStokes for m_kinvis = "
1622  << m_kinvis << " (<=> Re = " << 1 / m_kinvis << ")"
1623  << endl;
1624  SolveSteadyNavierStokes();
1625  Checkpoint_Output(Check);
1626  Check++;
1627  }
1628 
1629  Continuation();
1630 
1631  if (m_kinvis > m_kinvisMin)
1632  {
1633  cout << "We execute SolveSteadyNavierStokes for m_kinvis = "
1634  << m_kinvis << " (<=> Re = " << 1 / m_kinvis << ")"
1635  << endl;
1636  SolveSteadyNavierStokes();
1637  Checkpoint_Output(Check);
1638  Check++;
1639  }
1640  }
1641 
1642  Generaltimer.Stop();
1643  cout << "\nThe total calculation time is : "
1644  << Generaltimer.TimePerTest(1) / 60 << " minute(s). \n\n";
1645 
1646  break;
1647  }
1648  case eNoEquationType:
1649  default:
1650  ASSERTL0(false,
1651  "Unknown or undefined equation type for CoupledLinearNS");
1652  }
1653 }
1654 
1655 /** Virtual function to define if operator in DoSolve is negated
1656  * with regard to the strong form. This is currently only used in
1657  * Arnoldi solves. For Coupledd solver this is true since Stokes
1658  * operator is set up as a LHS rather than RHS operation
1659  */
1660 bool CoupledLinearNS::v_NegatedOp(void)
1661 {
1662  return true;
1663 }
1664 
1665 void CoupledLinearNS::Solve(void)
1666 {
1667  const unsigned int ncmpt = m_velocity.size();
1668  Array<OneD, Array<OneD, NekDouble>> forcing_phys(ncmpt);
1669  Array<OneD, Array<OneD, NekDouble>> forcing(ncmpt);
1670 
1671  for (int i = 0; i < ncmpt; ++i)
1672  {
1673  forcing_phys[i] =
1674  Array<OneD, NekDouble>(m_fields[m_velocity[0]]->GetNpoints(), 0.0);
1675  forcing[i] =
1676  Array<OneD, NekDouble>(m_fields[m_velocity[0]]->GetNcoeffs(), 0.0);
1677  }
1678 
1679  for (auto &x : m_forcing)
1680  {
1681  const NekDouble time = 0;
1682  x->Apply(m_fields, forcing_phys, forcing_phys, time);
1683  }
1684  for (unsigned int i = 0; i < ncmpt; ++i)
1685  {
1686  bool waveSpace = m_fields[m_velocity[i]]->GetWaveSpace();
1687  m_fields[i]->SetWaveSpace(true);
1688  m_fields[i]->IProductWRTBase(forcing_phys[i], forcing[i]);
1689  m_fields[i]->SetWaveSpace(waveSpace);
1690  }
1691 
1692  SolveLinearNS(forcing);
1693 }
1694 
1695 void CoupledLinearNS::DefineForcingTerm(void)
1696 {
1697  m_ForcingTerm = Array<OneD, Array<OneD, NekDouble>>(m_velocity.size());
1698  m_ForcingTerm_Coeffs =
1699  Array<OneD, Array<OneD, NekDouble>>(m_velocity.size());
1700 
1701  for (int i = 0; i < m_velocity.size(); ++i)
1702  {
1703  m_ForcingTerm[i] = Array<OneD, NekDouble>(
1704  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1705  m_ForcingTerm_Coeffs[i] =
1706  Array<OneD, NekDouble>(m_fields[m_velocity[i]]->GetNcoeffs(), 0.0);
1707  }
1708 
1709  if (m_session->DefinesFunction("ForcingTerm"))
1710  {
1711  std::vector<std::string> fieldStr;
1712  for (int i = 0; i < m_velocity.size(); ++i)
1713  {
1714  fieldStr.push_back(
1715  m_boundaryConditions->GetVariable(m_velocity[i]));
1716  }
1717  GetFunction("ForcingTerm")->Evaluate(fieldStr, m_ForcingTerm);
1718  for (int i = 0; i < m_velocity.size(); ++i)
1719  {
1720  m_fields[m_velocity[i]]->FwdTransLocalElmt(m_ForcingTerm[i],
1721  m_ForcingTerm_Coeffs[i]);
1722  }
1723  }
1724  else
1725  {
1726  cout << "'ForcingTerm' section has not been defined in the input file "
1727  "=> forcing=0"
1728  << endl;
1729  }
1730 }
1731 
1732 void CoupledLinearNS::SolveSteadyNavierStokes(void)
1733 {
1734  LibUtilities::Timer Newtontimer;
1735  Newtontimer.Start();
1736 
1737  Array<OneD, Array<OneD, NekDouble>> RHS_Coeffs(m_velocity.size());
1738  Array<OneD, Array<OneD, NekDouble>> RHS_Phys(m_velocity.size());
1739  Array<OneD, Array<OneD, NekDouble>> delta_velocity_Phys(m_velocity.size());
1740  Array<OneD, Array<OneD, NekDouble>> Velocity_Phys(m_velocity.size());
1741  Array<OneD, NekDouble> L2_norm(m_velocity.size(), 1.0);
1742  Array<OneD, NekDouble> Inf_norm(m_velocity.size(), 1.0);
1743 
1744  for (int i = 0; i < m_velocity.size(); ++i)
1745  {
1746  delta_velocity_Phys[i] = Array<OneD, NekDouble>(
1747  m_fields[m_velocity[i]]->GetTotPoints(), 1.0);
1748  Velocity_Phys[i] = Array<OneD, NekDouble>(
1749  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1750  }
1751 
1752  m_counter = 1;
1753 
1754  L2Norm(delta_velocity_Phys, L2_norm);
1755 
1756  // while(max(Inf_norm[0], Inf_norm[1]) > m_tol)
1757  while (max(L2_norm[0], L2_norm[1]) > m_tol)
1758  {
1759  if (m_counter == 1)
1760  // At the first Newton step, we use the solution of the
1761  // Stokes problem (if Restart=0 in input file) Or the
1762  // solution of the .rst file (if Restart=1 in input
1763  // file)
1764  {
1765  for (int i = 0; i < m_velocity.size(); ++i)
1766  {
1767  RHS_Coeffs[i] = Array<OneD, NekDouble>(
1768  m_fields[m_velocity[i]]->GetNcoeffs(), 0.0);
1769  RHS_Phys[i] = Array<OneD, NekDouble>(
1770  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1771  }
1772 
1773  for (int i = 0; i < m_velocity.size(); ++i)
1774  {
1775  m_fields[m_velocity[i]]->BwdTrans(
1776  m_fields[m_velocity[i]]->GetCoeffs(), Velocity_Phys[i]);
1777  }
1778 
1779  m_initialStep = true;
1780  EvaluateNewtonRHS(Velocity_Phys, RHS_Coeffs);
1781  SetUpCoupledMatrix(0.0, Velocity_Phys, true);
1782  SolveLinearNS(RHS_Coeffs);
1783  m_initialStep = false;
1784  }
1785  if (m_counter > 1)
1786  {
1787  EvaluateNewtonRHS(Velocity_Phys, RHS_Coeffs);
1788 
1789  if (m_counter % m_MatrixSetUpStep ==
1790  0) // Setting Up the matrix is expensive. We do it at each
1791  // "m_MatrixSetUpStep" step.
