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TetExp.cpp
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32 // Description:
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35 
36 #include <LocalRegions/TetExp.h>
37 #include <SpatialDomains/SegGeom.h>
38 #include <LibUtilities/Foundations/InterpCoeff.h>
39 #include <LibUtilities/Foundations/Interp.h>
40 
41 using namespace std;
42 
43 namespace Nektar
44 {
45  namespace LocalRegions
46  {
47  /**
48  * @class TetExp
49  * Defines a Tetrahedral local expansion.
50  */
51 
52  /**
53  * \brief Constructor using BasisKey class for quadrature points and
54  * order definition
55  *
56  * @param Ba Basis key for first coordinate.
57  * @param Bb Basis key for second coordinate.
58  * @param Bc Basis key for third coordinate.
59  */
60  TetExp::TetExp( const LibUtilities::BasisKey &Ba,
61  const LibUtilities::BasisKey &Bb,
62  const LibUtilities::BasisKey &Bc,
63  const SpatialDomains::TetGeomSharedPtr &geom
64  ):
65  StdExpansion (
66  LibUtilities::StdTetData::getNumberOfCoefficients(
67  Ba.GetNumModes(), Bb.GetNumModes(), Bc.GetNumModes()),
68  3, Ba, Bb, Bc),
69  StdExpansion3D(
70  LibUtilities::StdTetData::getNumberOfCoefficients(
71  Ba.GetNumModes(), Bb.GetNumModes(), Bc.GetNumModes()),
72  Ba, Bb, Bc),
73  StdRegions::StdTetExp(Ba,Bb,Bc),
74  Expansion (geom),
75  Expansion3D (geom),
76  m_matrixManager(
77  boost::bind(&TetExp::CreateMatrix, this, _1),
78  std::string("TetExpMatrix")),
79  m_staticCondMatrixManager(
80  boost::bind(&TetExp::CreateStaticCondMatrix, this, _1),
81  std::string("TetExpStaticCondMatrix"))
82  {
83  }
84 
85 
86  /**
87  * \brief Copy Constructor
88  */
89  TetExp::TetExp(const TetExp &T):
90  StdExpansion(T),
91  StdExpansion3D(T),
92  StdRegions::StdTetExp(T),
93  Expansion(T),
94  Expansion3D(T),
95  m_matrixManager(T.m_matrixManager),
96  m_staticCondMatrixManager(T.m_staticCondMatrixManager)
97  {
98  }
99 
100  /**
101  * \brief Destructor
102  */
103  TetExp::~TetExp()
104  {
105  }
106 
107 
108  //-----------------------------
109  // Integration Methods
110  //-----------------------------
111  /**
112  * \brief Integrate the physical point list \a inarray over region
113  *
114  * @param inarray Definition of function to be returned at
115  * quadrature point of expansion.
116  * @returns \f$\int^1_{-1}\int^1_{-1} \int^1_{-1}
117  * u(\eta_1, \eta_2, \eta_3) J[i,j,k] d \eta_1 d \eta_2 d \eta_3 \f$
118  * where \f$inarray[i,j,k] = u(\eta_{1i},\eta_{2j},\eta_{3k})
119  * \f$ and \f$ J[i,j,k] \f$ is the Jacobian evaluated at the quadrature
120  * point.
121  */
122  NekDouble TetExp::v_Integral(
123  const Array<OneD, const NekDouble> &inarray)
124  {
125  int nquad0 = m_base[0]->GetNumPoints();
126  int nquad1 = m_base[1]->GetNumPoints();
127  int nquad2 = m_base[2]->GetNumPoints();
128  Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
129  NekDouble retrunVal;
130  Array<OneD,NekDouble> tmp(nquad0*nquad1*nquad2);
131 
132  // multiply inarray with Jacobian
133  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
134  {
135  Vmath::Vmul(nquad0*nquad1*nquad2,&jac[0],1,
136  (NekDouble*)&inarray[0],1, &tmp[0],1);
137  }
138  else
139  {
140  Vmath::Smul(nquad0*nquad1*nquad2,(NekDouble) jac[0],
141  (NekDouble*)&inarray[0],1,&tmp[0],1);
142  }
143 
144  // call StdTetExp version;
145  retrunVal = StdTetExp::v_Integral(tmp);
146 
147  return retrunVal;
148  }
149 
150 
151  //-----------------------------
152  // Differentiation Methods
153  //-----------------------------
154  /**
155  * \brief Differentiate \a inarray in the three coordinate directions.
156  *
157  * @param inarray Input array of values at quadrature points to
158  * be differentiated.
159  * @param out_d0 Derivative in first coordinate direction.
160  * @param out_d1 Derivative in second coordinate direction.
161  * @param out_d2 Derivative in third coordinate direction.
162  */
163  void TetExp::v_PhysDeriv(
164  const Array<OneD, const NekDouble> &inarray,
165  Array<OneD, NekDouble> &out_d0,
166  Array<OneD, NekDouble> &out_d1,
167  Array<OneD, NekDouble> &out_d2)
168  {
169  int TotPts = m_base[0]->GetNumPoints()*m_base[1]->GetNumPoints()*
170  m_base[2]->GetNumPoints();
171 
172  Array<TwoD, const NekDouble> df =
173  m_metricinfo->GetDerivFactors(GetPointsKeys());
174  Array<OneD,NekDouble> Diff0 = Array<OneD,NekDouble>(3*TotPts);
175  Array<OneD,NekDouble> Diff1 = Diff0 + TotPts;
176  Array<OneD,NekDouble> Diff2 = Diff1 + TotPts;
177 
178  StdTetExp::v_PhysDeriv(inarray, Diff0, Diff1, Diff2);
179 
180  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
181  {
182  if(out_d0.num_elements())
183  {
184  Vmath::Vmul (TotPts,&df[0][0],1,&Diff0[0],1, &out_d0[0], 1);
185  Vmath::Vvtvp (TotPts,&df[1][0],1,&Diff1[0],1, &out_d0[0], 1,&out_d0[0],1);
186  Vmath::Vvtvp (TotPts,&df[2][0],1,&Diff2[0],1, &out_d0[0], 1,&out_d0[0],1);
187  }
188 
189  if(out_d1.num_elements())
190  {
191  Vmath::Vmul (TotPts,&df[3][0],1,&Diff0[0],1, &out_d1[0], 1);
192  Vmath::Vvtvp (TotPts,&df[4][0],1,&Diff1[0],1, &out_d1[0], 1,&out_d1[0],1);
193  Vmath::Vvtvp (TotPts,&df[5][0],1,&Diff2[0],1, &out_d1[0], 1,&out_d1[0],1);
194  }
195 
196  if(out_d2.num_elements())
197  {
198  Vmath::Vmul (TotPts,&df[6][0],1,&Diff0[0],1, &out_d2[0], 1);
199  Vmath::Vvtvp (TotPts,&df[7][0],1,&Diff1[0],1, &out_d2[0], 1, &out_d2[0],1);
200  Vmath::Vvtvp (TotPts,&df[8][0],1,&Diff2[0],1, &out_d2[0], 1, &out_d2[0],1);
201  }
202  }
203  else // regular geometry
204  {
205  if(out_d0.num_elements())
206  {
207  Vmath::Smul (TotPts,df[0][0],&Diff0[0],1, &out_d0[0], 1);
208  Blas::Daxpy (TotPts,df[1][0],&Diff1[0],1, &out_d0[0], 1);
209  Blas::Daxpy (TotPts,df[2][0],&Diff2[0],1, &out_d0[0], 1);
210  }
211 
212  if(out_d1.num_elements())
213  {
214  Vmath::Smul (TotPts,df[3][0],&Diff0[0],1, &out_d1[0], 1);
215  Blas::Daxpy (TotPts,df[4][0],&Diff1[0],1, &out_d1[0], 1);
216  Blas::Daxpy (TotPts,df[5][0],&Diff2[0],1, &out_d1[0], 1);
217  }
218 
219  if(out_d2.num_elements())
220  {
221  Vmath::Smul (TotPts,df[6][0],&Diff0[0],1, &out_d2[0], 1);
222  Blas::Daxpy (TotPts,df[7][0],&Diff1[0],1, &out_d2[0], 1);
223  Blas::Daxpy (TotPts,df[8][0],&Diff2[0],1, &out_d2[0], 1);
224  }
225  }
226  }
227 
228 
229  //-----------------------------
230  // Transforms
231  //-----------------------------
232  /**
233  * \brief Forward transform from physical quadrature space stored in
234  * \a inarray and evaluate the expansion coefficients and store
235  * in \a (this)->_coeffs
236  *
237  * @param inarray Array of physical quadrature points to be
238  * transformed.
239  * @param outarray Array of coefficients to update.
