MFEM
v3.3.2
Finite element discretization library
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#include <bilinearform.hpp>
Public Member Functions | |
BilinearForm (FiniteElementSpace *f) | |
Creates bilinear form associated with FE space *f. More... | |
BilinearForm (FiniteElementSpace *f, BilinearForm *bf, int ps=0) | |
int | Size () const |
Get the size of the BilinearForm as a square matrix. More... | |
void | EnableStaticCondensation () |
bool | StaticCondensationIsEnabled () const |
FiniteElementSpace * | SCFESpace () const |
Return the trace FE space associated with static condensation. More... | |
void | EnableHybridization (FiniteElementSpace *constr_space, BilinearFormIntegrator *constr_integ, const Array< int > &ess_tdof_list) |
void | UsePrecomputedSparsity (int ps=1) |
void | UseSparsity (int *I, int *J, bool isSorted) |
Use the given CSR sparsity pattern to allocate the internal SparseMatrix. More... | |
void | UseSparsity (SparseMatrix &A) |
Use the sparsity of A to allocate the internal SparseMatrix. More... | |
void | AllocateMatrix () |
Array< BilinearFormIntegrator * > * | GetDBFI () |
Array< BilinearFormIntegrator * > * | GetBBFI () |
Array< BilinearFormIntegrator * > * | GetFBFI () |
Array< BilinearFormIntegrator * > * | GetBFBFI () |
const double & | operator() (int i, int j) |
virtual double & | Elem (int i, int j) |
Returns reference to a_{ij}. More... | |
virtual const double & | Elem (int i, int j) const |
Returns constant reference to a_{ij}. More... | |
virtual void | Mult (const Vector &x, Vector &y) const |
Matrix vector multiplication. More... | |
void | FullMult (const Vector &x, Vector &y) const |
virtual void | AddMult (const Vector &x, Vector &y, const double a=1.0) const |
void | FullAddMult (const Vector &x, Vector &y) const |
virtual void | AddMultTranspose (const Vector &x, Vector &y, const double a=1.0) const |
void | FullAddMultTranspose (const Vector &x, Vector &y) const |
virtual void | MultTranspose (const Vector &x, Vector &y) const |
Action of the transpose operator: y=A^t(x) . The default behavior in class Operator is to generate an error. More... | |
double | InnerProduct (const Vector &x, const Vector &y) const |
virtual MatrixInverse * | Inverse () const |
Returns a pointer to (approximation) of the matrix inverse. More... | |
virtual void | Finalize (int skip_zeros=1) |
Finalizes the matrix initialization. More... | |
const SparseMatrix & | SpMat () const |
Returns a reference to the sparse matrix. More... | |
SparseMatrix & | SpMat () |
SparseMatrix * | LoseMat () |
const SparseMatrix & | SpMatElim () const |
Returns a reference to the sparse matrix of eliminated b.c. More... | |
SparseMatrix & | SpMatElim () |
void | AddDomainIntegrator (BilinearFormIntegrator *bfi) |
Adds new Domain Integrator. More... | |
void | AddBoundaryIntegrator (BilinearFormIntegrator *bfi) |
Adds new Boundary Integrator. More... | |
void | AddInteriorFaceIntegrator (BilinearFormIntegrator *bfi) |
Adds new interior Face Integrator. More... | |
void | AddBdrFaceIntegrator (BilinearFormIntegrator *bfi) |
Adds new boundary Face Integrator. More... | |
void | AddBdrFaceIntegrator (BilinearFormIntegrator *bfi, Array< int > &bdr_marker) |
Adds new boundary Face Integrator, restricted to specific boundary attributes. More... | |
void | operator= (const double a) |
void | Assemble (int skip_zeros=1) |
Assembles the form i.e. sums over all domain/bdr integrators. More... | |
virtual const Operator * | GetProlongation () const |
Get the finite element space prolongation matrix. More... | |
virtual const Operator * | GetRestriction () const |
Get the finite element space restriction matrix. More... | |
void | FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, SparseMatrix &A, Vector &X, Vector &B, int copy_interior=0) |
void | FormSystemMatrix (const Array< int > &ess_tdof_list, SparseMatrix &A) |
Form the linear system matrix A, see FormLinearSystem for details. More... | |
virtual void | RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x) |
void | ComputeElementMatrices () |
Compute and store internally all element matrices. More... | |
void | FreeElementMatrices () |
Free the memory used by the element matrices. More... | |
void | ComputeElementMatrix (int i, DenseMatrix &elmat) |
void | AssembleElementMatrix (int i, const DenseMatrix &elmat, Array< int > &vdofs, int skip_zeros=1) |
void | AssembleBdrElementMatrix (int i, const DenseMatrix &elmat, Array< int > &vdofs, int skip_zeros=1) |
void | EliminateEssentialBC (const Array< int > &bdr_attr_is_ess, Vector &sol, Vector &rhs, int d=0) |