1792  {
1793  SetUpCoupledMatrix(0.0, Velocity_Phys, true);
1794  }
1795  SolveLinearNS(RHS_Coeffs);
1796  }
1797 
1798  for (int i = 0; i < m_velocity.size(); ++i)
1799  {
1800  m_fields[m_velocity[i]]->BwdTrans(RHS_Coeffs[i], RHS_Phys[i]);
1801  m_fields[m_velocity[i]]->BwdTrans(
1802  m_fields[m_velocity[i]]->GetCoeffs(), delta_velocity_Phys[i]);
1803  }
1804 
1805  for (int i = 0; i < m_velocity.size(); ++i)
1806  {
1807  Vmath::Vadd(Velocity_Phys[i].size(), Velocity_Phys[i], 1,
1808  delta_velocity_Phys[i], 1, Velocity_Phys[i], 1);
1809  }
1810 
1811  // InfNorm(delta_velocity_Phys, Inf_norm);
1812  L2Norm(delta_velocity_Phys, L2_norm);
1813 
1814  if (max(Inf_norm[0], Inf_norm[1]) > 100)
1815  {
1816  cout << "\nThe Newton method has failed at m_kinvis = " << m_kinvis
1817  << " (<=> Re = " << 1 / m_kinvis << ")" << endl;
1818  ASSERTL0(0, "The Newton method has failed... \n");
1819  }
1820 
1821  cout << "\n";
1822  m_counter++;
1823  }
1824 
1825  if (m_counter > 1) // We save u:=u+\delta u in u->Coeffs
1826  {
1827  for (int i = 0; i < m_velocity.size(); ++i)
1828  {
1829  m_fields[m_velocity[i]]->FwdTrans(
1830  Velocity_Phys[i], m_fields[m_velocity[i]]->UpdateCoeffs());
1831  }
1832  }
1833 
1834  Newtontimer.Stop();
1835  cout << "We have done " << m_counter - 1 << " iteration(s) in "
1836  << Newtontimer.TimePerTest(1) / 60 << " minute(s). \n\n";
1837 }
1838 
1839 void CoupledLinearNS::Continuation(void)
1840 {
1841  Array<OneD, Array<OneD, NekDouble>> u_N(m_velocity.size());
1842  Array<OneD, Array<OneD, NekDouble>> tmp_RHS(m_velocity.size());
1843  Array<OneD, Array<OneD, NekDouble>> RHS(m_velocity.size());
1844  Array<OneD, Array<OneD, NekDouble>> u_star(m_velocity.size());
1845 
1846  cout << "We apply the continuation method: " << endl;
1847 
1848  for (int i = 0; i < m_velocity.size(); ++i)
1849  {
1850  u_N[i] = Array<OneD, NekDouble>(m_fields[m_velocity[i]]->GetTotPoints(),
1851  0.0);
1852  m_fields[m_velocity[i]]->BwdTrans(m_fields[m_velocity[i]]->GetCoeffs(),
1853  u_N[i]);
1854 
1855  RHS[i] = Array<OneD, NekDouble>(m_fields[m_velocity[i]]->GetTotPoints(),
1856  0.0);
1857  tmp_RHS[i] = Array<OneD, NekDouble>(
1858  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1859 
1860  m_fields[m_velocity[i]]->PhysDeriv(i, u_N[i], tmp_RHS[i]);
1861  Vmath::Smul(tmp_RHS[i].size(), m_kinvis, tmp_RHS[i], 1, tmp_RHS[i], 1);
1862 
1863  bool waveSpace = m_fields[m_velocity[i]]->GetWaveSpace();
1864  m_fields[m_velocity[i]]->SetWaveSpace(true);
1865  m_fields[m_velocity[i]]->IProductWRTDerivBase(i, tmp_RHS[i], RHS[i]);
1866  m_fields[m_velocity[i]]->SetWaveSpace(waveSpace);
1867  }
1868 
1869  SetUpCoupledMatrix(0.0, u_N, true);
1870  SolveLinearNS(RHS);
1871 
1872  for (int i = 0; i < m_velocity.size(); ++i)
1873  {
1874  u_star[i] = Array<OneD, NekDouble>(
1875  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1876  m_fields[m_velocity[i]]->BwdTrans(m_fields[m_velocity[i]]->GetCoeffs(),
1877  u_star[i]);
1878 
1879  // u_star(k+1) = u_N(k) + DeltaKinvis * u_star(k)
1880  Vmath::Smul(u_star[i].size(), m_kinvis, u_star[i], 1, u_star[i], 1);
1881  Vmath::Vadd(u_star[i].size(), u_star[i], 1, u_N[i], 1, u_star[i], 1);
1882 
1883  m_fields[m_velocity[i]]->FwdTrans(
1884  u_star[i], m_fields[m_velocity[i]]->UpdateCoeffs());
1885  }
1886 
1887  m_kinvis -= m_kinvis * m_KinvisPercentage / 100;
1888 }
1889 
1890 void CoupledLinearNS::InfNorm(Array<OneD, Array<OneD, NekDouble>> &inarray,
1891  Array<OneD, NekDouble> &outarray)
1892 {
1893  for (int i = 0; i < m_velocity.size(); ++i)
1894  {
1895  outarray[i] = 0.0;
1896  for (int j = 0; j < inarray[i].size(); ++j)
1897  {
1898  if (inarray[i][j] > outarray[i])
1899  {
1900  outarray[i] = inarray[i][j];
1901  }
1902  }
1903  cout << "InfNorm[" << i << "] = " << outarray[i] << endl;
1904  }
1905 }
1906 
1907 void CoupledLinearNS::L2Norm(Array<OneD, Array<OneD, NekDouble>> &inarray,
1908  Array<OneD, NekDouble> &outarray)
1909 {
1910  for (int i = 0; i < m_velocity.size(); ++i)
1911  {
1912  outarray[i] = 0.0;
1913  for (int j = 0; j < inarray[i].size(); ++j)
1914  {
1915  outarray[i] += inarray[i][j] * inarray[i][j];
1916  }
1917  outarray[i] = sqrt(outarray[i]);
1918  cout << "L2Norm[" << i << "] = " << outarray[i] << endl;
1919  }
1920 }
1921 
1922 void CoupledLinearNS::EvaluateNewtonRHS(
1923  Array<OneD, Array<OneD, NekDouble>> &Velocity,
1924  Array<OneD, Array<OneD, NekDouble>> &outarray)
1925 {
1926  Array<OneD, Array<OneD, NekDouble>> Eval_Adv(m_velocity.size());
1927  Array<OneD, Array<OneD, NekDouble>> tmp_DerVel(m_velocity.size());
1928  Array<OneD, Array<OneD, NekDouble>> AdvTerm(m_velocity.size());
1929  Array<OneD, Array<OneD, NekDouble>> ViscTerm(m_velocity.size());
1930  Array<OneD, Array<OneD, NekDouble>> Forc(m_velocity.size());
1931 
1932  for (int i = 0; i < m_velocity.size(); ++i)
1933  {
1934  Eval_Adv[i] = Array<OneD, NekDouble>(
1935  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1936  tmp_DerVel[i] = Array<OneD, NekDouble>(
1937  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1938 
1939  AdvTerm[i] = Array<OneD, NekDouble>(
1940  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1941  ViscTerm[i] = Array<OneD, NekDouble>(
1942  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1943  Forc[i] = Array<OneD, NekDouble>(
1944  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1945  outarray[i] = Array<OneD, NekDouble>(
1946  m_fields[m_velocity[i]]->GetTotPoints(), 0.0);
1947 
1948  m_fields[m_velocity[i]]->PhysDeriv(i, Velocity[i], tmp_DerVel[i]);
1949 
1950  Vmath::Smul(tmp_DerVel[i].size(), m_kinvis, tmp_DerVel[i], 1,
1951  tmp_DerVel[i], 1);
1952  }
1953 
1954  EvaluateAdvectionTerms(Velocity, Eval_Adv, m_time);
1955 
1956  for (int i = 0; i < m_velocity.size(); ++i)
