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MFEM
v4.5.2
Finite element discretization library
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MFEM
v4.5.2
Finite element discretization library
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An auxiliary Maxwell solver for a high-order curl-curl system without high-order assembly. More...
#include <auxiliary.hpp>
Public Member Functions | |
| MatrixFreeAMS (ParBilinearForm &aform, Operator &oper, ParFiniteElementSpace &nd_fespace, Coefficient *alpha_coeff, Coefficient *beta_coeff, MatrixCoefficient *beta_mcoeff, Array< int > &ess_bdr, #ifdef MFEM_USE_AMGX bool useAmgX=false, #endif int inner_pi_its=0, int inner_g_its=1, Solver *nd_smoother=NULL) | |
| Construct matrix-free AMS preconditioner. More... | |
| ~MatrixFreeAMS () | |
| void | SetOperator (const Operator &op) |
| Set/update the solver for the given operator. More... | |
| void | Mult (const Vector &x, Vector &y) const |
Operator application: y=A(x). More... | |
 Public Member Functions inherited from mfem::Solver | |
| Solver (int s=0, bool iter_mode=false) | |
| Initialize a square Solver with size s. More... | |
| Solver (int h, int w, bool iter_mode=false) | |
| Initialize a Solver with height h and width w. More... | |
| Public Member Functions inherited from mfem::Operator | |
| void | InitTVectors (const Operator *Po, const Operator *Ri, const Operator *Pi, Vector &x, Vector &b, Vector &X, Vector &B) const |
| Initializes memory for true vectors of linear system. More... | |
| 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 MemoryClass | GetMemoryClass () const |
| Return the MemoryClass preferred by the Operator. More... | |
| 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... | |
| virtual void | AddMult (const Vector &x, Vector &y, const double a=1.0) const |
Operator application: y+=A(x) (default) or y+=a*A(x). More... | |
| virtual void | AddMultTranspose (const Vector &x, Vector &y, const double a=1.0) const |
Operator transpose application: y+=A^t(x) (default) or y+=a*A^t(x). More... | |
| virtual void | ArrayMult (const Array< const Vector *> &X, Array< Vector *> &Y) const |
Operator application on a matrix: Y=A(X). More... | |
| virtual void | ArrayMultTranspose (const Array< const Vector *> &X, Array< Vector *> &Y) const |
Action of the transpose operator on a matrix: Y=A^t(X). More... | |
| virtual void | ArrayAddMult (const Array< const Vector *> &X, Array< Vector *> &Y, const double a=1.0) const |
Operator application on a matrix: Y+=A(X) (default) or Y+=a*A(X). More... | |
| virtual void | ArrayAddMultTranspose (const Array< const Vector *> &X, Array< Vector *> &Y, const double a=1.0) const |
Operator transpose application on a matrix: Y+=A^t(X) (default) or Y+=a*A^t(X). 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... | |
| virtual void | AssembleDiagonal (Vector &diag) const |
| Computes the diagonal entries into diag. Typically, this operation only makes sense for linear Operators. In some cases, only an approximation of the diagonal is computed. More... | |
| virtual const Operator * | GetProlongation () const |
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity. More... | |
| virtual const Operator * | GetRestriction () const |
Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity. More... | |
| virtual const Operator * | GetOutputProlongation () const |
Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity. More... | |
| virtual const Operator * | GetOutputRestrictionTranspose () const |
| Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators. More... | |
| virtual const Operator * | GetOutputRestriction () const |
Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. NULL means identity. 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 | FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B) |
| Form a column-constrained linear system using a matrix-free approach. More... | |
| virtual void | RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x) |
| Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem() or Operator::FormRectangularLinearSystem(). More... | |
| void | FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A) |
| Return in A a parallel (on truedofs) version of this square operator. More... | |
| void | FormRectangularSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Operator *&A) |