void | EliminateEssentialBC (const Array< int > &bdr_attr_is_ess, int d=0) |
void | EliminateEssentialBCDiag (const Array< int > &bdr_attr_is_ess, double value) |
Perform elimination and set the diagonal entry to the given value. More... | |
void | EliminateVDofs (const Array< int > &vdofs, Vector &sol, Vector &rhs, int d=0) |
Eliminate the given vdofs. NOTE: here, vdofs is a list of DOFs. More... | |
void | EliminateVDofs (const Array< int > &vdofs, int d=0) |
void | EliminateEssentialBCFromDofs (const Array< int > &ess_dofs, Vector &sol, Vector &rhs, int d=0) |
void | EliminateEssentialBCFromDofs (const Array< int > &ess_dofs, int d=0) |
void | EliminateEssentialBCFromDofsDiag (const Array< int > &ess_dofs, double value) |
Perform elimination and set the diagonal entry to the given value. More... | |
void | EliminateVDofsInRHS (const Array< int > &vdofs, const Vector &x, Vector &b) |
double | FullInnerProduct (const Vector &x, const Vector &y) const |
virtual void | Update (FiniteElementSpace *nfes=NULL) |
FiniteElementSpace * | GetFES () |
(DEPRECATED) Return the FE space associated with the BilinearForm. More... | |
FiniteElementSpace * | FESpace () |
Return the FE space associated with the BilinearForm. More... | |
const FiniteElementSpace * | FESpace () const |
Read-only access to the associated FiniteElementSpace. More... | |
virtual | ~BilinearForm () |
Destroys bilinear form. More... | |
Public Member Functions inherited from mfem::Matrix | |
Matrix (int s) | |
Creates a square matrix of size s. More... | |
Matrix (int h, int w) | |
Creates a matrix of the given height and width. More... | |
virtual void | Print (std::ostream &out=mfem::out, int width_=4) const |
Prints matrix to stream out. More... | |
virtual | ~Matrix () |
Destroys matrix. More... | |
Public Member Functions inherited from mfem::Operator | |
Operator (int s=0) | |
Construct a square Operator with given size s (default 0). More... | |
Operator (int h, int w) | |
Construct an Operator with the given height (output size) and width (input size). More... | |
int | Height () const |
Get the height (size of output) of the Operator. Synonym with NumRows(). More... | |
int | NumRows () const |
Get the number of rows (size of output) of the Operator. Synonym with Height(). More... | |
int | Width () const |
Get the width (size of input) of the Operator. Synonym with NumCols(). More... | |
int | NumCols () const |
Get the number of columns (size of input) of the Operator. Synonym with Width(). More... | |
virtual Operator & | GetGradient (const Vector &x) const |
Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error. More... | |
void | FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0) |
Form a constrained linear system using a matrix-free approach. More... | |
void | PrintMatlab (std::ostream &out, int n=0, int m=0) const |
Prints operator with input size n and output size m in Matlab format. More... | |
virtual | ~Operator () |
Virtual destructor. More... | |
Protected Member Functions | |
void | AllocMat () |
void | ConformingAssemble () |
BilinearForm () | |
Protected Attributes | |
SparseMatrix * | mat |
Sparse matrix to be associated with the form. More... | |
SparseMatrix * | mat_e |
Matrix used to eliminate b.c. More... | |
FiniteElementSpace * | fes |
FE space on which the form lives. More... | |
long | sequence |
int | extern_bfs |
Array< BilinearFormIntegrator * > | dbfi |
Set of Domain Integrators to be applied. More... | |
Array< BilinearFormIntegrator * > | bbfi |
Set of Boundary Integrators to be applied. More... | |
Array< BilinearFormIntegrator * > | fbfi |
Set of interior face Integrators to be applied. More... | |
Array< BilinearFormIntegrator * > | bfbfi |
Set of boundary face Integrators to be applied. More... | |
Array< Array< int > * > | bfbfi_marker |
DenseMatrix | elemmat |
Array< int > | vdofs |
DenseTensor * | element_matrices |
StaticCondensation * | static_cond |
Hybridization * | hybridization |
int | precompute_sparsity |
Protected Attributes inherited from mfem::Operator | |
int | height |
Dimension of the output / number of rows in the matrix. More... | |
int | width |
Dimension of the input / number of columns in the matrix. More... | |
Additional Inherited Members | |
Public Types inherited from mfem::Operator | |
enum | Type { MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC } |
Enumeration defining IDs for some classes derived from Operator. More... | |
Class for bilinear form - "Matrix" with associated FE space and BLFIntegrators.