1957  {
1958  bool waveSpace = m_fields[m_velocity[i]]->GetWaveSpace();
1959  m_fields[m_velocity[i]]->SetWaveSpace(true);
1960  m_fields[m_velocity[i]]->IProductWRTBase(Eval_Adv[i],
1961  AdvTerm[i]); //(w, (u.grad)u)
1962  m_fields[m_velocity[i]]->IProductWRTDerivBase(
1963  i, tmp_DerVel[i], ViscTerm[i]); //(grad w, grad u)
1964  m_fields[m_velocity[i]]->IProductWRTBase(m_ForcingTerm[i],
1965  Forc[i]); //(w, f)
1966  m_fields[m_velocity[i]]->SetWaveSpace(waveSpace);
1967 
1968  Vmath::Vsub(outarray[i].size(), outarray[i], 1, AdvTerm[i], 1,
1969  outarray[i], 1);
1970  Vmath::Vsub(outarray[i].size(), outarray[i], 1, ViscTerm[i], 1,
1971  outarray[i], 1);
1972 
1973  Vmath::Vadd(outarray[i].size(), outarray[i], 1, Forc[i], 1, outarray[i],
1974  1);
1975  }
1976 }
1977 
1978 const SpatialDomains::ExpansionInfoMap &CoupledLinearNS::GenPressureExp(
1979  const SpatialDomains::ExpansionInfoMap &VelExp)
1980 {
1981  int i;
1982  SpatialDomains::ExpansionInfoMapShPtr returnval;
1983  returnval =
1984  MemoryManager<SpatialDomains::ExpansionInfoMap>::AllocateSharedPtr();
1985 
1986  int nummodes;
1987 
1988  for (auto &expMapIter : VelExp)
1989  {
1990  LibUtilities::BasisKeyVector BasisVec;
1991 
1992  for (i = 0; i < expMapIter.second->m_basisKeyVector.size(); ++i)
1993  {
1994  LibUtilities::BasisKey B = expMapIter.second->m_basisKeyVector[i];
1995  nummodes = B.GetNumModes();
1996  ASSERTL0(nummodes > 3,
1997  "Velocity polynomial space not sufficiently high (>= 4)");
1998  // Should probably set to be an orthogonal basis.
1999  LibUtilities::BasisKey newB(B.GetBasisType(), nummodes - 2,
2000  B.GetPointsKey());
2001  BasisVec.push_back(newB);
2002  }
2003 
2004  // Put new expansion into list.
2005  SpatialDomains::ExpansionInfoShPtr expansionElementShPtr =
2006  MemoryManager<SpatialDomains::ExpansionInfo>::AllocateSharedPtr(
2007  expMapIter.second->m_geomShPtr, BasisVec);
2008  (*returnval)[expMapIter.first] = expansionElementShPtr;
2009  }
2010 
2011  // Save expansion into graph.
2012  m_graph->SetExpansionInfo("p", returnval);
2013 
2014  return *returnval;
2015 }
2016 
2017 /**
2018  * @param forcing A list of forcing functions for each velocity
2019  * component
2020  *
2021  * The routine involves two levels of static
2022  * condensations. Initially we require a statically condensed
2023  * forcing function which requires the following manipulation
2024  *
2025  * \f[ {F\_bnd} = {\bf f}_{bnd} -m\_B \,m\_Cinv\, {\bf f}_{int},
2026  * \hspace{1cm} F\_p = m\_D\_{int}\, m\_Cinv\, {\bf f}_{int} \f]
2027  *
2028  * Where \f${\bf f}_{bnd}\f$ denote the forcing degrees of
2029  * freedom of the elemental velocities on the boundary of the
2030  * element, \f${\bf f}_{int}\f$ denote the forcing degrees of
2031  * freedom of the elemental velocities on the interior of the
2032  * element. (see detailed description for more details).
2033  *
2034  * This vector is further manipulated into
2035  *
2036  * \f[ Fh\_{bnd} = \left [ \begin{array}{c} f\_{bnd} -m\_B \,
2037  * m\_Cinv\, {\bf f}_{int}\\ \left [m\_D\_{int} \, m\_Cinv \,{\bf
2038  * f}_{int} \right]_0 \end{array}\right ] \hspace{1cm} [Fh\_p]_{i} =
2039  * \begin{array}{c} [m\_D\_{int} \, m\_Cinv \, {\bf
2040  * f}_{int}]_{i+1} \end{array} \f]
2041  *
2042  * where \f$-{[}m\_D\_{int}^T\, m\_Cinv \,{\bf f}_{int}]_0\f$
2043  * which is corresponds to the mean mode of the pressure degrees
2044  * of freedom and is now added to the boundary system and the
2045  * remainder of the block becomes the interior forcing for the
2046  * inner static condensation (see detailed description for more
2047  * details) which is set up in a GlobalLinSysDirectStaticCond
2048  * class.
2049  *
2050  * Finally we perform the final maniplation of the forcing to
2051  * using hte
2052  * \f[ Fh\_{bnd} = Fh\_{bnd} - m\_Bh \,m\_Chinv \, Fh\_p \f]
2053  *
2054  * We can now call the solver to the global coupled boundary
2055  * system (through the call to #m_CoupledBndSys->Solve) to obtain
2056  * the velocity boundary solution as the mean pressure solution,
2057  * i.e.
2058  *
2059  * \f[ {\cal A}^T(\hat{A} - \hat{C}^T \hat{D}^{-1} \hat{B} ){\cal
2060  * A} \, Bnd = Fh\_{bnd} \f]
2061  *
2062  * Once we know the solution to the above the rest of the pressure
2063  * modes are recoverable thorugh
2064  *
2065  * \f[ Ph = m\_Dhinv\, (Bnd - m\_Ch^T \, Fh_{bnd}) \f]
2066  *
2067  * We can now unpack \f$ Fh\_{bnd} \f$ (last elemental mode) and
2068  * \f$ Ph \f$ into #m_pressure and \f$ F_p\f$ and \f$ Fh\_{bnd}\f$
2069  * into a closed pack list of boundary velocoity degrees of
2070  * freedom stored in \f$ F\_bnd\f$.
2071  *
2072  * Finally the interior velocity degrees of freedom are then
2073  * obtained through the relationship
2074  *
2075  * \f[ F\_{int} = m\_Cinv\ ( F\_{int} + m\_D\_{int}^T\,
2076  * F\_p - m\_Btilde^T\, Bnd) \f]
2077  *
2078  * We then unpack the solution back to the MultiRegion structures
2079  * #m_velocity and #m_pressure
2080  */
2081 void CoupledLinearNS::SolveLinearNS(
2082  const Array<OneD, Array<OneD, NekDouble>> &forcing)
2083 {
2084  int i, n;
2085  Array<OneD, MultiRegions::ExpListSharedPtr> vel_fields(m_velocity.size());
2086  Array<OneD, Array<OneD, NekDouble>> force(m_velocity.size());
2087 
2088  // Impose Dirichlet conditions on velocity fields
2089  for (i = 0; i < m_velocity.size(); ++i)
2090  {
2091  Vmath::Zero(m_fields[i]->GetNcoeffs(), m_fields[i]->UpdateCoeffs(), 1);
2092  m_fields[i]->ImposeDirichletConditions(m_fields[i]->UpdateCoeffs());
2093  }
2094 
2095  if (m_HomogeneousType == eHomogeneous1D)
2096  {
2097  int ncoeffsplane = m_fields[m_velocity[0]]->GetPlane(0)->GetNcoeffs();
2098  for (n = 0; n < m_npointsZ / 2; ++n)
2099  {
2100  // Get the a Fourier mode of velocity and forcing components.