240  */
241  void TetExp::v_FwdTrans(
242  const Array<OneD, const NekDouble> & inarray,
243  Array<OneD,NekDouble> &outarray)
244  {
245  if((m_base[0]->Collocation())&&(m_base[1]->Collocation())&&(m_base[2]->Collocation()))
246  {
247  Vmath::Vcopy(GetNcoeffs(),&inarray[0],1,&outarray[0],1);
248  }
249  else
250  {
251  IProductWRTBase(inarray,outarray);
252 
253  // get Mass matrix inverse
254  MatrixKey masskey(StdRegions::eInvMass,
255  DetShapeType(),*this);
256  DNekScalMatSharedPtr matsys = m_matrixManager[masskey];
257 
258  // copy inarray in case inarray == outarray
259  DNekVec in (m_ncoeffs,outarray);
260  DNekVec out(m_ncoeffs,outarray,eWrapper);
261 
262  out = (*matsys)*in;
263  }
264  }
265 
266  //-----------------------------
267  // Inner product functions
268  //-----------------------------
269  /**
270  * \brief Calculate the inner product of inarray with respect to the
271  * basis B=m_base0*m_base1*m_base2 and put into outarray:
272  *
273  * \f$ \begin{array}{rcl} I_{pqr} = (\phi_{pqr}, u)_{\delta}
274  * & = & \sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \sum_{k=0}^{nq_2}
275  * \psi_{p}^{a} (\eta_{1i}) \psi_{pq}^{b} (\eta_{2j}) \psi_{pqr}^{c}
276  * (\eta_{3k}) w_i w_j w_k u(\eta_{1,i} \eta_{2,j} \eta_{3,k})
277  * J_{i,j,k}\\ & = & \sum_{i=0}^{nq_0} \psi_p^a(\eta_{1,i})
278  * \sum_{j=0}^{nq_1} \psi_{pq}^b(\eta_{2,j}) \sum_{k=0}^{nq_2}
279  * \psi_{pqr}^c u(\eta_{1i},\eta_{2j},\eta_{3k}) J_{i,j,k}
280  * \end{array} \f$ \n
281  * where
282  * \f$ \phi_{pqr} (\xi_1 , \xi_2 , \xi_3)
283  * = \psi_p^a (\eta_1) \psi_{pq}^b (\eta_2) \psi_{pqr}^c (\eta_3) \f$
284  * which can be implemented as \n
285  * \f$f_{pqr} (\xi_{3k})
286  * = \sum_{k=0}^{nq_3} \psi_{pqr}^c u(\eta_{1i},\eta_{2j},\eta_{3k})
287  * J_{i,j,k} = {\bf B_3 U} \f$ \n
288  * \f$ g_{pq} (\xi_{3k})
289  * = \sum_{j=0}^{nq_1} \psi_{pq}^b (\xi_{2j}) f_{pqr} (\xi_{3k})
290  * = {\bf B_2 F} \f$ \n
291  * \f$ (\phi_{pqr}, u)_{\delta}
292  * = \sum_{k=0}^{nq_0} \psi_{p}^a (\xi_{3k}) g_{pq} (\xi_{3k})
293  * = {\bf B_1 G} \f$
294  */
295  void TetExp::v_IProductWRTBase(
296  const Array<OneD, const NekDouble> &inarray,
297  Array<OneD, NekDouble> &outarray)
298  {
299  v_IProductWRTBase_SumFac(inarray, outarray);
300  }
301 
302  void TetExp::v_IProductWRTBase_SumFac(
303  const Array<OneD, const NekDouble> &inarray,
304  Array<OneD, NekDouble> &outarray,
305  bool multiplybyweights)
306  {
307  const int nquad0 = m_base[0]->GetNumPoints();
308  const int nquad1 = m_base[1]->GetNumPoints();
309  const int nquad2 = m_base[2]->GetNumPoints();
310  const int order0 = m_base[0]->GetNumModes();
311  const int order1 = m_base[1]->GetNumModes();
312  Array<OneD, NekDouble> wsp(nquad1*nquad2*order0 +
313  nquad2*order0*(order1+1)/2);
314 
315  if(multiplybyweights)
316  {
317  Array<OneD, NekDouble> tmp(nquad0*nquad1*nquad2);
318 
319  MultiplyByQuadratureMetric(inarray, tmp);
320  IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
321  m_base[1]->GetBdata(),
322  m_base[2]->GetBdata(),
323  tmp,outarray,wsp,
324  true,true,true);
325  }
326  else
327  {
328  IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
329  m_base[1]->GetBdata(),
330  m_base[2]->GetBdata(),
331  inarray,outarray,wsp,
332  true,true,true);
333  }
334  }
335 
336  /**
337  * @brief Calculates the inner product \f$ I_{pqr} = (u,
338  * \partial_{x_i} \phi_{pqr}) \f$.
339  *
340  * The derivative of the basis functions is performed using the chain
341  * rule in order to incorporate the geometric factors. Assuming that
342  * the basis functions are a tensor product
343  * \f$\phi_{pqr}(\eta_1,\eta_2,\eta_3) =
344  * \phi_1(\eta_1)\phi_2(\eta_2)\phi_3(\eta_3)\f$, this yields the
345  * result
346  *
347  * \f[
348  * I_{pqr} = \sum_{j=1}^3 \left(u, \frac{\partial u}{\partial \eta_j}
349  * \frac{\partial \eta_j}{\partial x_i}\right)
350  * \f]
351  *
352  * In the prismatic element, we must also incorporate a second set of
353  * geometric factors which incorporate the collapsed co-ordinate
354  * system, so that
355  *
356  * \f[ \frac{\partial\eta_j}{\partial x_i} = \sum_{k=1}^3
357  * \frac{\partial\eta_j}{\partial\xi_k}\frac{\partial\xi_k}{\partial
358  * x_i} \f]
359  *
360  * These derivatives can be found on p152 of Sherwin & Karniadakis.
361  *
362  * @param dir Direction in which to take the derivative.
363  * @param inarray The function \f$ u \f$.
364  * @param outarray Value of the inner product.
365  */
366  void TetExp::v_IProductWRTDerivBase(
367  const int dir,
368  const Array<OneD, const NekDouble> &inarray,
369  Array<OneD, NekDouble> &outarray)
370  {
371  const int nquad0 = m_base[0]->GetNumPoints();
372  const int nquad1 = m_base[1]->GetNumPoints();
373  const int nquad2 = m_base[2]->GetNumPoints();
374  const int order0 = m_base[0]->GetNumModes ();
375  const int order1 = m_base[1]->GetNumModes ();
376  const int nqtot = nquad0*nquad1*nquad2;
377  int i, j;
378 
379  const Array<OneD, const NekDouble> &z0 = m_base[0]->GetZ();
380  const Array<OneD, const NekDouble> &z1 = m_base[1]->GetZ();
381  const Array<OneD, const NekDouble> &z2 = m_base[2]->GetZ();
382 
383  Array<OneD, NekDouble> h0 (nqtot);
384  Array<OneD, NekDouble> h1 (nqtot);
385  Array<OneD, NekDouble> h2 (nqtot);
386  Array<OneD, NekDouble> h3 (nqtot);
387  Array<OneD, NekDouble> tmp1 (nqtot);
388  Array<OneD, NekDouble> tmp2 (nqtot);
389  Array<OneD, NekDouble> tmp3 (nqtot);
390  Array<OneD, NekDouble> tmp4 (nqtot);
391  Array<OneD, NekDouble> tmp5 (nqtot);
392  Array<OneD, NekDouble> tmp6 (m_ncoeffs);
393  Array<OneD, NekDouble> wsp (nquad1*nquad2*order0 +
394  nquad2*order0*(order1+1)/2);
395 
396  const Array<TwoD, const NekDouble>& df =
397  m_metricinfo->GetDerivFactors(GetPointsKeys());
398 
399  MultiplyByQuadratureMetric(inarray,tmp1);
400 
401  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
402  {
403  Vmath::Vmul(nqtot,&df[3*dir][0], 1,tmp1.get(),1,tmp2.get(),1);
404  Vmath::Vmul(nqtot,&df[3*dir+1][0],1,tmp1.get(),1,tmp3.get(),1);
405  Vmath::Vmul(nqtot,&df[3*dir+2][0],1,tmp1.get(),1,tmp4.get(),1);
406  }
407  else
408  {
409  Vmath::Smul(nqtot, df[3*dir ][0],tmp1.get(),1,tmp2.get(), 1);
410  Vmath::Smul(nqtot, df[3*dir+1][0],tmp1.get(),1,tmp3.get(), 1);
411  Vmath::Smul(nqtot, df[3*dir+2][0],tmp1.get(),1,tmp4.get(), 1);
412  }
413 
414  const int nq01 = nquad0*nquad1;
415  const int nq12 = nquad1*nquad2;
416 
417  for(j = 0; j < nquad2; ++j)
418  {
419  for(i = 0; i < nquad1; ++i)
420  {
421  Vmath::Fill(nquad0, 4.0/(1.0-z1[i])/(1.0-z2[j]),
422  &h0[0]+i*nquad0 + j*nq01,1);
423  Vmath::Fill(nquad0, 2.0/(1.0-z1[i])/(1.0-z2[j]),
424  &h1[0]+i*nquad0 + j*nq01,1);
425  Vmath::Fill(nquad0, 2.0/(1.0-z2[j]),
426  &h2[0]+i*nquad0 + j*nq01,1);
427  Vmath::Fill(nquad0, (1.0+z1[i])/(1.0-z2[j]),
428  &h3[0]+i*nquad0 + j*nq01,1);
429  }
430  }
431 
432  for(i = 0; i < nquad0; i++)
433  {
434  Blas::Dscal(nq12, 1+z0[i], &h1[0]+i, nquad0);
435  }
436 
437  // Assemble terms for first IP.
438  Vmath::Vvtvvtp(nqtot, &tmp2[0], 1, &h0[0], 1,
439  &tmp3[0], 1, &h1[0], 1,
440  &tmp5[0], 1);
441  Vmath::Vvtvp (nqtot, &tmp4[0], 1, &h1[0], 1,
442  &tmp5[0], 1, &tmp5[0], 1);
443 
444  IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),
445  m_base[1]->GetBdata (),
446  m_base[2]->GetBdata (),
447  tmp5,outarray,wsp,
448  true,true,true);
449 
450  // Assemble terms for second IP.
451  Vmath::Vvtvvtp(nqtot, &tmp3[0], 1, &h2[0], 1,
452  &tmp4[0], 1, &h3[0], 1,
453  &tmp5[0], 1);
454 
455  IProductWRTBase_SumFacKernel(m_base[0]->GetBdata (),
456  m_base[1]->GetDbdata(),
457  m_base[2]->GetBdata (),
458  tmp5,tmp6,wsp,
459  true,true,true);
460  Vmath::Vadd(m_ncoeffs, tmp6, 1, outarray, 1, outarray, 1);
461 
462  // Do third IP.
463  IProductWRTBase_SumFacKernel(m_base[0]->GetBdata (),
464  m_base[1]->GetBdata (),
465  m_base[2]->GetDbdata(),
466  tmp4,tmp6,wsp,
467  true,true,true);
468 
469  // Sum contributions.