Definition at line 29 of file bilinearform.hpp.
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Definition at line 75 of file bilinearform.hpp.
mfem::BilinearForm::BilinearForm | ( | FiniteElementSpace * | f | ) |
Creates bilinear form associated with FE space *f.
Definition at line 65 of file bilinearform.cpp.
mfem::BilinearForm::BilinearForm | ( | FiniteElementSpace * | f, |
BilinearForm * | bf, | ||
int | ps = 0 |
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Definition at line 78 of file bilinearform.cpp.
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Destroys bilinear form.
Definition at line 874 of file bilinearform.cpp.
void mfem::BilinearForm::AddBdrFaceIntegrator | ( | BilinearFormIntegrator * | bfi | ) |
Adds new boundary Face Integrator.
Definition at line 215 of file bilinearform.cpp.
void mfem::BilinearForm::AddBdrFaceIntegrator | ( | BilinearFormIntegrator * | bfi, |
Array< int > & | bdr_marker | ||
) |
Adds new boundary Face Integrator, restricted to specific boundary attributes.
Definition at line 221 of file bilinearform.cpp.
void mfem::BilinearForm::AddBoundaryIntegrator | ( | BilinearFormIntegrator * | bfi | ) |
Adds new Boundary Integrator.
Definition at line 205 of file bilinearform.cpp.
void mfem::BilinearForm::AddDomainIntegrator | ( | BilinearFormIntegrator * | bfi | ) |
Adds new Domain Integrator.
Definition at line 200 of file bilinearform.cpp.
void mfem::BilinearForm::AddInteriorFaceIntegrator | ( | BilinearFormIntegrator * | bfi | ) |
Adds new interior Face Integrator.
Definition at line 210 of file bilinearform.cpp.
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Definition at line 159 of file bilinearform.hpp.
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Definition at line 165 of file bilinearform.hpp.
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Pre-allocate the internal SparseMatrix before assembly. If the flag 'precompute sparsity' is set, the matrix is allocated in CSR format (i.e. finalized) and the entries are initialized with zeros.
Definition at line 135 of file bilinearform.hpp.
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Definition at line 20 of file bilinearform.cpp.
void mfem::BilinearForm::Assemble | ( | int | skip_zeros = 1 | ) |
Assembles the form i.e. sums over all domain/bdr integrators.
Definition at line 300 of file bilinearform.cpp.
void mfem::BilinearForm::AssembleBdrElementMatrix | ( | int | i, |
const DenseMatrix & | elmat, | ||
Array< int > & | vdofs, | ||
int | skip_zeros = 1 |
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Definition at line 278 of file bilinearform.cpp.
void mfem::BilinearForm::AssembleElementMatrix | ( | int | i, |
const DenseMatrix & | elmat, | ||
Array< int > & | vdofs, | ||
int | skip_zeros = 1 |
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Definition at line 256 of file bilinearform.cpp.
void mfem::BilinearForm::ComputeElementMatrices | ( | ) |
Compute and store internally all element matrices.
Definition at line 658 of file bilinearform.cpp.
void mfem::BilinearForm::ComputeElementMatrix | ( | int | i, |
DenseMatrix & | elmat | ||
) |
Definition at line 228 of file bilinearform.cpp.
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Definition at line 471 of file bilinearform.cpp.
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Returns reference to a_{ij}.
Implements mfem::Matrix.
Definition at line 177 of file bilinearform.cpp.
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Returns constant reference to a_{ij}.
Implements mfem::Matrix.
Definition at line 182 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateEssentialBC | ( | const Array< int > & | bdr_attr_is_ess, |
Vector & | sol, | ||
Vector & | rhs, | ||
int | d = 0 |
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Eliminate essential boundary DOFs from the system. The array 'bdr_attr_is_ess' marks boundary attributes that constitute the essential part of the boundary. If d == 0, the diagonal at the essential DOFs is set to 1.0, otherwise it is left the same.
Definition at line 700 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateEssentialBC | ( | const Array< int > & | bdr_attr_is_ess, |
int | d = 0 |
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Definition at line 717 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateEssentialBCDiag | ( | const Array< int > & | bdr_attr_is_ess, |
double | value | ||
) |
Perform elimination and set the diagonal entry to the given value.