2101  for (i = 0; i < m_velocity.size(); ++i)
2102  {
2103  vel_fields[i] = m_fields[m_velocity[i]]->GetPlane(2 * n);
2104  // Note this needs to correlate with how we pass forcing
2105  force[i] = forcing[i] + 2 * n * ncoeffsplane;
2106  }
2107 
2108  SolveLinearNS(force, vel_fields, m_pressure->GetPlane(2 * n), n);
2109  }
2110  for (i = 0; i < m_velocity.size(); ++i)
2111  {
2112  m_fields[m_velocity[i]]->SetPhysState(false);
2113  }
2114  m_pressure->SetPhysState(false);
2115  }
2116  else
2117  {
2118  for (i = 0; i < m_velocity.size(); ++i)
2119  {
2120  vel_fields[i] = m_fields[m_velocity[i]];
2121  // Note this needs to correlate with how we pass forcing
2122  force[i] = forcing[i];
2123  }
2124  SolveLinearNS(force, vel_fields, m_pressure);
2125  }
2126 }
2127 
2128 void CoupledLinearNS::SolveLinearNS(
2129  Array<OneD, Array<OneD, NekDouble>> &forcing,
2130  Array<OneD, MultiRegions::ExpListSharedPtr> &fields,
2131  MultiRegions::ExpListSharedPtr &pressure, const int mode)
2132 {
2133  int i, j, k, n, cnt, cnt1;
2134  int nbnd, nint, offset;
2135  int nvel = m_velocity.size();
2136  int nel = fields[0]->GetNumElmts();
2137  Array<OneD, unsigned int> bmap, imap;
2138 
2139  Array<OneD, NekDouble> f_bnd(m_mat[mode].m_BCinv->GetRows());
2140  NekVector<NekDouble> F_bnd(f_bnd.size(), f_bnd, eWrapper);
2141  Array<OneD, NekDouble> f_int(m_mat[mode].m_BCinv->GetColumns());
2142  NekVector<NekDouble> F_int(f_int.size(), f_int, eWrapper);
2143 
2144  int nz_loc;
2145  int nplanecoeffs =
2146  fields[m_velocity[0]]
2147  ->GetNcoeffs(); // this is fine since we pass the nplane coeff data.
2148 
2149  if (mode) // Homogeneous mode flag
2150  {
2151  nz_loc = 2;
2152  }
2153  else
2154  {
2155  if (m_singleMode)
2156  {
2157  nz_loc = 2;
2158  }
2159  else
2160  {
2161  nz_loc = 1;
2162  if (m_HomogeneousType == eHomogeneous1D)
2163  {
2164  Array<OneD, NekDouble> tmp;
2165  // Zero fields to set complex mode to zero;
2166  for (i = 0; i < fields.size(); ++i)
2167  {
2168  Vmath::Zero(nplanecoeffs,
2169  tmp = fields[i]->UpdateCoeffs() + nplanecoeffs,
2170  1);
2171  }
2172  Vmath::Zero(2 * pressure->GetNcoeffs(),
2173  pressure->UpdateCoeffs(), 1);
2174  }
2175  }
2176  }
2177 
2178  for (k = 0; k < nvel; ++k)
2179  {
2180  MultiRegions::ContFieldSharedPtr cfield =
2181  std::dynamic_pointer_cast<MultiRegions::ContField>(fields[k]);
2182 
2183  Array<OneD, NekDouble> sign =
2184  cfield->GetLocalToGlobalMap()->GetBndCondCoeffsToLocalCoeffsSign();
2185  const Array<OneD, const int> map =
2186  cfield->GetLocalToGlobalMap()->GetBndCondCoeffsToLocalCoeffsMap();
2187 
2188  // Add weak boundary conditions to forcing
2189  const Array<OneD, SpatialDomains::BoundaryConditionShPtr> bndConds =
2190  fields[k]->GetBndConditions();
2191  Array<OneD, const MultiRegions::ExpListSharedPtr> bndCondExp;
2192 
2193  if (m_HomogeneousType == eHomogeneous1D)
2194  {
2195  bndCondExp =
2196  m_fields[k]->GetPlane(2 * mode)->GetBndCondExpansions();
2197  }
2198  else
2199  {
2200  bndCondExp = m_fields[k]->GetBndCondExpansions();
2201  }
2202 
2203  for (n = 0; n < nz_loc; ++n)
2204  {
2205  int bndcnt = 0;
2206  for (i = 0; i < bndCondExp.size(); ++i)
2207  {
2208  const Array<OneD, const NekDouble> bndcoeffs =
2209  bndCondExp[i]->GetCoeffs();
2210 
2211  cnt = 0;
2212  if (bndConds[i]->GetBoundaryConditionType() ==
2213  SpatialDomains::eNeumann ||
2214  bndConds[i]->GetBoundaryConditionType() ==
2215  SpatialDomains::eRobin)
2216  {
2217  if (m_locToGloMap[mode]->GetSignChange())
2218  {
2219  for (j = 0; j < (bndCondExp[i])->GetNcoeffs(); j++)
2220  {
2221  forcing[k][n * nplanecoeffs + map[bndcnt + j]] +=
2222  sign[bndcnt + j] * bndcoeffs[j];
2223  }
2224  }
2225  else
2226  {
2227  for (j = 0; j < (bndCondExp[i])->GetNcoeffs(); j++)
2228  {
2229  forcing[k][n * nplanecoeffs + map[bndcnt + j]] +=
2230  bndcoeffs[j];
2231  }
2232  }
2233  }
2234 
2235  bndcnt += bndCondExp[i]->GetNcoeffs();
2236  }
2237  }
2238  }
2239 
2240  Array<OneD, NekDouble> bnd(m_locToGloMap[mode]->GetNumLocalCoeffs(), 0.0);
2241 
2242  // Construct f_bnd and f_int and fill in bnd from inarray
2243  // (with Dirichlet BCs imposed)
2244  int bndoffset = 0;
2245  cnt = cnt1 = 0;
2246  for (i = 0; i < nel; ++i) // loop over elements
2247  {
2248  fields[m_velocity[0]]->GetExp(i)->GetBoundaryMap(bmap);
2249  fields[m_velocity[0]]->GetExp(i)->GetInteriorMap(imap);
2250  nbnd = bmap.size();
2251  nint = imap.size();
2252  offset = fields[m_velocity[0]]->GetCoeff_Offset(i);
2253 
2254  for (j = 0; j < nvel; ++j) // loop over velocity fields
2255  {
2256  Array<OneD, NekDouble> incoeffs = fields[j]->UpdateCoeffs();
2257 
2258  for (n = 0; n < nz_loc; ++n)
2259  {
2260  for (k = 0; k < nbnd; ++k)
2261  {
2262  f_bnd[cnt + k] =
2263  forcing[j][n * nplanecoeffs + offset + bmap[k]];
2264 
2265  bnd[bndoffset + (n + j * nz_loc) * nbnd + k] =
2266  incoeffs[n * nplanecoeffs + offset + bmap[k]];
2267  }
2268  for (k = 0; k < nint; ++k)
2269  {
2270  f_int[cnt1 + k] =
2271  forcing[j][n * nplanecoeffs + offset + imap[k]];
2272  }
2273 
2274  cnt += nbnd;
2275  cnt1 += nint;
2276  }
2277  }
2278  bndoffset +=
2279  nvel * nz_loc * nbnd + nz_loc * (pressure->GetExp(i)->GetNcoeffs());
2280  }
2281 
2282  Array<OneD, NekDouble> f_p(m_mat[mode].m_D_int->GetRows());
2283  NekVector<NekDouble> F_p(f_p.size(), f_p, eWrapper);
2284  NekVector<NekDouble> F_p_tmp(m_mat[mode].m_Cinv->GetRows());
2285 
