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StdExpansion2D.h
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2 //
3 // File StdExpansion2D.h
4 //
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9 // Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
10 // Department of Aeronautics, Imperial College London (UK), and Scientific
11 // Computing and Imaging Institute, University of Utah (USA).
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31 //
32 // Description: Daughter of StdExpansion. This class contains routine
33 // which are common to 2D expansion. Typically this inolves physiocal
34 // space operations.
35 //
36 ///////////////////////////////////////////////////////////////////////////////
37 
38 #ifndef STDEXP2D_H
39 #define STDEXP2D_H
40 
43 
44 namespace Nektar
45 {
46 namespace StdRegions
47 {
48 
49  class StdExpansion2D: virtual public StdExpansion
50  {
51  public:
54  const LibUtilities::BasisKey &Bb);
55  STD_REGIONS_EXPORT StdExpansion2D(const StdExpansion2D &T);
57 
58  // Generic operations in different element
59 
60  /** \brief Calculate the 2D derivative in the local
61  * tensor/collapsed coordinate at the physical points
62  *
63  * This function is independent of the expansion basis and can
64  * therefore be defined for all tensor product distribution of
65  * quadrature points in a generic manner. The key operations are:
66  *
67  * - \f$ \frac{d}{d\eta_1} \rightarrow {\bf D^T_0 u } \f$ \n
68  * - \f$ \frac{d}{d\eta_2} \rightarrow {\bf D_1 u } \f$
69  *
70  * \param inarray array of physical points to be differentiated
71  * \param outarray_d0 the resulting array of derivative in the
72  * \f$\eta_1\f$ direction will be stored in outarray_d0 as output
73  * of the function
74  * \param outarray_d1 the resulting array of derivative in the
75  * \f$\eta_2\f$ direction will be stored in outarray_d1 as output
76  * of the function
77  *
78  * Recall that:
79  * \f$
80  * \hspace{1cm} \begin{array}{llll}
81  * \mbox{Shape} & \mbox{Cartesian coordinate range} &
82  * \mbox{Collapsed coord.} &
83  * \mbox{Collapsed coordinate definition}\\
84  * \mbox{Quadrilateral} & -1 \leq \xi_1,\xi_2 \leq 1
85  * & -1 \leq \eta_1,\eta_2 \leq 1
86  * & \eta_1 = \xi_1, \eta_2 = \xi_2\\
87  * \mbox{Triangle} & -1 \leq \xi_1,\xi_2; \xi_1+\xi_2 \leq 0
88  * & -1 \leq \eta_1,\eta_2 \leq 1
89  * & \eta_1 = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \eta_2 = \xi_2 \\
90  * \end{array} \f$
91  */
93  const Array<OneD, const NekDouble>& inarray,
94  Array<OneD, NekDouble> &outarray_d0,
95  Array<OneD, NekDouble> &outarray_d1);
96 
98  const Array<OneD, const NekDouble>& inarray,
100  const Array<OneD, const NekDouble>& w1);
101 
103  const Array<OneD, const NekDouble>& base0,
104  const Array<OneD, const NekDouble>& base1,
105  const Array<OneD, const NekDouble>& inarray,
106  Array<OneD, NekDouble> &outarray,
108  bool doCheckCollDir0 = true,
109  bool doCheckCollDir1 = true);
110 
112  const Array<OneD, const NekDouble>& base0,
113  const Array<OneD, const NekDouble>& base1,
114  const Array<OneD, const NekDouble>& inarray,
115  Array<OneD, NekDouble> &outarray,
117  bool doCheckCollDir0 = true,
118  bool doCheckCollDir1 = true);
119 
120  protected:
121 
122  /** \brief This function evaluates the expansion at a single
123  * (arbitrary) point of the domain
124  *
125  * This function is a wrapper around the virtual function
126  * \a v_PhysEvaluate()
127  *
128  * Based on the value of the expansion at the quadrature points,
129  * this function calculates the value of the expansion at an
130  * arbitrary single points (with coordinates \f$ \mathbf{x_c}\f$
131  * given by the pointer \a coords). This operation, equivalent to
132  * \f[ u(\mathbf{x_c}) = \sum_p \phi_p(\mathbf{x_c}) \hat{u}_p \f]
133  * is evaluated using Lagrangian interpolants through the quadrature
134  * points:
135  * \f[ u(\mathbf{x_c}) = \sum_p h_p(\mathbf{x_c}) u_p\f]
136  *
137  * This function requires that the physical value array
138  * \f$\mathbf{u}\f$ (implemented as the attribute #m_phys)
139  * is set.
140  *
141  * \param coords the coordinates of the single point
142  * \return returns the value of the expansion at the single point
143  */
145  const Array<OneD, const NekDouble>& coords,
146  const Array<OneD, const NekDouble>& physvals);
147 
150  const Array<OneD, const NekDouble> & physvals);
151 
153  const Array<OneD, const NekDouble>& base0,
154  const Array<OneD, const NekDouble>& base1,
155  const Array<OneD, const NekDouble>& inarray,
156  Array<OneD, NekDouble> &outarray,
158  bool doCheckCollDir0,
159  bool doCheckCollDir1) = 0;
160 
162  const Array<OneD, const NekDouble>& base0,
163  const Array<OneD, const NekDouble>& base1,
164  const Array<OneD, const NekDouble>& inarray,
165  Array<OneD, NekDouble> &outarray,
167  bool doCheckCollDir0,
168  bool doCheckCollDir1) = 0;
169 
171  const Array<OneD, const NekDouble> &inarray,
172  Array<OneD, NekDouble> &outarray,
173  const StdRegions::StdMatrixKey &mkey);
175  const Array<OneD, const NekDouble> &inarray,
176  Array<OneD, NekDouble> &outarray,
177  const StdRegions::StdMatrixKey &mkey);
178 
179  STD_REGIONS_EXPORT virtual int v_GetTraceNcoeffs(const int i) const
180  {
181  return GetEdgeNcoeffs(i);
182  }
183 
184  private:
185 
186  // Virtual Functions ----------------------------------------
187  virtual int v_GetShapeDimension() const
188  {
189  return 2;
190  }
191 
192  virtual int v_GetNfaces() const
193  {
194  return 0;
195  }
196 
197  virtual int v_GetCoordim(void)
198  {
199  return 2;
200  }
201  };
202 
203  typedef boost::shared_ptr<StdExpansion2D> StdExpansion2DSharedPtr;
204 
205 } //end of namespace
206 } //end of namespace
207 
208 #endif //STDEXP2D_H
virtual int v_GetTraceNcoeffs(const int i) const
virtual int v_GetShapeDimension() const
void BwdTrans_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)
virtual void v_IProductWRTBase_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0
NekDouble Integral(const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &w0, const Array< OneD, const NekDouble > &w1)
virtual void v_LaplacianMatrixOp_MatFree(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)
int GetEdgeNcoeffs(const int i) const
This function returns the number of expansion coefficients belonging to the i-th edge.
Definition: StdExpansion.h:287
void PhysTensorDeriv(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d0, Array< OneD, NekDouble > &outarray_d1)
Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points...
boost::shared_ptr< StdExpansion2D > StdExpansion2DSharedPtr
The base class for all shapes.
Definition: StdExpansion.h:69
virtual NekDouble v_PhysEvaluate(const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
This function evaluates the expansion at a single (arbitrary) point of the domain.
double NekDouble
#define STD_REGIONS_EXPORT
void IProductWRTBase_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)
Describes the specification for a Basis.
Definition: Basis.h:50
virtual void v_BwdTrans_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0
virtual void v_HelmholtzMatrixOp_MatFree(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)