Definition at line 734 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateEssentialBCFromDofs | ( | const Array< int > & | ess_dofs, |
Vector & | sol, | ||
Vector & | rhs, | ||
int | d = 0 |
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Similar to EliminateVDofs but here ess_dofs is a marker (boolean) array on all vdofs (ess_dofs[i] < 0 is true).
Definition at line 789 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateEssentialBCFromDofs | ( | const Array< int > & | ess_dofs, |
int | d = 0 |
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Similar to EliminateVDofs but here ess_dofs is a marker (boolean) array on all vdofs (ess_dofs[i] < 0 is true).
Definition at line 803 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateEssentialBCFromDofsDiag | ( | const Array< int > & | ess_dofs, |
double | value | ||
) |
Perform elimination and set the diagonal entry to the given value.
Definition at line 815 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateVDofs | ( | const Array< int > & | vdofs, |
Vector & | sol, | ||
Vector & | rhs, | ||
int | d = 0 |
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Eliminate the given vdofs. NOTE: here, vdofs is a list of DOFs.
Definition at line 751 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateVDofs | ( | const Array< int > & | vdofs, |
int | d = 0 |
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Eliminate the given vdofs storing the eliminated part internally; this method works in conjunction with EliminateVDofsInRHS and allows elimination of boundary conditions in multiple right-hand sides. In this method, vdofs is a list of DOFs.
Definition at line 768 of file bilinearform.cpp.
void mfem::BilinearForm::EliminateVDofsInRHS | ( | const Array< int > & | vdofs, |
const Vector & | x, | ||
Vector & | b | ||
) |
Use the stored eliminated part of the matrix (see EliminateVDofs) to modify r.h.s.; vdofs is a list of DOFs (non-directional, i.e. >= 0).
Definition at line 827 of file bilinearform.cpp.
void mfem::BilinearForm::EnableHybridization | ( | FiniteElementSpace * | constr_space, |
BilinearFormIntegrator * | constr_integ, | ||
const Array< int > & | ess_tdof_list | ||
) |
Enable hybridization; for details see the description for class Hybridization in fem/hybridization.hpp. This method should be called before assembly.
Definition at line 141 of file bilinearform.cpp.
void mfem::BilinearForm::EnableStaticCondensation | ( | ) |
Enable the use of static condensation. For details see the description for class StaticCondensation in fem/staticcond.hpp This method should be called before assembly. If the number of unknowns after static condensation is not reduced, it is not enabled.
Definition at line 124 of file bilinearform.cpp.
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Return the FE space associated with the BilinearForm.
Definition at line 338 of file bilinearform.hpp.
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Read-only access to the associated FiniteElementSpace.
Definition at line 340 of file bilinearform.hpp.
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Finalizes the matrix initialization.
Reimplemented from mfem::Matrix.
Definition at line 192 of file bilinearform.cpp.
void mfem::BilinearForm::FormLinearSystem | ( | const Array< int > & | ess_tdof_list, |
Vector & | x, | ||
Vector & | b, | ||
SparseMatrix & | A, | ||
Vector & | X, | ||
Vector & | B, | ||
int | copy_interior = 0 |
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Form the linear system A X = B, corresponding to the current bilinear form and b(.), by applying any necessary transformations such as: eliminating boundary conditions; applying conforming constraints for non-conforming AMR; static condensation; hybridization.
The GridFunction-size vector x must contain the essential b.c. The BilinearForm and the LinearForm-size vector b must be assembled.
The vector X is initialized with a suitable initial guess: when using hybridization, the vector X is set to zero; otherwise, the essential entries of X are set to the corresponding b.c. and all other entries are set to zero (copy_interior == 0) or copied from x (copy_interior != 0).
This method can be called multiple times (with the same ess_tdof_list array) to initialize different right-hand sides and boundary condition values.
After solving the linear system, the finite element solution x can be recovered by calling RecoverFEMSolution (with the same vectors X, b, and x).
NOTE: If there are no transformations, X simply reuses the data of x.
Definition at line 506 of file bilinearform.cpp.
void mfem::BilinearForm::FormSystemMatrix | ( | const Array< int > & | ess_tdof_list, |
SparseMatrix & | A | ||
) |
Form the linear system matrix A, see FormLinearSystem for details.
Definition at line 572 of file bilinearform.cpp.
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Free the memory used by the element matrices.
Definition at line 280 of file bilinearform.hpp.
Definition at line 162 of file bilinearform.hpp.