2286  // fbnd does not currently hold the pressure mean
2287  F_bnd = F_bnd - (*m_mat[mode].m_BCinv) * F_int;
2288  F_p_tmp = (*m_mat[mode].m_Cinv) * F_int;
2289  F_p = (*m_mat[mode].m_D_int) * F_p_tmp;
2290 
2291  // construct inner forcing
2292  Array<OneD, NekDouble> fh_bnd(m_locToGloMap[mode]->GetNumLocalCoeffs(),
2293  0.0);
2294 
2295  offset = cnt = 0;
2296  for (i = 0; i < nel; ++i)
2297  {
2298  nbnd = nz_loc * fields[0]->GetExp(i)->NumBndryCoeffs();
2299 
2300  for (j = 0; j < nvel; ++j)
2301  {
2302  for (k = 0; k < nbnd; ++k)
2303  {
2304  fh_bnd[offset + j * nbnd + k] = f_bnd[cnt + k];
2305  }
2306  cnt += nbnd;
2307  }
2308 
2309  nint = pressure->GetExp(i)->GetNcoeffs();
2310  offset += nvel * nbnd + nint * nz_loc;
2311  }
2312 
2313  offset = cnt1 = 0;
2314  for (i = 0; i < nel; ++i)
2315  {
2316  nbnd = nz_loc * fields[0]->GetExp(i)->NumBndryCoeffs();
2317  nint = pressure->GetExp(i)->GetNcoeffs();
2318 
2319  for (n = 0; n < nz_loc; ++n)
2320  {
2321  for (j = 0; j < nint; ++j)
2322  {
2323  fh_bnd[offset + nvel * nbnd + n * nint + j] = f_p[cnt1 + j];
2324  }
2325  cnt1 += nint;
2326  }
2327  offset += nvel * nbnd + nz_loc * nint;
2328  }
2329  m_mat[mode].m_CoupledBndSys->Solve(fh_bnd, bnd, m_locToGloMap[mode]);
2330 
2331  // unpack pressure and velocity boundary systems.
2332  offset = cnt = 0;
2333  int totpcoeffs = pressure->GetNcoeffs();
2334  Array<OneD, NekDouble> p_coeffs = pressure->UpdateCoeffs();
2335  for (i = 0; i < nel; ++i)
2336  {
2337  nbnd = nz_loc * fields[0]->GetExp(i)->NumBndryCoeffs();
2338  nint = pressure->GetExp(i)->GetNcoeffs();
2339  for (j = 0; j < nvel; ++j)
2340  {
2341  for (k = 0; k < nbnd; ++k)
2342  {
2343  f_bnd[cnt + k] = bnd[offset + j * nbnd + k];
2344  }
2345  cnt += nbnd;
2346  }
2347  offset += nvel * nbnd + nint * nz_loc;
2348  }
2349 
2350  pressure->SetPhysState(false);
2351 
2352  offset = cnt = cnt1 = 0;
2353  for (i = 0; i < nel; ++i)
2354  {
2355  nint = pressure->GetExp(i)->GetNcoeffs();
2356  nbnd = fields[0]->GetExp(i)->NumBndryCoeffs();
2357  cnt1 = pressure->GetCoeff_Offset(i);
2358 
2359  for (n = 0; n < nz_loc; ++n)
2360  {
2361  for (j = 0; j < nint; ++j)
2362  {
2363  p_coeffs[n * totpcoeffs + cnt1 + j] = f_p[cnt + j] =
2364  bnd[offset + nvel * nz_loc * nbnd + n * nint + j];
2365  }
2366  cnt += nint;
2367  }
2368  offset += (nvel * nbnd + nint) * nz_loc;
2369  }
2370 
2371  // Back solve first level of static condensation for interior
2372  // velocity space and store in F_int
2373  F_int = F_int + Transpose(*m_mat[mode].m_D_int) * F_p -
2374  Transpose(*m_mat[mode].m_Btilde) * F_bnd;
2375  F_int = (*m_mat[mode].m_Cinv) * F_int;
2376 
2377  // Unpack solution from Bnd and F_int to v_coeffs
2378  cnt = cnt1 = 0;
2379  for (i = 0; i < nel; ++i) // loop over elements
2380  {
2381  fields[0]->GetExp(i)->GetBoundaryMap(bmap);
2382  fields[0]->GetExp(i)->GetInteriorMap(imap);
2383  nbnd = bmap.size();
2384  nint = imap.size();
2385  offset = fields[0]->GetCoeff_Offset(i);
2386 
2387  for (j = 0; j < nvel; ++j) // loop over velocity fields
2388  {
2389  for (n = 0; n < nz_loc; ++n)
2390  {
2391  for (k = 0; k < nbnd; ++k)
2392  {
2393  fields[j]->SetCoeff(n * nplanecoeffs + offset + bmap[k],
2394  f_bnd[cnt + k]);
2395  }
2396 
2397  for (k = 0; k < nint; ++k)
2398  {
2399  fields[j]->SetCoeff(n * nplanecoeffs + offset + imap[k],
2400  f_int[cnt1 + k]);
2401  }
2402  cnt += nbnd;
2403  cnt1 += nint;
2404  }
2405  }
2406  }
2407 
2408  for (j = 0; j < nvel; ++j)
2409  {
2410  fields[j]->SetPhysState(false);
2411  }
2412 }
2413 
2414 void CoupledLinearNS::v_Output(void)
2415 {
2416  std::vector<Array<OneD, NekDouble>> fieldcoeffs(m_fields.size() + 1);
2417  std::vector<std::string> variables(m_fields.size() + 1);
2418  int i;
2419 
2420  for (i = 0; i < m_fields.size(); ++i)
2421  {
2422  fieldcoeffs[i] = m_fields[i]->UpdateCoeffs();
2423  variables[i] = m_boundaryConditions->GetVariable(i);
2424  }
2425 
2426  fieldcoeffs[i] = Array<OneD, NekDouble>(m_fields[0]->GetNcoeffs());
2427  // project pressure field to velocity space
2428  if (m_singleMode == true)
2429  {
2430  Array<OneD, NekDouble> tmpfieldcoeffs(m_fields[0]->GetNcoeffs() / 2);
2431  m_pressure->GetPlane(0)->BwdTrans(
2432  m_pressure->GetPlane(0)->GetCoeffs(),
2433  m_pressure->GetPlane(0)->UpdatePhys());
2434  m_pressure->GetPlane(1)->BwdTrans(
2435  m_pressure->GetPlane(1)->GetCoeffs(),
2436  m_pressure->GetPlane(1)->UpdatePhys());
2437  m_fields[0]->GetPlane(0)->FwdTransLocalElmt(
2438  m_pressure->GetPlane(0)->GetPhys(), fieldcoeffs[i]);
2439  m_fields[0]->GetPlane(1)->FwdTransLocalElmt(
2440  m_pressure->GetPlane(1)->GetPhys(), tmpfieldcoeffs);
2441  for (int e = 0; e < m_fields[0]->GetNcoeffs() / 2; e++)
2442  {
2443  fieldcoeffs[i][e + m_fields[0]->GetNcoeffs() / 2] =
2444  tmpfieldcoeffs[e];
2445  }
2446  }
2447  else
2448  {
2449  m_pressure->BwdTrans(m_pressure->GetCoeffs(), m_pressure->UpdatePhys());
2450  m_fields[0]->FwdTransLocalElmt(m_pressure->GetPhys(), fieldcoeffs[i]);
2451  }
2452  variables[i] = "p";
2453 
2454  std::string outname = m_sessionName + ".fld";
2455 
2456  WriteFld(outname, m_fields[0], fieldcoeffs, variables);
2457 }
2458 
2459 int CoupledLinearNS::v_GetForceDimension()
2460 {
2461  return m_session->GetVariables().size();
2462 }
2463 } // namespace Nektar
ASSERTL0
#define ASSERTL0(condition, msg)
Definition: ErrorUtil.hpp:215
ASSERTL1
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode....