470  Vmath::Vadd(m_ncoeffs, tmp6, 1, outarray, 1, outarray, 1);
471  }
472 
473 
474  //-----------------------------
475  // Evaluation functions
476  //-----------------------------
477 
478  /**
479  * Given the local cartesian coordinate \a Lcoord evaluate the
480  * value of physvals at this point by calling through to the
481  * StdExpansion method
482  */
483  NekDouble TetExp::v_StdPhysEvaluate(
484  const Array<OneD, const NekDouble> &Lcoord,
485  const Array<OneD, const NekDouble> &physvals)
486  {
487  // Evaluate point in local (eta) coordinates.
488  return StdTetExp::v_PhysEvaluate(Lcoord,physvals);
489  }
490 
491  /**
492  * @param coord Physical space coordinate
493  * @returns Evaluation of expansion at given coordinate.
494  */
495  NekDouble TetExp::v_PhysEvaluate(
496  const Array<OneD, const NekDouble> &coord,
497  const Array<OneD, const NekDouble> & physvals)
498  {
499  ASSERTL0(m_geom,"m_geom not defined");
500 
501  Array<OneD,NekDouble> Lcoord = Array<OneD,NekDouble>(3);
502 
503  // Get the local (eta) coordinates of the point
504  m_geom->GetLocCoords(coord,Lcoord);
505 
506  // Evaluate point in local (eta) coordinates.
507  return StdTetExp::v_PhysEvaluate(Lcoord,physvals);
508  }
509 
510  /**
511  * \brief Get the coordinates "coords" at the local coordinates "Lcoords"
512  */
513  void TetExp::v_GetCoord(
514  const Array<OneD, const NekDouble> &Lcoords,
515  Array<OneD,NekDouble> &coords)
516  {
517  int i;
518 
519  ASSERTL1(Lcoords[0] <= -1.0 && Lcoords[0] >= 1.0 &&
520  Lcoords[1] <= -1.0 && Lcoords[1] >= 1.0 &&
521  Lcoords[2] <= -1.0 && Lcoords[2] >= 1.0,
522  "Local coordinates are not in region [-1,1]");
523 
524  // m_geom->FillGeom(); // TODO: implement FillGeom()
525 
526  for(i = 0; i < m_geom->GetCoordim(); ++i)
527  {
528  coords[i] = m_geom->GetCoord(i,Lcoords);
529  }
530  }
531 
532  void TetExp::v_GetCoords(
533  Array<OneD, NekDouble> &coords_0,
534  Array<OneD, NekDouble> &coords_1,
535  Array<OneD, NekDouble> &coords_2)
536  {
537  Expansion::v_GetCoords(coords_0, coords_1, coords_2);
538  }
539 
540 
541  //-----------------------------
542  // Helper functions
543  //-----------------------------
544 
545  /**
546  * \brief Return Shape of region, using ShapeType enum list.
547  */
548  LibUtilities::ShapeType TetExp::v_DetShapeType() const
549  {
550  return LibUtilities::eTetrahedron;
551  }
552 
553  StdRegions::StdExpansionSharedPtr TetExp::v_GetStdExp(void) const
554  {
555  return MemoryManager<StdRegions::StdTetExp>
556  ::AllocateSharedPtr(m_base[0]->GetBasisKey(),
557  m_base[1]->GetBasisKey(),
558  m_base[2]->GetBasisKey());
559  }
560 
561  int TetExp::v_GetCoordim()
562  {
563  return m_geom->GetCoordim();
564  }
565 
566  void TetExp::v_ExtractDataToCoeffs(
567  const NekDouble *data,
568  const std::vector<unsigned int > &nummodes,
569  const int mode_offset,
570  NekDouble * coeffs)
571  {
572  int data_order0 = nummodes[mode_offset];
573  int fillorder0 = min(m_base[0]->GetNumModes(),data_order0);
574  int data_order1 = nummodes[mode_offset+1];
575  int order1 = m_base[1]->GetNumModes();
576  int fillorder1 = min(order1,data_order1);
577  int data_order2 = nummodes[mode_offset+2];
578  int order2 = m_base[2]->GetNumModes();
579  int fillorder2 = min(order2,data_order2);
580 
581  switch(m_base[0]->GetBasisType())
582  {
583  case LibUtilities::eModified_A:
584  {
585  int i,j;
586  int cnt = 0;
587  int cnt1 = 0;
588 
589  ASSERTL1(m_base[1]->GetBasisType() ==
590  LibUtilities::eModified_B,
591  "Extraction routine not set up for this basis");
592  ASSERTL1(m_base[2]->GetBasisType() ==
593  LibUtilities::eModified_C,
594  "Extraction routine not set up for this basis");
595 
596  Vmath::Zero(m_ncoeffs,coeffs,1);
597  for(j = 0; j < fillorder0; ++j)
598  {
599  for(i = 0; i < fillorder1-j; ++i)
600  {
601  Vmath::Vcopy(fillorder2-j-i, &data[cnt], 1,
602  &coeffs[cnt1], 1);
603  cnt += data_order2-j-i;
604  cnt1 += order2-j-i;
605  }
606 
607  // count out data for j iteration
608  for(i = fillorder1-j; i < data_order1-j; ++i)
609  {
610  cnt += data_order2-j-i;
611  }
612 
613  for(i = fillorder1-j; i < order1-j; ++i)
614  {
615  cnt1 += order2-j-i;
616  }
617 
618  }
619  }
620  break;
621  default:
622  ASSERTL0(false, "basis is either not set up or not "
623  "hierarchicial");
624  }
625  }
626 
627  /**
628  * \brief Returns the physical values at the quadrature points of a face
629  */
630  void TetExp::v_GetFacePhysMap(const int face,
631  Array<OneD, int> &outarray)
632  {
633  int nquad0 = m_base[0]->GetNumPoints();
634  int nquad1 = m_base[1]->GetNumPoints();
635  int nquad2 = m_base[2]->GetNumPoints();
636 
637  int nq0 = 0;
638  int nq1 = 0;
639 
640  // get forward aligned faces.
641  switch(face)
642  {
643  case 0:
644  {
645  nq0 = nquad0;
646  nq1 = nquad1;
647  if(outarray.num_elements()!=nq0*nq1)
648  {
649  outarray = Array<OneD, int>(nq0*nq1);
650  }
651 
652  for (int i = 0; i < nquad0*nquad1; ++i)
653  {
654  outarray[i] = i;
655  }
656 
657  break;
658  }
659  case 1:
660  {
661  nq0 = nquad0;
662  nq1 = nquad2;
663  if(outarray.num_elements()!=nq0*nq1)
664  {
665  outarray = Array<OneD, int>(nq0*nq1);
666  }
667 
668  //Direction A and B positive
669  for (int k=0; k<nquad2; k++)
670  {
671  for(int i = 0; i < nquad0; ++i)
672  {
673  outarray[k*nquad0+i] = (nquad0*nquad1*k)+i;
674  }
675  }
676  break;
677  }
678  case 2:
679  {
680  nq0 = nquad1;
681  nq1 = nquad2;
682  if(outarray.num_elements()!=nq0*nq1)
683  {
684  outarray = Array<OneD, int>(nq0*nq1);
685  }
686 
687  //Directions A and B positive
688  for(int j = 0; j < nquad1*nquad2; ++j)
689  {
690  outarray[j] = nquad0-1 + j*nquad0;
691  }
692  break;
693  }
694  case 3:
695  {
696  nq0 = nquad1;
697  nq1 = nquad2;
698  if(outarray.num_elements() != nq0*nq1)
699  {
700  outarray = Array<OneD, int>(nq0*nq1);
701  }
702 
703  //Directions A and B positive
704  for(int j = 0; j < nquad1*nquad2; ++j)
705  {
706  outarray[j] = j*nquad0;
707  }
708  }
709  break;
710  default:
711  ASSERTL0(false,"face value (> 3) is out of range");
712  break;
713  }
714  }
715 
716 
717  /**
718  * \brief Compute the normal of a triangular face
719  */
720  void TetExp::v_ComputeFaceNormal(const int face)
721  {
722  int i;
723  const SpatialDomains::GeomFactorsSharedPtr &geomFactors =
724  GetGeom()->GetMetricInfo();
725  LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
726  SpatialDomains::GeomType type = geomFactors->GetGtype();
727  const Array<TwoD, const NekDouble> &df = geomFactors->GetDerivFactors(ptsKeys);
728  const Array<OneD, const NekDouble> &jac = geomFactors->GetJac(ptsKeys);
729 
730  LibUtilities::BasisKey tobasis0 = DetFaceBasisKey(face,0);
731  LibUtilities::BasisKey tobasis1 = DetFaceBasisKey(face,1);
732 
733  // number of face quadrature points
734  int nq_face = tobasis0.GetNumPoints()*tobasis1.GetNumPoints();
735 
736  int vCoordDim = GetCoordim();
737 
738  m_faceNormals[face] = Array<OneD, Array<OneD, NekDouble> >(vCoordDim);
739  Array<OneD, Array<OneD, NekDouble> > &normal = m_faceNormals[face];
740  for (i = 0; i < vCoordDim; ++i)
741  {
742  normal[i] = Array<OneD, NekDouble>(nq_face);
743  }
744 
745  // Regular geometry case
746  if (type == SpatialDomains::eRegular ||
747  type == SpatialDomains::eMovingRegular)
748  {
749  NekDouble fac;
750 