| Return in A a parallel (on truedofs) version of this rectangular operator (including constraints). More... | |
| void | FormDiscreteOperator (Operator *&A) |
| Return in A a parallel (on truedofs) version of this rectangular operator. More... | |
| void | PrintMatlab (std::ostream &out, int n, int m=0) const |
| Prints operator with input size n and output size m in Matlab format. More... | |
| virtual void | PrintMatlab (std::ostream &out) const |
| Prints operator in Matlab format. More... | |
| virtual | ~Operator () |
| Virtual destructor. More... | |
| Type | GetType () const |
| Return the type ID of the Operator class. More... | |
Additional Inherited Members | |
| Public Types inherited from mfem::Operator | |
| enum | DiagonalPolicy { DIAG_ZERO, DIAG_ONE, DIAG_KEEP } |
| Defines operator diagonal policy upon elimination of rows and/or columns. More... | |
| enum | Type { ANY_TYPE, MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC, Complex_Operator, MFEM_ComplexSparseMat, Complex_Hypre_ParCSR, Complex_DenseMat, MFEM_Block_Matrix, MFEM_Block_Operator } |
| Enumeration defining IDs for some classes derived from Operator. More... | |
| Public Attributes inherited from mfem::Solver | |
| bool | iterative_mode |
| If true, use the second argument of Mult() as an initial guess. More... | |
| Protected Member Functions inherited from mfem::Operator | |
| void | FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout) |
| see FormSystemOperator() More... | |
| void | FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout) |
| see FormRectangularSystemOperator() More... | |
| Operator * | SetupRAP (const Operator *Pi, const Operator *Po) |
| Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt". More... | |
| 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... | |
An auxiliary Maxwell solver for a high-order curl-curl system without high-order assembly.
The auxiliary space solves are done using a low-order refined approach, but all the interpolation operators, residuals, etc. are done in a matrix-free manner.
See Barker and Kolev, Matrix-free preconditioning for high-order H(curl) discretizations (https://doi.org/10.1002/nla.2348)
Definition at line 168 of file auxiliary.hpp.
| mfem::MatrixFreeAMS::MatrixFreeAMS | ( | ParBilinearForm & | aform, |
| Operator & | oper, | ||
| ParFiniteElementSpace & | nd_fespace, | ||
| Coefficient * | alpha_coeff, | ||
| Coefficient * | beta_coeff, | ||
| MatrixCoefficient * | beta_mcoeff, | ||
| Array< int > & | ess_bdr, | ||
| #ifdef MFEM_USE_AMGX bool | useAmgX = false, |
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| #endif int | inner_pi_its = 0, |
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| int | inner_g_its = 1, |
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| Solver * | nd_smoother = NULL |
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| ) |
Construct matrix-free AMS preconditioner.
| aform | BilinearForm for curl-curl problem, generally will have a CurlCurlIntegrator and possibly a VectorFEMassIntegrator. |
| oper | Operator to precondition. |
| nd_fespace | Underlying Nedelec finite element space. |
| alpha_coeff | Coefficient on curl-curl term in Maxwell problem (can be null, in which case constant 1 is assumed) |
| beta_coeff | (scalar) coefficient on mass term in Maxwell problem |
| beta_mcoeff | (matrix) coefficient on mass term |
| ess_bdr | Boundary attributes that are marked essential. In contrast to other MFEM cases, these are attributes not dofs, because we need to apply these boundary conditions to different bilinear forms. |
| useAmgX | Use AmgX (instead of hypre) for LOR problems |
| inner_pi_its | Number of CG iterations on auxiliary pi space, may need more for difficult coefficients |
| inner_g_its | Number of CG iterations on auxiliary g space, may need more for difficult coefficients |
| nd_smoother | Optional user-provided smoother for Nedelec space, this object takes ownership and will delete. |
Definition at line 426 of file auxiliary.cpp.
| mfem::MatrixFreeAMS::~MatrixFreeAMS | ( | ) |
Definition at line 499 of file auxiliary.cpp.
Operator application: y=A(x).
Implements mfem::Operator.
Definition at line 208 of file auxiliary.hpp.
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inlinevirtual |
Set/update the solver for the given operator.
Implements mfem::Solver.
Definition at line 206 of file auxiliary.hpp.
1.8.14