Definition: ErrorUtil.hpp:249
sign
#define sign(a, b)
return the sign(b)*a
Definition: Polylib.cpp:15
Nektar::CoupledLinearNS::v_TransPhysToCoeff
virtual void v_TransPhysToCoeff(void)
Virtual function for transformation to coefficient space.
Definition: CoupledLinearNS.cpp:1574
Nektar::CoupledLinearNS::m_locToGloMap
Array< OneD, CoupledLocalToGlobalC0ContMapSharedPtr > m_locToGloMap
Definition: CoupledLinearNS.h:162
Nektar::CoupledLinearNS::v_Output
virtual void v_Output(void)
Definition: CoupledLinearNS.cpp:2414
Nektar::CoupledLinearNS::EvaluateNewtonRHS
void EvaluateNewtonRHS(Array< OneD, Array< OneD, NekDouble >> &Velocity, Array< OneD, Array< OneD, NekDouble >> &outarray)
Definition: CoupledLinearNS.cpp:1922
Nektar::CoupledLinearNS::SetUpCoupledMatrix
void SetUpCoupledMatrix(const NekDouble lambda=0.0, const Array< OneD, Array< OneD, NekDouble >> &Advfield=NullNekDoubleArrayOfArray, bool IsLinearNSEquation=true)
Definition: CoupledLinearNS.cpp:198
Nektar::CoupledLinearNS::GenPressureExp
const SpatialDomains::ExpansionInfoMap & GenPressureExp(const SpatialDomains::ExpansionInfoMap &VelExp)
Definition: CoupledLinearNS.cpp:1978
Nektar::CoupledLinearNS::v_DoSolve
virtual void v_DoSolve(void)
Solves an unsteady problem.
Definition: CoupledLinearNS.cpp:1585
Nektar::CoupledLinearNS::EvaluateAdvection
void EvaluateAdvection(const Array< OneD, const Array< OneD, NekDouble >> &inarray, Array< OneD, Array< OneD, NekDouble >> &outarray, const NekDouble time)
Definition: CoupledLinearNS.cpp:1510
Nektar::CoupledLinearNS::InfNorm
void InfNorm(Array< OneD, Array< OneD, NekDouble >> &inarray, Array< OneD, NekDouble > &outarray)
Definition: CoupledLinearNS.cpp:1890
Nektar::CoupledLinearNS::v_NegatedOp
virtual bool v_NegatedOp(void)
Definition: CoupledLinearNS.cpp:1660
Nektar::CoupledLinearNS::SolveUnsteadyStokesSystem
void SolveUnsteadyStokesSystem(const Array< OneD, const Array< OneD, NekDouble >> &inarray, Array< OneD, Array< OneD, NekDouble >> &outarray, const NekDouble time, const NekDouble a_iixDt)
Definition: CoupledLinearNS.cpp:1523
Nektar::CoupledLinearNS::SolveLinearNS
void SolveLinearNS(const Array< OneD, Array< OneD, NekDouble >> &forcing)
Definition: CoupledLinearNS.cpp:2081
Nektar::CoupledLinearNS::v_GetForceDimension
virtual int v_GetForceDimension(void)
Definition: CoupledLinearNS.cpp:2459
Nektar::CoupledLinearNS::m_zeroMode
bool m_zeroMode
Id to identify when single mode is mean mode (i.e. beta=0);.
Definition: CoupledLinearNS.h:172
Nektar::CoupledLinearNS::m_ForcingTerm_Coeffs
Array< OneD, Array< OneD, NekDouble > > m_ForcingTerm_Coeffs
Definition: CoupledLinearNS.h:160
Nektar::CoupledLinearNS::L2Norm
void L2Norm(Array< OneD, Array< OneD, NekDouble >> &inarray, Array< OneD, NekDouble > &outarray)
Definition: CoupledLinearNS.cpp:1907
Nektar::CoupledLinearNS::m_ForcingTerm
Array< OneD, Array< OneD, NekDouble > > m_ForcingTerm
Definition: CoupledLinearNS.h:159
Nektar::CoupledLinearNS::v_InitObject
virtual void v_InitObject(bool DeclareField=true)
Init object for UnsteadySystem class.
Definition: CoupledLinearNS.cpp:67
Nektar::CoupledLinearNS::v_DoInitialise
virtual void v_DoInitialise(void)
Sets up initial conditions.
Definition: CoupledLinearNS.cpp:1359
Nektar::CoupledLinearNS::m_mat
Array< OneD, CoupledSolverMatrices > m_mat
Definition: CoupledLinearNS.h:185
Nektar::CoupledLinearNS::v_TransCoeffToPhys
virtual void v_TransCoeffToPhys(void)
Virtual function for transformation to physical space.
Definition: CoupledLinearNS.cpp:1563
Nektar::CoupledLinearNS::v_GenerateSummary
virtual void v_GenerateSummary(SolverUtils::SummaryList &s)
Print a summary of time stepping parameters.
Definition: CoupledLinearNS.cpp:1354
Nektar::IncNavierStokes
This class is the base class for Navier Stokes problems.
Definition: IncNavierStokes.h:135
Nektar::IncNavierStokes::m_pressure
MultiRegions::ExpListSharedPtr m_pressure
Pointer to field holding pressure field.
Definition: IncNavierStokes.h:209
Nektar::IncNavierStokes::m_kinvis
NekDouble m_kinvis
Kinematic viscosity.
Definition: IncNavierStokes.h:211
Nektar::IncNavierStokes::v_InitObject
virtual void v_InitObject(bool DeclareField=true) override
Init object for UnsteadySystem class.
Definition: IncNavierStokes.cpp:91
Nektar::IncNavierStokes::m_extrapolation
ExtrapolateSharedPtr m_extrapolation
Definition: IncNavierStokes.h:190
Nektar::IncNavierStokes::m_velocity
Array< OneD, int > m_velocity
int which identifies which components of m_fields contains the velocity (u,v,w);
Definition: IncNavierStokes.h:206
Nektar::IncNavierStokes::EvaluateAdvectionTerms
void EvaluateAdvectionTerms(const Array< OneD, const Array< OneD, NekDouble >> &inarray, Array< OneD, Array< OneD, NekDouble >> &outarray, const NekDouble time)
Definition: IncNavierStokes.cpp:399
Nektar::IncNavierStokes::m_equationType
EquationType m_equationType
equation type;
Definition: IncNavierStokes.h:216
Nektar::IncNavierStokes::m_nConvectiveFields
int m_nConvectiveFields
Number of fields to be convected;.