751  // Set up normals
752  switch (face)
753  {
754  case 0:
755  {
756  for (i = 0; i < vCoordDim; ++i)
757  {
758  normal[i][0] = -df[3*i+2][0];
759  }
760 
761  break;
762  }
763  case 1:
764  {
765  for (i = 0; i < vCoordDim; ++i)
766  {
767  normal[i][0] = -df[3*i+1][0];
768  }
769 
770  break;
771  }
772  case 2:
773  {
774  for (i = 0; i < vCoordDim; ++i)
775  {
776  normal[i][0] = df[3*i][0]+df[3*i+1][0]+
777  df[3*i+2][0];
778  }
779 
780  break;
781  }
782  case 3:
783  {
784  for(i = 0; i < vCoordDim; ++i)
785  {
786  normal[i][0] = -df[3*i][0];
787  }
788  break;
789  }
790  default:
791  ASSERTL0(false,"face is out of range (edge < 3)");
792  }
793 
794  // normalise
795  fac = 0.0;
796  for (i = 0; i < vCoordDim; ++i)
797  {
798  fac += normal[i][0]*normal[i][0];
799  }
800  fac = 1.0/sqrt(fac);
801 
802  for (i = 0; i < vCoordDim; ++i)
803  {
804  Vmath::Fill(nq_face,fac*normal[i][0],normal[i],1);
805  }
806  }
807  else
808  {
809  // Set up deformed normals
810  int j, k;
811 
812  int nq0 = ptsKeys[0].GetNumPoints();
813  int nq1 = ptsKeys[1].GetNumPoints();
814  int nq2 = ptsKeys[2].GetNumPoints();
815  int nqtot;
816  int nq01 =nq0*nq1;
817 
818  // number of elemental quad points
819  if (face == 0)
820  {
821  nqtot = nq01;
822  }
823  else if (face == 1)
824  {
825  nqtot = nq0*nq2;
826  }
827  else
828  {
829  nqtot = nq1*nq2;
830  }
831 
832  LibUtilities::PointsKey points0;
833  LibUtilities::PointsKey points1;
834 
835  Array<OneD, NekDouble> faceJac(nqtot);
836  Array<OneD,NekDouble> normals(vCoordDim*nqtot, 0.0);
837 
838  // Extract Jacobian along face and recover local derivates
839  // (dx/dr) for polynomial interpolation by multiplying m_gmat by
840  // jacobian
841  switch (face)
842  {
843  case 0:
844  {
845  for(j = 0; j < nq01; ++j)
846  {
847  normals[j] = -df[2][j]*jac[j];
848  normals[nqtot+j] = -df[5][j]*jac[j];
849  normals[2*nqtot+j] = -df[8][j]*jac[j];
850  faceJac[j] = jac[j];
851  }
852 
853  points0 = ptsKeys[0];
854  points1 = ptsKeys[1];
855  break;
856  }
857 
858  case 1:
859  {
860  for (j = 0; j < nq0; ++j)
861  {
862  for(k = 0; k < nq2; ++k)
863  {
864  int tmp = j+nq01*k;
865  normals[j+k*nq0] =
866  -df[1][tmp]*jac[tmp];
867  normals[nqtot+j+k*nq0] =
868  -df[4][tmp]*jac[tmp];
869  normals[2*nqtot+j+k*nq0] =
870  -df[7][tmp]*jac[tmp];
871  faceJac[j+k*nq0] = jac[tmp];
872  }
873  }
874 
875  points0 = ptsKeys[0];
876  points1 = ptsKeys[2];
877  break;
878  }
879 
880  case 2:
881  {
882  for (j = 0; j < nq1; ++j)
883  {
884  for(k = 0; k < nq2; ++k)
885  {
886  int tmp = nq0-1+nq0*j+nq01*k;
887  normals[j+k*nq1] =
888  (df[0][tmp]+df[1][tmp]+df[2][tmp])*
889  jac[tmp];
890  normals[nqtot+j+k*nq1] =
891  (df[3][tmp]+df[4][tmp]+df[5][tmp])*
892  jac[tmp];
893  normals[2*nqtot+j+k*nq1] =
894  (df[6][tmp]+df[7][tmp]+df[8][tmp])*
895  jac[tmp];
896  faceJac[j+k*nq1] = jac[tmp];
897  }
898  }
899 
900  points0 = ptsKeys[1];
901  points1 = ptsKeys[2];
902  break;
903  }
904 
905  case 3:
906  {
907  for (j = 0; j < nq1; ++j)
908  {
909  for(k = 0; k < nq2; ++k)
910  {
911  int tmp = j*nq0+nq01*k;
912  normals[j+k*nq1] =
913  -df[0][tmp]*jac[tmp];
914  normals[nqtot+j+k*nq1] =
915  -df[3][tmp]*jac[tmp];
916  normals[2*nqtot+j+k*nq1] =
917  -df[6][tmp]*jac[tmp];
918  faceJac[j+k*nq1] = jac[tmp];
919  }
920  }
921 
922  points0 = ptsKeys[1];
923  points1 = ptsKeys[2];
924  break;
925  }
926 
927  default:
928  ASSERTL0(false,"face is out of range (face < 3)");
929  }
930 
931  Array<OneD,NekDouble> work (nq_face, 0.0);
932  // Interpolate Jacobian and invert
933  LibUtilities::Interp2D(points0, points1, faceJac,
934  tobasis0.GetPointsKey(),
935  tobasis1.GetPointsKey(),
936  work);
937  Vmath::Sdiv(nq_face, 1.0, &work[0], 1, &work[0], 1);
938 
939  // Interpolate normal and multiply by inverse Jacobian.
940  for(i = 0; i < vCoordDim; ++i)
941  {
942  LibUtilities::Interp2D(points0, points1,
943  &normals[i*nqtot],
944  tobasis0.GetPointsKey(),
945  tobasis1.GetPointsKey(),
946  &normal[i][0]);
947  Vmath::Vmul(nq_face,work,1,normal[i],1,normal[i],1);
948  }
949 
950  // Normalise to obtain unit normals.
951  Vmath::Zero(nq_face,work,1);
952  for(i = 0; i < GetCoordim(); ++i)
953  {
954  Vmath::Vvtvp(nq_face,normal[i],1,normal[i],1,work,1,work,1);
955  }
956 
957  Vmath::Vsqrt(nq_face,work,1,work,1);
958  Vmath::Sdiv (nq_face,1.0,work,1,work,1);
959 
960  for(i = 0; i < GetCoordim(); ++i)
961  {
962  Vmath::Vmul(nq_face,normal[i],1,work,1,normal[i],1);
963  }
964  }
965  }
966 
967  //-----------------------------
968  // Operator creation functions
969  //-----------------------------
970  void TetExp::v_HelmholtzMatrixOp(
971  const Array<OneD, const NekDouble> &inarray,
972  Array<OneD,NekDouble> &outarray,
973  const StdRegions::StdMatrixKey &mkey)
974  {
975  TetExp::v_HelmholtzMatrixOp_MatFree(inarray,outarray,mkey);
976  }
977 
978 
979  void TetExp::v_LaplacianMatrixOp(
980  const Array<OneD, const NekDouble> &inarray,
981  Array<OneD,NekDouble> &outarray,
982  const StdRegions::StdMatrixKey &mkey)
983  {
984  TetExp::v_LaplacianMatrixOp_MatFree(inarray,outarray,mkey);
985  }
986 
987  void TetExp::v_LaplacianMatrixOp(
988  const int k1,
989  const int k2,
990  const Array<OneD, const NekDouble> &inarray,
991  Array<OneD,NekDouble> &outarray,
992  const StdRegions::StdMatrixKey &mkey)
993  {
994  StdExpansion::LaplacianMatrixOp_MatFree(k1,k2,inarray,outarray,
995  mkey);
996  }
997 
998  void TetExp::v_SVVLaplacianFilter(
999  Array<OneD, NekDouble> &array,
1000  const StdRegions::StdMatrixKey &mkey)
1001  {
1002  int nq = GetTotPoints();
1003 
1004  // Calculate sqrt of the Jacobian
1005  Array<OneD, const NekDouble> jac =
1006  m_metricinfo->GetJac(GetPointsKeys());
1007  Array<OneD, NekDouble> sqrt_jac(nq);
1008  if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
1009  {
1010  Vmath::Vsqrt(nq,jac,1,sqrt_jac,1);
1011  }
1012  else
1013  {
1014  Vmath::Fill(nq,sqrt(jac[0]),sqrt_jac,1);
1015  }
1016 
1017  // Multiply array by sqrt(Jac)
1018  Vmath::Vmul(nq,sqrt_jac,1,array,1,array,1);
1019 
1020  // Apply std region filter
1021  StdTetExp::v_SVVLaplacianFilter( array, mkey);
1022 
1023  // Divide by sqrt(Jac)
1024  Vmath::Vdiv(nq,array,1,sqrt_jac,1,array,1);
1025  }
1026 
1027 
1028  //-----------------------------
1029  // Matrix creation functions
1030  //-----------------------------
1031  DNekMatSharedPtr TetExp::v_GenMatrix(
1032  const StdRegions::StdMatrixKey &mkey)
1033  {
1034  DNekMatSharedPtr returnval;
1035 
1036  switch(mkey.GetMatrixType())
1037  {
1038  case StdRegions::eHybridDGHelmholtz:
1039  case StdRegions::eHybridDGLamToU:
1040  case StdRegions::eHybridDGLamToQ0:
1041  case StdRegions::eHybridDGLamToQ1:
1042  case StdRegions::eHybridDGLamToQ2:
1043  case StdRegions::eHybridDGHelmBndLam:
1044  case StdRegions::eInvLaplacianWithUnityMean:
1045  returnval = Expansion3D::v_GenMatrix(mkey);
1046  break;
1047  default:
1048  returnval = StdTetExp::v_GenMatrix(mkey);
1049  }
1050 
1051  return returnval;
1052  }
1053 
1054 
1055  DNekScalMatSharedPtr TetExp::CreateMatrix(const MatrixKey &mkey)
1056  {
1057  DNekScalMatSharedPtr returnval;
1058  LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
1059 
1060  ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,"Geometric information is not set up");
1061 
1062  switch(mkey.GetMatrixType())