Definition at line 169 of file bilinearform.hpp.
Definition at line 328 of file bilinearform.hpp.
Definition at line 156 of file bilinearform.hpp.
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Definition at line 139 of file bilinearform.hpp.
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Definition at line 143 of file bilinearform.hpp.
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Definition at line 137 of file bilinearform.hpp.
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Definition at line 141 of file bilinearform.hpp.
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(DEPRECATED) Return the FE space associated with the BilinearForm.
Definition at line 335 of file bilinearform.hpp.
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Get the finite element space prolongation matrix.
Reimplemented from mfem::Operator.
Reimplemented in mfem::ParBilinearForm.
Definition at line 236 of file bilinearform.hpp.
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Get the finite element space restriction matrix.
Reimplemented from mfem::Operator.
Reimplemented in mfem::ParBilinearForm.
Definition at line 239 of file bilinearform.hpp.
Definition at line 175 of file bilinearform.hpp.
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Returns a pointer to (approximation) of the matrix inverse.
Implements mfem::Matrix.
Definition at line 187 of file bilinearform.cpp.
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Definition at line 195 of file bilinearform.hpp.
Matrix vector multiplication.
Implements mfem::Operator.
Definition at line 154 of file bilinearform.hpp.
Action of the transpose operator: y=A^t(x)
. The default behavior in class Operator is to generate an error.
Reimplemented from mfem::Operator.
Definition at line 172 of file bilinearform.hpp.
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Definition at line 145 of file bilinearform.hpp.
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Definition at line 226 of file bilinearform.hpp.
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Call this method after solving a linear system constructed using the FormLinearSystem method to recover the solution as a GridFunction-size vector in x. Use the same arguments as in the FormLinearSystem call.
Reimplemented from mfem::Operator.
Reimplemented in mfem::ParBilinearForm.
Definition at line 610 of file bilinearform.cpp.
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Return the trace FE space associated with static condensation.
Definition at line 103 of file bilinearform.hpp.
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Get the size of the BilinearForm as a square matrix.
Definition at line 90 of file bilinearform.hpp.
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Returns a reference to the sparse matrix.
Definition at line 185 of file bilinearform.hpp.
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Definition at line 190 of file bilinearform.hpp.
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Returns a reference to the sparse matrix of eliminated b.c.
Definition at line 198 of file bilinearform.hpp.
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Definition at line 203 of file bilinearform.hpp.
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Check if static condensation was actually enabled by a previous call to EnableStaticCondensation.
Definition at line 100 of file bilinearform.hpp.
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Reimplemented in mfem::ParBilinearForm.
Definition at line 834 of file bilinearform.cpp.
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For scalar FE spaces, precompute the sparsity pattern of the matrix (assuming dense element matrices) based on the types of integrators present in the bilinear form.
Definition at line 116 of file bilinearform.hpp.
void mfem::BilinearForm::UseSparsity | ( | int * | I, |
int * | J, | ||
bool | isSorted | ||
) |
Use the given CSR sparsity pattern to allocate the internal SparseMatrix.
Definition at line 151 of file bilinearform.cpp.
void mfem::BilinearForm::UseSparsity | ( | SparseMatrix & | A | ) |
Use the sparsity of A to allocate the internal SparseMatrix.
Definition at line 167 of file bilinearform.cpp.
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Set of Boundary Integrators to be applied.
Definition at line 51 of file bilinearform.hpp.
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Set of boundary face Integrators to be applied.
Definition at line 57 of file bilinearform.hpp.
Definition at line 58 of file bilinearform.hpp.
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Set of Domain Integrators to be applied.
Definition at line 48 of file bilinearform.hpp.
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Definition at line 63 of file bilinearform.hpp.
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Definition at line 60 of file bilinearform.hpp.
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Definition at line 45 of file bilinearform.hpp.
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Set of interior face Integrators to be applied.
Definition at line 54 of file bilinearform.hpp.
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FE space on which the form lives.
Definition at line 39 of file bilinearform.hpp.
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Definition at line 66 of file bilinearform.hpp.
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Sparse matrix to be associated with the form.
Definition at line 33 of file bilinearform.hpp.
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Matrix used to eliminate b.c.
Definition at line 36 of file bilinearform.hpp.
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Definition at line 68 of file bilinearform.hpp.
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Indicates the Mesh::sequence corresponding to the current state of the BilinearForm.
Definition at line 43 of file bilinearform.hpp.
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Definition at line 65 of file bilinearform.hpp.
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Definition at line 61 of file bilinearform.hpp.