Definition: IncNavierStokes.h:202
Nektar::IncNavierStokes::m_forcing
std::vector< SolverUtils::ForcingSharedPtr > m_forcing
Forcing terms.
Definition: IncNavierStokes.h:199
Nektar::LibUtilities::BasisKey
Describes the specification for a Basis.
Definition: Basis.h:50
Nektar::LibUtilities::BasisKey::GetBasisType
BasisType GetBasisType() const
Return type of expansion basis.
Definition: Basis.h:141
Nektar::LibUtilities::BasisKey::GetPointsKey
PointsKey GetPointsKey() const
Return distribution of points.
Definition: Basis.h:147
Nektar::LibUtilities::BasisKey::GetNumModes
int GetNumModes() const
Returns the order of the basis.
Definition: Basis.h:83
Nektar::LibUtilities::NekFactory::RegisterCreatorFunction
tKey RegisterCreatorFunction(tKey idKey, CreatorFunction classCreator, std::string pDesc="")
Register a class with the factory.
Definition: NekFactory.hpp:198
Nektar::LibUtilities::NekFactory::CreateInstance
tBaseSharedPtr CreateInstance(tKey idKey, tParam... args)
Create an instance of the class referred to by idKey.
Definition: NekFactory.hpp:144
Nektar::LibUtilities::TimeIntegrationSchemeOperators::DefineOdeRhs
void DefineOdeRhs(FuncPointerT func, ObjectPointerT obj)
Definition: TimeIntegrationSchemeOperators.h:88
Nektar::LibUtilities::TimeIntegrationSchemeOperators::DefineImplicitSolve
void DefineImplicitSolve(FuncPointerT func, ObjectPointerT obj)
Definition: TimeIntegrationSchemeOperators.h:120
Nektar::LibUtilities::Timer::TimePerTest
NekDouble TimePerTest(unsigned int n)
Returns amount of seconds per iteration in a test with n iterations.
Definition: Timer.cpp:68
Nektar::MemoryManager
General purpose memory allocation routines with the ability to allocate from thread specific memory p...
Definition: NekMemoryManager.hpp:83
Nektar::MemoryManager::AllocateSharedPtr
static std::shared_ptr< DataType > AllocateSharedPtr(const Args &...args)
Allocate a shared pointer from the memory pool.
Definition: NekMemoryManager.hpp:168
Nektar::SolverUtils::AdvectionSystem::m_advObject
SolverUtils::AdvectionSharedPtr m_advObject
Advection term.
Definition: AdvectionSystem.h:70
Nektar::SolverUtils::EquationSystem::m_useFFT
bool m_useFFT
Flag to determine if FFT is used for homogeneous transform.
Definition: EquationSystem.h:378
Nektar::SolverUtils::EquationSystem::m_graph
SpatialDomains::MeshGraphSharedPtr m_graph
Pointer to graph defining mesh.
Definition: EquationSystem.h:339
Nektar::SolverUtils::EquationSystem::m_time
NekDouble m_time
Current time of simulation.
Definition: EquationSystem.h:343
Nektar::SolverUtils::EquationSystem::m_fields
Array< OneD, MultiRegions::ExpListSharedPtr > m_fields
Array holding all dependent variables.
Definition: EquationSystem.h:335
Nektar::SolverUtils::EquationSystem::m_lambda
NekDouble m_lambda
Lambda constant in real system if one required.
Definition: EquationSystem.h:354
Nektar::SolverUtils::EquationSystem::m_npointsZ
int m_npointsZ
number of points in Z direction (if homogeneous)
Definition: EquationSystem.h:430
Nektar::SolverUtils::EquationSystem::Checkpoint_Output
SOLVER_UTILS_EXPORT void Checkpoint_Output(const int n)
Write checkpoint file of m_fields.
Definition: EquationSystem.cpp:1086
Nektar::SolverUtils::EquationSystem::WriteFld
SOLVER_UTILS_EXPORT void WriteFld(const std::string &outname)
Write field data to the given filename.
Definition: EquationSystem.cpp:1123
Nektar::SolverUtils::EquationSystem::m_sessionName
std::string m_sessionName
Name of the session.
Definition: EquationSystem.h:341
Nektar::SolverUtils::EquationSystem::m_session
LibUtilities::SessionReaderSharedPtr m_session
The session reader.
Definition: EquationSystem.h:328
Nektar::SolverUtils::EquationSystem::m_singleMode
bool m_singleMode
Flag to determine if single homogeneous mode is used.
Definition: EquationSystem.h:372
Nektar::SolverUtils::EquationSystem::m_HomogeneousType
enum HomogeneousType m_HomogeneousType
Definition: EquationSystem.h:422
Nektar::SolverUtils::EquationSystem::GetNpoints
SOLVER_UTILS_EXPORT int GetNpoints()
Definition: EquationSystem.h:730
Nektar::SolverUtils::EquationSystem::m_homogen_dealiasing
bool m_homogen_dealiasing
Flag to determine if dealiasing is used for homogeneous simulations.
Definition: EquationSystem.h:383
Nektar::SolverUtils::EquationSystem::GetNcoeffs
SOLVER_UTILS_EXPORT int GetNcoeffs()
Definition: EquationSystem.h:662
Nektar::SolverUtils::EquationSystem::m_boundaryConditions
SpatialDomains::BoundaryConditionsSharedPtr m_boundaryConditions
Pointer to boundary conditions object.
Definition: EquationSystem.h:337
Nektar::SolverUtils::EquationSystem::m_LhomZ
NekDouble m_LhomZ
physical length in Z direction (if homogeneous)
Definition: EquationSystem.h:426
Nektar::SolverUtils::EquationSystem::SetInitialConditions
SOLVER_UTILS_EXPORT void SetInitialConditions(NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)
Initialise the data in the dependent fields.
Definition: EquationSystem.h:636
Nektar::SolverUtils::EquationSystem::GetFunction
SOLVER_UTILS_EXPORT SessionFunctionSharedPtr GetFunction(std::string name, const MultiRegions::ExpListSharedPtr &field=MultiRegions::NullExpListSharedPtr, bool cache=false)
Get a SessionFunction by name.
Definition: EquationSystem.cpp:681
Nektar::SolverUtils::EquationSystem::GetTotPoints
SOLVER_UTILS_EXPORT int GetTotPoints()
Definition: EquationSystem.h:720
Nektar::SolverUtils::UnsteadySystem
Base class for unsteady solvers.
Definition: UnsteadySystem.h:49
Nektar::SolverUtils::UnsteadySystem::m_ode
LibUtilities::TimeIntegrationSchemeOperators m_ode
The time integration scheme operators to use.
Definition: UnsteadySystem.h:85
Nektar::SolverUtils::UnsteadySystem::v_DoSolve
virtual SOLVER_UTILS_EXPORT void v_DoSolve()
Solves an unsteady problem.
Definition: UnsteadySystem.cpp:192
Blas::Dcopy
static void Dcopy(const int &n, const double *x, const int &incx, double *y, const int &incy)
BLAS level 1: Copy x to y.