1063  {
1064  case StdRegions::eMass:
1065  {
1066  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
1067  mkey.GetNVarCoeff())
1068  {
1069  NekDouble one = 1.0;
1070  DNekMatSharedPtr mat = GenMatrix(mkey);
1071  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
1072  }
1073  else
1074  {
1075  NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
1076  DNekMatSharedPtr mat = GetStdMatrix(mkey);
1077  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,mat);
1078  }
1079  }
1080  break;
1081  case StdRegions::eInvMass:
1082  {
1083  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
1084  {
1085  NekDouble one = 1.0;
1086  StdRegions::StdMatrixKey masskey(StdRegions::eMass,DetShapeType(),
1087  *this);
1088  DNekMatSharedPtr mat = GenMatrix(masskey);
1089  mat->Invert();
1090  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
1091  }
1092  else
1093  {
1094  NekDouble fac = 1.0/(m_metricinfo->GetJac(ptsKeys))[0];
1095  DNekMatSharedPtr mat = GetStdMatrix(mkey);
1096  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(fac,mat);
1097  }
1098  }
1099  break;
1100  case StdRegions::eWeakDeriv0:
1101  case StdRegions::eWeakDeriv1:
1102  case StdRegions::eWeakDeriv2:
1103  {
1104  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
1105  mkey.GetNVarCoeff())
1106  {
1107  NekDouble one = 1.0;
1108  DNekMatSharedPtr mat = GenMatrix(mkey);
1109 
1110  returnval = MemoryManager<DNekScalMat>
1111  ::AllocateSharedPtr(one,mat);
1112  }
1113  else
1114  {
1115  NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
1116  Array<TwoD, const NekDouble> df
1117  = m_metricinfo->GetDerivFactors(ptsKeys);
1118  int dir = 0;
1119 
1120  switch(mkey.GetMatrixType())
1121  {
1122  case StdRegions::eWeakDeriv0:
1123  dir = 0;
1124  break;
1125  case StdRegions::eWeakDeriv1:
1126  dir = 1;
1127  break;
1128  case StdRegions::eWeakDeriv2:
1129  dir = 2;
1130  break;
1131  default:
1132  break;
1133  }
1134 
1135  MatrixKey deriv0key(StdRegions::eWeakDeriv0,
1136  mkey.GetShapeType(), *this);
1137  MatrixKey deriv1key(StdRegions::eWeakDeriv1,
1138  mkey.GetShapeType(), *this);
1139  MatrixKey deriv2key(StdRegions::eWeakDeriv2,
1140  mkey.GetShapeType(), *this);
1141 
1142  DNekMat &deriv0 = *GetStdMatrix(deriv0key);
1143  DNekMat &deriv1 = *GetStdMatrix(deriv1key);
1144  DNekMat &deriv2 = *GetStdMatrix(deriv2key);
1145 
1146  int rows = deriv0.GetRows();
1147  int cols = deriv1.GetColumns();
1148 
1149  DNekMatSharedPtr WeakDeriv = MemoryManager<DNekMat>
1150  ::AllocateSharedPtr(rows,cols);
1151  (*WeakDeriv) = df[3*dir][0]*deriv0
1152  + df[3*dir+1][0]*deriv1
1153  + df[3*dir+2][0]*deriv2;
1154 
1155  returnval = MemoryManager<DNekScalMat>
1156  ::AllocateSharedPtr(jac,WeakDeriv);
1157  }
1158  }
1159  break;
1160  case StdRegions::eLaplacian:
1161  {
1162  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
1163  (mkey.GetNVarCoeff() > 0)||(mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio)))
1164  {
1165  NekDouble one = 1.0;
1166  DNekMatSharedPtr mat = GenMatrix(mkey);
1167 
1168  returnval = MemoryManager<DNekScalMat>
1169  ::AllocateSharedPtr(one,mat);
1170  }
1171  else
1172  {
1173  MatrixKey lap00key(StdRegions::eLaplacian00,
1174  mkey.GetShapeType(), *this);
1175  MatrixKey lap01key(StdRegions::eLaplacian01,
1176  mkey.GetShapeType(), *this);
1177  MatrixKey lap02key(StdRegions::eLaplacian02,
1178  mkey.GetShapeType(), *this);
1179  MatrixKey lap11key(StdRegions::eLaplacian11,
1180  mkey.GetShapeType(), *this);
1181  MatrixKey lap12key(StdRegions::eLaplacian12,
1182  mkey.GetShapeType(), *this);
1183  MatrixKey lap22key(StdRegions::eLaplacian22,
1184  mkey.GetShapeType(), *this);
1185 
1186  DNekMat &lap00 = *GetStdMatrix(lap00key);
1187  DNekMat &lap01 = *GetStdMatrix(lap01key);
1188  DNekMat &lap02 = *GetStdMatrix(lap02key);
1189  DNekMat &lap11 = *GetStdMatrix(lap11key);
1190  DNekMat &lap12 = *GetStdMatrix(lap12key);
1191  DNekMat &lap22 = *GetStdMatrix(lap22key);
1192 
1193  NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
1194  Array<TwoD, const NekDouble> gmat
1195  = m_metricinfo->GetGmat(ptsKeys);
1196 
1197  int rows = lap00.GetRows();
1198  int cols = lap00.GetColumns();
1199 
1200  DNekMatSharedPtr lap = MemoryManager<DNekMat>
1201  ::AllocateSharedPtr(rows,cols);
1202 
1203  (*lap) = gmat[0][0]*lap00
1204  + gmat[4][0]*lap11
1205  + gmat[8][0]*lap22
1206  + gmat[3][0]*(lap01 + Transpose(lap01))
1207  + gmat[6][0]*(lap02 + Transpose(lap02))
1208  + gmat[7][0]*(lap12 + Transpose(lap12));
1209 
1210  returnval = MemoryManager<DNekScalMat>
1211  ::AllocateSharedPtr(jac,lap);
1212  }
1213  }
1214  break;
1215  case StdRegions::eHelmholtz:
1216  {
1217  NekDouble factor = mkey.GetConstFactor(StdRegions::eFactorLambda);
1218  MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
1219  DNekScalMat &MassMat = *(this->m_matrixManager[masskey]);
1220  MatrixKey lapkey(StdRegions::eLaplacian, mkey.GetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
1221  DNekScalMat &LapMat = *(this->m_matrixManager[lapkey]);
1222 
1223  int rows = LapMat.GetRows();
1224  int cols = LapMat.GetColumns();
1225 
1226  DNekMatSharedPtr helm = MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols);
1227 
1228  NekDouble one = 1.0;
1229  (*helm) = LapMat + factor*MassMat;
1230 
1231  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one, helm);
1232  }
1233  break;
1234  case StdRegions::eIProductWRTBase:
1235  {
1236  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
1237  {
1238  NekDouble one = 1.0;
1239  DNekMatSharedPtr mat = GenMatrix(mkey);
1240  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
1241  }
1242  else
1243  {
1244  NekDouble jac = (m_metricinfo->GetJac(ptsKeys))[0];
1245  DNekMatSharedPtr mat = GetStdMatrix(mkey);
1246  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(jac,mat);
1247  }
1248  }
1249  break;
1250  case StdRegions::eHybridDGHelmholtz:
1251  case StdRegions::eHybridDGLamToU:
1252  case StdRegions::eHybridDGLamToQ0:
1253  case StdRegions::eHybridDGLamToQ1:
1254  case StdRegions::eHybridDGLamToQ2:
1255  case StdRegions::eHybridDGHelmBndLam:
1256  case StdRegions::eInvLaplacianWithUnityMean:
1257  {
1258  NekDouble one = 1.0;
1259 
1260  DNekMatSharedPtr mat = GenMatrix(mkey);
1261  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
1262  }
1263  break;
1264  case StdRegions::eInvHybridDGHelmholtz:
1265  {
1266  NekDouble one = 1.0;
1267 
1268  MatrixKey hkey(StdRegions::eHybridDGHelmholtz, DetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
1269  DNekMatSharedPtr mat = GenMatrix(hkey);
1270 
1271  mat->Invert();
1272  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
1273  }
1274  break;
1275  case StdRegions::ePreconLinearSpace:
1276  {
1277  NekDouble one = 1.0;
1278  MatrixKey helmkey(StdRegions::eHelmholtz, mkey.GetShapeType(), *this, mkey.GetConstFactors(), mkey.GetVarCoeffs());
1279  DNekScalBlkMatSharedPtr helmStatCond = GetLocStaticCondMatrix(helmkey);
1280  DNekScalMatSharedPtr A =helmStatCond->GetBlock(0,0);
1281  DNekMatSharedPtr R=BuildVertexMatrix(A);
1282 
1283  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,R);
1284  }
1285  break;
1286  case StdRegions::ePreconLinearSpaceMass:
1287  {
1288  NekDouble one = 1.0;
1289  MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
1290  DNekScalBlkMatSharedPtr massStatCond = GetLocStaticCondMatrix(masskey);
1291  DNekScalMatSharedPtr A =massStatCond->GetBlock(0,0);
1292  DNekMatSharedPtr R=BuildVertexMatrix(A);
1293 
1294  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,R);
1295  }
1296  break;
1297  case StdRegions::ePreconR:
1298  {
1299  NekDouble one = 1.0;
1300  MatrixKey helmkey(StdRegions::eHelmholtz, mkey.GetShapeType(), *this,mkey.GetConstFactors(), mkey.GetVarCoeffs());
1301  DNekScalBlkMatSharedPtr helmStatCond = GetLocStaticCondMatrix(helmkey);
1302  DNekScalMatSharedPtr A =helmStatCond->GetBlock(0,0);
1303 
1304  DNekScalMatSharedPtr Atmp;
1305  DNekMatSharedPtr R=BuildTransformationMatrix(A,mkey.GetMatrixType());
1306 
1307  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,R);
1308  }
1309  break;
1310  case StdRegions::ePreconRT:
1311  {
1312  NekDouble one = 1.0;
1313  MatrixKey helmkey(StdRegions::eHelmholtz, mkey.GetShapeType(), *this,mkey.GetConstFactors(), mkey.GetVarCoeffs());
1314  DNekScalBlkMatSharedPtr helmStatCond = GetLocStaticCondMatrix(helmkey);
1315  DNekScalMatSharedPtr A =helmStatCond->GetBlock(0,0);
1316 
1317  DNekScalMatSharedPtr Atmp;
1318  DNekMatSharedPtr RT=BuildTransformationMatrix(A,mkey.GetMatrixType());
1319 
1320  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,RT);
1321  }
1322  break;
1323  case StdRegions::ePreconRMass:
1324  {
1325  NekDouble one = 1.0;
1326  MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
1327  DNekScalBlkMatSharedPtr StatCond = GetLocStaticCondMatrix(masskey);
1328  DNekScalMatSharedPtr A =StatCond->GetBlock(0,0);
1329 
1330  DNekScalMatSharedPtr Atmp;
1331  DNekMatSharedPtr R=BuildTransformationMatrix(A,mkey.GetMatrixType());
1332 
1333  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,R);
1334  }
1335  break;
1336  case StdRegions::ePreconRTMass:
1337  {
1338  NekDouble one = 1.0;
1339  MatrixKey masskey(StdRegions::eMass, mkey.GetShapeType(), *this);
1340  DNekScalBlkMatSharedPtr massStatCond = GetLocStaticCondMatrix(masskey);
1341  DNekScalMatSharedPtr A =massStatCond->GetBlock(0,0);
1342 
1343  DNekScalMatSharedPtr Atmp;
1344  DNekMatSharedPtr RT=BuildTransformationMatrix(A,mkey.GetMatrixType());
1345 
1346  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,RT);
1347  }
1348  break;
1349  default:
1350  {
1351  //ASSERTL0(false, "Missing definition for " + (*StdRegions::MatrixTypeMap[mkey.GetMatrixType()]));
1352  NekDouble one = 1.0;
1353  DNekMatSharedPtr mat = GenMatrix(mkey);
1354 
1355  returnval = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,mat);
1356  }
1357  break;
1358  }
1359 
1360  return returnval;
1361  }
1362 
1363 
1364  DNekScalBlkMatSharedPtr TetExp::CreateStaticCondMatrix(
1365  const MatrixKey &mkey)
1366  {
1367  DNekScalBlkMatSharedPtr returnval;
1368 
1369  ASSERTL2(m_metricinfo->GetGtype() != SpatialDomains::eNoGeomType,"Geometric information is not set up");
1370 
1371  // set up block matrix system
1372  unsigned int nbdry = NumBndryCoeffs();
1373  unsigned int nint = (unsigned int)(m_ncoeffs - nbdry);
1374  unsigned int exp_size[] = {nbdry, nint};
1375  unsigned int nblks = 2;
1376  returnval = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(nblks, nblks, exp_size, exp_size);
1377 
1378  NekDouble factor = 1.0;
1379  MatrixStorage AMatStorage = eFULL;
1380 
1381  switch(mkey.GetMatrixType())
1382  {
1383  case StdRegions::eLaplacian:
1384  case StdRegions::eHelmholtz: // special case since Helmholtz not defined in StdRegions
1385  // use Deformed case for both regular and deformed geometries
1386  factor = 1.0;
1387  goto UseLocRegionsMatrix;
1388  break;
1389  default:
1390  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed ||
1391  mkey.GetNVarCoeff())
1392  {
1393  factor = 1.0;
1394  goto UseLocRegionsMatrix;
1395  }
1396  else
1397  {
1398  DNekScalMatSharedPtr mat = GetLocMatrix(mkey);
1399  factor = mat->Scale();
1400  goto UseStdRegionsMatrix;
1401  }
1402  break;
1403  UseStdRegionsMatrix:
1404  {
1405  NekDouble invfactor = 1.0/factor;
1406  NekDouble one = 1.0;
1407  DNekBlkMatSharedPtr mat = GetStdStaticCondMatrix(mkey);
1408  DNekScalMatSharedPtr Atmp;
1409  DNekMatSharedPtr Asubmat;
1410 
1411  //TODO: check below
1412  returnval->SetBlock(0,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,Asubmat = mat->GetBlock(0,0)));
1413  returnval->SetBlock(0,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,Asubmat = mat->GetBlock(0,1)));
1414  returnval->SetBlock(1,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,Asubmat = mat->GetBlock(1,0)));
1415  returnval->SetBlock(1,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(invfactor,Asubmat = mat->GetBlock(1,1)));
1416  }
1417  break;
1418  UseLocRegionsMatrix:
1419  {
1420  int i,j;
1421  NekDouble invfactor = 1.0/factor;
1422  NekDouble one = 1.0;
1423  DNekScalMat &mat = *GetLocMatrix(mkey);
1424  DNekMatSharedPtr A = MemoryManager<DNekMat>::AllocateSharedPtr(nbdry,nbdry,AMatStorage);
1425  DNekMatSharedPtr B = MemoryManager<DNekMat>::AllocateSharedPtr(nbdry,nint);
1426  DNekMatSharedPtr C = MemoryManager<DNekMat>::AllocateSharedPtr(nint,nbdry);
1427  DNekMatSharedPtr D = MemoryManager<DNekMat>::AllocateSharedPtr(nint,nint);
1428 
1429  Array<OneD,unsigned int> bmap(nbdry);
1430  Array<OneD,unsigned int> imap(nint);
1431  GetBoundaryMap(bmap);
1432  GetInteriorMap(imap);
1433 
1434  for(i = 0; i < nbdry; ++i)
1435  {
1436  for(j = 0; j < nbdry; ++j)
1437  {
1438  (*A)(i,j) = mat(bmap[i],bmap[j]);
1439  }
1440 
1441  for(j = 0; j < nint; ++j)
1442  {
1443  (*B)(i,j) = mat(bmap[i],imap[j]);
1444  }
1445  }
1446 
1447  for(i = 0; i < nint; ++i)
1448  {
1449  for(j = 0; j < nbdry; ++j)
1450  {
1451  (*C)(i,j) = mat(imap[i],bmap[j]);
1452  }
1453 
1454  for(j = 0; j < nint; ++j)
1455  {
1456  (*D)(i,j) = mat(imap[i],imap[j]);
1457  }
1458  }
1459 
1460  // Calculate static condensed system
1461  if(nint)
1462  {
1463  D->Invert();
1464  (*B) = (*B)*(*D);
1465  (*A) = (*A) - (*B)*(*C);
1466  }
1467 
1468  DNekScalMatSharedPtr Atmp;
1469 
1470  returnval->SetBlock(0,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,A));
1471  returnval->SetBlock(0,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(one,B));
1472  returnval->SetBlock(1,0,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(factor,C));
1473  returnval->SetBlock(1,1,Atmp = MemoryManager<DNekScalMat>::AllocateSharedPtr(invfactor,D));
1474 
1475  }
1476  break;
1477  }
1478  return returnval;
1479  }
1480 
1481 
1482  DNekMatSharedPtr TetExp::v_CreateStdMatrix(
1483  const StdRegions::StdMatrixKey &mkey)
1484  {
1485  LibUtilities::BasisKey bkey0 = m_base[0]->GetBasisKey();
1486  LibUtilities::BasisKey bkey1 = m_base[1]->GetBasisKey();
1487  LibUtilities::BasisKey bkey2 = m_base[2]->GetBasisKey();
1488  StdRegions::StdTetExpSharedPtr tmp = MemoryManager<StdTetExp>::AllocateSharedPtr(bkey0, bkey1, bkey2);
1489 
1490  return tmp->GetStdMatrix(mkey);
1491  }
1492 
1493  DNekScalMatSharedPtr TetExp::v_GetLocMatrix(const MatrixKey &mkey)
1494  {
1495  return m_matrixManager[mkey];
1496  }
1497 
1498  DNekScalBlkMatSharedPtr TetExp::v_GetLocStaticCondMatrix(const MatrixKey &mkey)
1499  {
1500  return m_staticCondMatrixManager[mkey];
1501  }
1502 
1503  void TetExp::v_DropLocStaticCondMatrix(const MatrixKey &mkey)
1504  {
1505  m_staticCondMatrixManager.DeleteObject(mkey);
1506  }
1507 
1508  void TetExp::GeneralMatrixOp_MatOp(