Definition: Blas.hpp:147
Blas::Dgemm
static void Dgemm(const char &transa, const char &transb, const int &m, const int &n, const int &k, const double &alpha, const double *a, const int &lda, const double *b, const int &ldb, const double &beta, double *c, const int &ldc)
BLAS level 3: Matrix-matrix multiply C = A x B where op(A)[m x k], op(B)[k x n], C[m x n] DGEMM perfo...
Definition: Blas.hpp:368
CG_Iterations.pressure
pressure
Definition: CG_Iterations.py:229
Nektar::LibUtilities::BasisKeyVector
std::vector< BasisKey > BasisKeyVector
Name for a vector of BasisKeys.
Definition: FoundationsFwd.hpp:67
Nektar::LibUtilities::SessionReaderSharedPtr
std::shared_ptr< SessionReader > SessionReaderSharedPtr
Definition: SessionReader.h:115
Nektar::LibUtilities::beta
@ beta
Gauss Radau pinned at x=-1,.
Definition: PointsType.h:61
Nektar::MultiRegions::DirCartesianMap
MultiRegions::Direction const DirCartesianMap[]
Definition: ExpList.h:89
Nektar::MultiRegions::ExpListSharedPtr
std::shared_ptr< ExpList > ExpListSharedPtr
Shared pointer to an ExpList object.
Definition: LocTraceToTraceMap.h:55
Nektar::MultiRegions::ContFieldSharedPtr
std::shared_ptr< ContField > ContFieldSharedPtr
Definition: ContField.h:277
Nektar::NekConstants::kNekUnsetDouble
static const NekDouble kNekUnsetDouble
Definition: NektarUnivConsts.hpp:47
Nektar::SolverUtils::SummaryList
std::vector< std::pair< std::string, std::string > > SummaryList
Definition: Misc.h:48
Nektar::SolverUtils::GetEquationSystemFactory
EquationSystemFactory & GetEquationSystemFactory()
Definition: EquationSystem.cpp:85
Nektar::SolverUtils::AddSummaryItem
void AddSummaryItem(SummaryList &l, const std::string &name, const std::string &value)
Adds a summary item to the summary info list.
Definition: Misc.cpp:49
Nektar::SpatialDomains::ExpansionInfoMapShPtr
std::shared_ptr< ExpansionInfoMap > ExpansionInfoMapShPtr
Definition: MeshGraph.h:145
Nektar::SpatialDomains::ExpansionInfoShPtr
std::shared_ptr< ExpansionInfo > ExpansionInfoShPtr
Definition: MeshGraph.h:140
Nektar::SpatialDomains::MeshGraphSharedPtr
std::shared_ptr< MeshGraph > MeshGraphSharedPtr
Definition: MeshGraph.h:172
Nektar::SpatialDomains::ExpansionInfoMap
std::map< int, ExpansionInfoShPtr > ExpansionInfoMap
Definition: MeshGraph.h:143
Nektar::StdRegions::StdExpansionSharedPtr
std::shared_ptr< StdExpansion > StdExpansionSharedPtr
Definition: StdExpansion.h:1632
Nektar::StdRegions::ConstFactorMap
std::map< ConstFactorType, NekDouble > ConstFactorMap
Definition: StdRegions.hpp:282
Nektar
The above copyright notice and this permission notice shall be included.
Definition: CoupledSolver.h:1
Nektar::DNekScalMatSharedPtr
std::shared_ptr< DNekScalMat > DNekScalMatSharedPtr
Definition: NekMatrixFwd.hpp:68
Nektar::eSteadyNavierStokes
@ eSteadyNavierStokes
Definition: IncNavierStokes.h:63
Nektar::eUnsteadyStokes
@ eUnsteadyStokes
Definition: IncNavierStokes.h:60
Nektar::eUnsteadyNavierStokes
@ eUnsteadyNavierStokes
Definition: IncNavierStokes.h:62
Nektar::eSteadyLinearisedNS
@ eSteadyLinearisedNS
Definition: IncNavierStokes.h:59
Nektar::eNoEquationType
@ eNoEquationType
Definition: IncNavierStokes.h:56
Nektar::Transpose
NekMatrix< InnerMatrixType, BlockMatrixTag > Transpose(NekMatrix< InnerMatrixType, BlockMatrixTag > &rhs)
Definition: BlockMatrix.hpp:236
Nektar::NullNekDoubleArrayOfArray
static Array< OneD, Array< OneD, NekDouble > > NullNekDoubleArrayOfArray
Definition: SharedArray.hpp:884
Nektar::DNekScalBlkMatSharedPtr
std::shared_ptr< DNekScalBlkMat > DNekScalBlkMatSharedPtr
Definition: NekTypeDefs.hpp:79
Nektar::GetExtrapolateFactory
ExtrapolateFactory & GetExtrapolateFactory()
Definition: Extrapolate.cpp:48
Nektar::CoupledLocalToGlobalC0ContMapSharedPtr
std::shared_ptr< CoupledLocalToGlobalC0ContMap > CoupledLocalToGlobalC0ContMapSharedPtr
Definition: CoupledLocalToGlobalC0ContMap.h:65
Nektar::DNekMatSharedPtr
std::shared_ptr< DNekMat > DNekMatSharedPtr
Definition: NekTypeDefs.hpp:75
Nektar::NekDouble
double NekDouble
Definition: NektarUnivTypeDefs.hpp:43
Vmath::Vmul
void Vmul(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Multiply vector z = x*y.
Definition: Vmath.cpp:209
Vmath::Neg
void Neg(int n, T *x, const int incx)
Negate x = -x.
Definition: Vmath.cpp:518
Vmath::Vadd
void Vadd(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Add vector z = x+y.
Definition: Vmath.cpp:359
Vmath::Smul
void Smul(int n, const T alpha, const T *x, const int incx, T *y, const int incy)
Scalar multiply y = alpha*x.
Definition: Vmath.cpp:248
Vmath::Zero
void Zero(int n, T *x, const int incx)
Zero vector.
Definition: Vmath.cpp:492
Vmath::Vsub
void Vsub(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Subtract vector z = x-y.
Definition: Vmath.cpp:419
tinysimd::sqrt
scalarT< T > sqrt(scalarT< T > in)
Definition: scalar.hpp:291
Nektar::coupledSolverMatrices::m_D_int
DNekScalBlkMatSharedPtr m_D_int
Inner product of pressure system with divergence of the interior velocity space .
Definition: CoupledLinearNS.h:81
Nektar::coupledSolverMatrices::m_D_bnd
DNekScalBlkMatSharedPtr m_D_bnd
Inner product of pressure system with divergence of the boundary velocity space .
Definition: CoupledLinearNS.h:75
Nektar::coupledSolverMatrices::m_Cinv
DNekScalBlkMatSharedPtr m_Cinv
Interior-Interior Laplaican plus linearised convective terms inverted, i.e. the inverse of .
Definition: CoupledLinearNS.h:69
Nektar::coupledSolverMatrices::m_Btilde
DNekScalBlkMatSharedPtr m_Btilde
Interior-boundary Laplacian plus linearised convective terms .
Definition: CoupledLinearNS.h:62
Nektar::coupledSolverMatrices::m_BCinv
DNekScalBlkMatSharedPtr m_BCinv
Boundary-interior Laplacian plus linearised convective terms pre-multiplying Cinv: .
Definition: CoupledLinearNS.h:56
Nektar::coupledSolverMatrices::m_CoupledBndSys
MultiRegions::GlobalLinSysSharedPtr m_CoupledBndSys
Definition: CoupledLinearNS.h:83
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