1509  const Array<OneD, const NekDouble> &inarray,
1510  Array<OneD,NekDouble> &outarray,
1511  const StdRegions::StdMatrixKey &mkey)
1512  {
1513  DNekScalMatSharedPtr mat = GetLocMatrix(mkey);
1514 
1515  if(inarray.get() == outarray.get())
1516  {
1517  Array<OneD,NekDouble> tmp(m_ncoeffs);
1518  Vmath::Vcopy(m_ncoeffs,inarray.get(),1,tmp.get(),1);
1519 
1520  Blas::Dgemv('N',m_ncoeffs,m_ncoeffs,mat->Scale(),(mat->GetOwnedMatrix())->GetPtr().get(),
1521  m_ncoeffs, tmp.get(), 1, 0.0, outarray.get(), 1);
1522  }
1523  else
1524  {
1525  Blas::Dgemv('N',m_ncoeffs,m_ncoeffs,mat->Scale(),(mat->GetOwnedMatrix())->GetPtr().get(),
1526  m_ncoeffs, inarray.get(), 1, 0.0, outarray.get(), 1);
1527  }
1528  }
1529 
1530 
1531  void TetExp::v_LaplacianMatrixOp_MatFree_Kernel(
1532  const Array<OneD, const NekDouble> &inarray,
1533  Array<OneD, NekDouble> &outarray,
1534  Array<OneD, NekDouble> &wsp)
1535  {
1536  // This implementation is only valid when there are no
1537  // coefficients associated to the Laplacian operator
1538  if (m_metrics.count(eMetricLaplacian00) == 0)
1539  {
1540  ComputeLaplacianMetric();
1541  }
1542 
1543  int nquad0 = m_base[0]->GetNumPoints();
1544  int nquad1 = m_base[1]->GetNumPoints();
1545  int nquad2 = m_base[2]->GetNumPoints();
1546  int nqtot = nquad0*nquad1*nquad2;
1547 
1548  ASSERTL1(wsp.num_elements() >= 6*nqtot,
1549  "Insufficient workspace size.");
1550  ASSERTL1(m_ncoeffs <= nqtot,
1551  "Workspace not set up for ncoeffs > nqtot");
1552 
1553  const Array<OneD, const NekDouble>& base0 = m_base[0]->GetBdata();
1554  const Array<OneD, const NekDouble>& base1 = m_base[1]->GetBdata();
1555  const Array<OneD, const NekDouble>& base2 = m_base[2]->GetBdata();
1556  const Array<OneD, const NekDouble>& dbase0 = m_base[0]->GetDbdata();
1557  const Array<OneD, const NekDouble>& dbase1 = m_base[1]->GetDbdata();
1558  const Array<OneD, const NekDouble>& dbase2 = m_base[2]->GetDbdata();
1559  const Array<OneD, const NekDouble>& metric00 = m_metrics[eMetricLaplacian00];
1560  const Array<OneD, const NekDouble>& metric01 = m_metrics[eMetricLaplacian01];
1561  const Array<OneD, const NekDouble>& metric02 = m_metrics[eMetricLaplacian02];
1562  const Array<OneD, const NekDouble>& metric11 = m_metrics[eMetricLaplacian11];
1563  const Array<OneD, const NekDouble>& metric12 = m_metrics[eMetricLaplacian12];
1564  const Array<OneD, const NekDouble>& metric22 = m_metrics[eMetricLaplacian22];
1565 
1566  // Allocate temporary storage
1567  Array<OneD,NekDouble> wsp0 (2*nqtot, wsp);
1568  Array<OneD,NekDouble> wsp1 ( nqtot, wsp+1*nqtot);
1569  Array<OneD,NekDouble> wsp2 ( nqtot, wsp+2*nqtot);
1570  Array<OneD,NekDouble> wsp3 ( nqtot, wsp+3*nqtot);
1571  Array<OneD,NekDouble> wsp4 ( nqtot, wsp+4*nqtot);
1572  Array<OneD,NekDouble> wsp5 ( nqtot, wsp+5*nqtot);
1573 
1574  // LAPLACIAN MATRIX OPERATION
1575  // wsp1 = du_dxi1 = D_xi1 * inarray = D_xi1 * u
1576  // wsp2 = du_dxi2 = D_xi2 * inarray = D_xi2 * u
1577  // wsp2 = du_dxi3 = D_xi3 * inarray = D_xi3 * u
1578  StdExpansion3D::PhysTensorDeriv(inarray,wsp0,wsp1,wsp2);
1579 
1580  // wsp0 = k = g0 * wsp1 + g1 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
1581  // wsp2 = l = g1 * wsp1 + g2 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
1582  // where g0, g1 and g2 are the metric terms set up in the GeomFactors class
1583  // especially for this purpose
1584  Vmath::Vvtvvtp(nqtot,&metric00[0],1,&wsp0[0],1,&metric01[0],1,&wsp1[0],1,&wsp3[0],1);
1585  Vmath::Vvtvp (nqtot,&metric02[0],1,&wsp2[0],1,&wsp3[0],1,&wsp3[0],1);
1586  Vmath::Vvtvvtp(nqtot,&metric01[0],1,&wsp0[0],1,&metric11[0],1,&wsp1[0],1,&wsp4[0],1);
1587  Vmath::Vvtvp (nqtot,&metric12[0],1,&wsp2[0],1,&wsp4[0],1,&wsp4[0],1);
1588  Vmath::Vvtvvtp(nqtot,&metric02[0],1,&wsp0[0],1,&metric12[0],1,&wsp1[0],1,&wsp5[0],1);
1589  Vmath::Vvtvp (nqtot,&metric22[0],1,&wsp2[0],1,&wsp5[0],1,&wsp5[0],1);
1590 
1591  // outarray = m = (D_xi1 * B)^T * k
1592  // wsp1 = n = (D_xi2 * B)^T * l
1593  IProductWRTBase_SumFacKernel(dbase0,base1,base2,wsp3,outarray,wsp0,false,true,true);
1594  IProductWRTBase_SumFacKernel(base0,dbase1,base2,wsp4,wsp2, wsp0,true,false,true);
1595  Vmath::Vadd(m_ncoeffs,wsp2.get(),1,outarray.get(),1,outarray.get(),1);
1596  IProductWRTBase_SumFacKernel(base0,base1,dbase2,wsp5,wsp2, wsp0,true,true,false);
1597  Vmath::Vadd(m_ncoeffs,wsp2.get(),1,outarray.get(),1,outarray.get(),1);
1598  }
1599 
1600 
1601  void TetExp::v_ComputeLaplacianMetric()
1602  {
1603  if (m_metrics.count(eMetricQuadrature) == 0)
1604  {
1605  ComputeQuadratureMetric();
1606  }
1607 
1608  int i, j;
1609  const unsigned int nqtot = GetTotPoints();
1610  const unsigned int dim = 3;
1611  const MetricType m[3][3] = { {eMetricLaplacian00, eMetricLaplacian01, eMetricLaplacian02},
1612  {eMetricLaplacian01, eMetricLaplacian11, eMetricLaplacian12},
1613  {eMetricLaplacian02, eMetricLaplacian12, eMetricLaplacian22}
1614  };
1615 
1616  for (unsigned int i = 0; i < dim; ++i)
1617  {
1618  for (unsigned int j = i; j < dim; ++j)
1619  {
1620  m_metrics[m[i][j]] = Array<OneD, NekDouble>(nqtot);
1621  }
1622  }
1623 
1624  // Define shorthand synonyms for m_metrics storage
1625  Array<OneD,NekDouble> g0 (m_metrics[m[0][0]]);
1626  Array<OneD,NekDouble> g1 (m_metrics[m[1][1]]);
1627  Array<OneD,NekDouble> g2 (m_metrics[m[2][2]]);
1628  Array<OneD,NekDouble> g3 (m_metrics[m[0][1]]);
1629  Array<OneD,NekDouble> g4 (m_metrics[m[0][2]]);
1630  Array<OneD,NekDouble> g5 (m_metrics[m[1][2]]);
1631 
1632  // Allocate temporary storage
1633  Array<OneD,NekDouble> alloc(7*nqtot,0.0);
1634  Array<OneD,NekDouble> h0 (alloc); // h0
1635  Array<OneD,NekDouble> h1 (alloc+ 1*nqtot);// h1
1636  Array<OneD,NekDouble> h2 (alloc+ 2*nqtot);// h2
1637  Array<OneD,NekDouble> h3 (alloc+ 3*nqtot);// h3
1638  Array<OneD,NekDouble> wsp4 (alloc+ 4*nqtot);// wsp4
1639  Array<OneD,NekDouble> wsp5 (alloc+ 5*nqtot);// wsp5
1640  Array<OneD,NekDouble> wsp6 (alloc+ 6*nqtot);// wsp6
1641  // Reuse some of the storage as workspace
1642  Array<OneD,NekDouble> wsp7 (alloc); // wsp7
1643  Array<OneD,NekDouble> wsp8 (alloc+ 1*nqtot);// wsp8
1644  Array<OneD,NekDouble> wsp9 (alloc+ 2*nqtot);// wsp9
1645 
1646  const Array<TwoD, const NekDouble>& df =
1647  m_metricinfo->GetDerivFactors(GetPointsKeys());
1648  const Array<OneD, const NekDouble>& z0 = m_base[0]->GetZ();
1649  const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
1650  const Array<OneD, const NekDouble>& z2 = m_base[2]->GetZ();
1651  const unsigned int nquad0 = m_base[0]->GetNumPoints();
1652  const unsigned int nquad1 = m_base[1]->GetNumPoints();
1653  const unsigned int nquad2 = m_base[2]->GetNumPoints();
1654 
1655  for(j = 0; j < nquad2; ++j)
1656  {
1657  for(i = 0; i < nquad1; ++i)
1658  {
1659  Vmath::Fill(nquad0, 4.0/(1.0-z1[i])/(1.0-z2[j]), &h0[0]+i*nquad0 + j*nquad0*nquad1,1);
1660  Vmath::Fill(nquad0, 2.0/(1.0-z1[i])/(1.0-z2[j]), &h1[0]+i*nquad0 + j*nquad0*nquad1,1);
1661  Vmath::Fill(nquad0, 2.0/(1.0-z2[j]), &h2[0]+i*nquad0 + j*nquad0*nquad1,1);
1662  Vmath::Fill(nquad0, (1.0+z1[i])/(1.0-z2[j]), &h3[0]+i*nquad0 + j*nquad0*nquad1,1);
1663  }
1664  }
1665  for(i = 0; i < nquad0; i++)
1666  {
1667  Blas::Dscal(nquad1*nquad2, 1+z0[i], &h1[0]+i, nquad0);
1668  }
1669 
1670  // Step 3. Construct combined metric terms for physical space to
1671  // collapsed coordinate system.
1672  // Order of construction optimised to minimise temporary storage
1673  if(m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
1674  {
1675  // wsp4
1676  Vmath::Vadd(nqtot, &df[1][0], 1, &df[2][0], 1, &wsp4[0], 1);
1677  Vmath::Vvtvvtp(nqtot, &df[0][0], 1, &h0[0], 1, &wsp4[0], 1, &h1[0], 1, &wsp4[0], 1);
1678  // wsp5
1679  Vmath::Vadd(nqtot, &df[4][0], 1, &df[5][0], 1, &wsp5[0], 1);
1680  Vmath::Vvtvvtp(nqtot, &df[3][0], 1, &h0[0], 1, &wsp5[0], 1, &h1[0], 1, &wsp5[0], 1);
1681  // wsp6
1682  Vmath::Vadd(nqtot, &df[7][0], 1, &df[8][0], 1, &wsp6[0], 1);
1683  Vmath::Vvtvvtp(nqtot, &df[6][0], 1, &h0[0], 1, &wsp6[0], 1, &h1[0], 1, &wsp6[0], 1);
1684 
1685  // g0
1686  Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp4[0], 1, &wsp5[0], 1, &wsp5[0], 1, &g0[0], 1);
1687  Vmath::Vvtvp (nqtot, &wsp6[0], 1, &wsp6[0], 1, &g0[0], 1, &g0[0], 1);
1688 
1689  // g4
1690  Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &wsp4[0], 1, &df[5][0], 1, &wsp5[0], 1, &g4[0], 1);
1691  Vmath::Vvtvp (nqtot, &df[8][0], 1, &wsp6[0], 1, &g4[0], 1, &g4[0], 1);
1692 
1693  // overwrite h0, h1, h2
1694  // wsp7 (h2f1 + h3f2)
1695  Vmath::Vvtvvtp(nqtot, &df[1][0], 1, &h2[0], 1, &df[2][0], 1, &h3[0], 1, &wsp7[0], 1);
1696  // wsp8 (h2f4 + h3f5)
1697  Vmath::Vvtvvtp(nqtot, &df[4][0], 1, &h2[0], 1, &df[5][0], 1, &h3[0], 1, &wsp8[0], 1);
1698  // wsp9 (h2f7 + h3f8)
1699  Vmath::Vvtvvtp(nqtot, &df[7][0], 1, &h2[0], 1, &df[8][0], 1, &h3[0], 1, &wsp9[0], 1);
1700 
1701  // g3
1702  Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp7[0], 1, &wsp5[0], 1, &wsp8[0], 1, &g3[0], 1);
1703  Vmath::Vvtvp (nqtot, &wsp6[0], 1, &wsp9[0], 1, &g3[0], 1, &g3[0], 1);
1704 
1705  // overwrite wsp4, wsp5, wsp6
1706  // g1
1707  Vmath::Vvtvvtp(nqtot, &wsp7[0], 1, &wsp7[0], 1, &wsp8[0], 1, &wsp8[0], 1, &g1[0], 1);
1708  Vmath::Vvtvp (nqtot, &wsp9[0], 1, &wsp9[0], 1, &g1[0], 1, &g1[0], 1);
1709 
1710  // g5
1711  Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &wsp7[0], 1, &df[5][0], 1, &wsp8[0], 1, &g5[0], 1);
1712  Vmath::Vvtvp (nqtot, &df[8][0], 1, &wsp9[0], 1, &g5[0], 1, &g5[0], 1);
1713 
1714  // g2
1715  Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &df[2][0], 1, &df[5][0], 1, &df[5][0], 1, &g2[0], 1);
1716  Vmath::Vvtvp (nqtot, &df[8][0], 1, &df[8][0], 1, &g2[0], 1, &g2[0], 1);
1717  }
1718  else
1719  {
1720  // wsp4
1721  Vmath::Svtsvtp(nqtot, df[0][0], &h0[0], 1, df[1][0] + df[2][0], &h1[0], 1, &wsp4[0], 1);
1722  // wsp5
1723  Vmath::Svtsvtp(nqtot, df[3][0], &h0[0], 1, df[4][0] + df[5][0], &h1[0], 1, &wsp5[0], 1);
1724  // wsp6
1725  Vmath::Svtsvtp(nqtot, df[6][0], &h0[0], 1, df[7][0] + df[8][0], &h1[0], 1, &wsp6[0], 1);
1726 
1727  // g0
1728  Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp4[0], 1, &wsp5[0], 1, &wsp5[0], 1, &g0[0], 1);
1729  Vmath::Vvtvp (nqtot, &wsp6[0], 1, &wsp6[0], 1, &g0[0], 1, &g0[0], 1);
1730 
1731  // g4
1732  Vmath::Svtsvtp(nqtot, df[2][0], &wsp4[0], 1, df[5][0], &wsp5[0], 1, &g4[0], 1);
1733  Vmath::Svtvp (nqtot, df[8][0], &wsp6[0], 1, &g4[0], 1, &g4[0], 1);
1734 
1735  // overwrite h0, h1, h2
1736  // wsp7 (h2f1 + h3f2)
1737  Vmath::Svtsvtp(nqtot, df[1][0], &h2[0], 1, df[2][0], &h3[0], 1, &wsp7[0], 1);
1738  // wsp8 (h2f4 + h3f5)
1739  Vmath::Svtsvtp(nqtot, df[4][0], &h2[0], 1, df[5][0], &h3[0], 1, &wsp8[0], 1);
1740  // wsp9 (h2f7 + h3f8)
1741  Vmath::Svtsvtp(nqtot, df[7][0], &h2[0], 1, df[8][0], &h3[0], 1, &wsp9[0], 1);
1742 
1743  // g3
1744  Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp7[0], 1, &wsp5[0], 1, &wsp8[0], 1, &g3[0], 1);
1745  Vmath::Vvtvp (nqtot, &wsp6[0], 1, &wsp9[0], 1, &g3[0], 1, &g3[0], 1);
1746 
1747  // overwrite wsp4, wsp5, wsp6
1748  // g1
1749  Vmath::Vvtvvtp(nqtot, &wsp7[0], 1, &wsp7[0], 1, &wsp8[0], 1, &wsp8[0], 1, &g1[0], 1);
1750  Vmath::Vvtvp (nqtot, &wsp9[0], 1, &wsp9[0], 1, &g1[0], 1, &g1[0], 1);
1751 
1752  // g5
1753  Vmath::Svtsvtp(nqtot, df[2][0], &wsp7[0], 1, df[5][0], &wsp8[0], 1, &g5[0], 1);
1754  Vmath::Svtvp (nqtot, df[8][0], &wsp9[0], 1, &g5[0], 1, &g5[0], 1);
1755 
1756  // g2
1757  Vmath::Fill(nqtot, df[2][0]*df[2][0] + df[5][0]*df[5][0] + df[8][0]*df[8][0], &g2[0], 1);
1758  }
1759 
1760  for (unsigned int i = 0; i < dim; ++i)
1761  {
1762  for (unsigned int j = i; j < dim; ++j)
1763  {
1764  MultiplyByQuadratureMetric(m_metrics[m[i][j]],
1765  m_metrics[m[i][j]]);
1766 
1767  }
1768  }
1769 
1770 
1771  }
1772  }//end of namespace
1773 }//end of namespace
Nektar::StdRegions::StdExpansion::GetPointsKeys
const LibUtilities::PointsKeyVector GetPointsKeys() const
Definition: StdExpansion.h:1328
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Definition: StdMatrixKey.h:142
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Integrate the physical point list inarray over region.
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Definition: StdMatrixKey.h:168
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Definition: Points.h:220
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Definition: StdMatrixKey.h:82
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Allocate a shared pointer from the memory pool.
Definition: NekMemoryManager.hpp:235
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virtual void v_LaplacianMatrixOp_MatFree(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)
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sqrt y = sqrt(x)
Definition: Vmath.cpp:394
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General purpose memory allocation routines with the ability to allocate from thread specific memory p...
Definition: NekMemoryManager.hpp:102
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virtual NekDouble v_StdPhysEvaluate(const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
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this function calculates the inner product of a given function f with the different modes of the expa...
Definition: StdExpansion.h:629
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Fill a vector with a constant value.
Definition: Vmath.cpp:46
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void Svtvp(int n, const T alpha, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
svtvp (scalar times vector plus vector): z = alpha*x + y
Definition: Vmath.cpp:471
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Definition: Vmath.cpp:428
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Principle Modified Functions .
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std
STL namespace.
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Scalar multiply y = alpha/y.
Definition: Vmath.cpp:257
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virtual void v_IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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Definition: TetExp.cpp:295
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Definition: Vmath.cpp:227
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Definition: TetExp.cpp:566
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Definition: TetExp.cpp:1482
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Definition: Vmath.cpp:199
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Definition: Basis.h:128
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Defines a specification for a set of points.
Definition: Points.h:58
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Compute the normal of a triangular face.
Definition: TetExp.cpp:720
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Definition: NektarUnivTypeDefs.hpp:44
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Returns the physical values at the quadrature points of a face.
Definition: TetExp.cpp:630
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Definition: StdExpansion3D.h:204
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Definition: TetExp.cpp:1498
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Definition: StdExpansion.h:165
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Definition: TetExp.cpp:553
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Definition: NekTypeDefs.hpp:72
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Definition: Expansion.cpp:85
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Definition: TetExp.cpp:495
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Definition: TetExp.cpp:561
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Definition: Expansion3D.cpp:383
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Return distribution of points.
Definition: Basis.h:145
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Definition: Expansion.cpp:150
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Definition: GeomFactors.h:62
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vvtvvtp (vector times vector plus vector times vector):
Definition: Vmath.cpp:523
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Calculates the inner product .
Definition: TetExp.cpp:366
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Definition: ErrorUtil.hpp:213
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Definition: SpatialDomains.hpp:55
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Definition: TetGeom.h:106
TetExp.h
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Definition: TetExp.cpp:513
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Definition: StdExpansion.h:131
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Definition: TetExp.cpp:1055
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vvtvvtp (scalar times vector plus scalar times vector):
Definition: Vmath.cpp:577
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Definition: StdExpansion.h:324
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Definition: StdTetExp.h:268
InterpCoeff.h
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Indicates the type of element geometry.
Definition: SpatialDomains.hpp:52
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Differentiate inarray in the three coordinate directions.
Definition: TetExp.cpp:163
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Zero vector.
Definition: Vmath.cpp:359
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Definition: StdExpansion.h:1873
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Definition: StdExpansion3D.cpp:248
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#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode...
Definition: ErrorUtil.hpp:191
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Definition: StdExpansion.h:1422
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Definition: Vmath.cpp:1047
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Geometry is curved or has non-constant factors.
Definition: SpatialDomains.hpp:57
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void GetBoundaryMap(Array< OneD, unsigned int > &outarray)
Definition: StdExpansion.h:816
Nektar::LocalRegions::TetExp::v_DropLocStaticCondMatrix
void v_DropLocStaticCondMatrix(const MatrixKey &mkey)
Definition: TetExp.cpp:1503
Nektar::LibUtilities::BasisKey
Describes the specification for a Basis.
Definition: Basis.h:50
Nektar::LocalRegions::TetExp::v_ComputeLaplacianMetric
virtual void v_ComputeLaplacianMetric()
Definition: TetExp.cpp:1601
Nektar::LocalRegions::TetExp::v_GetCoords
virtual void v_GetCoords(Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3)
Definition: TetExp.cpp:532
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:285
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:169
Nektar::LocalRegions::TetExp::v_DetShapeType
virtual LibUtilities::ShapeType v_DetShapeType() const
Return Shape of region, using ShapeType enum list.
Definition: TetExp.cpp:548
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