 MFEM  v4.3.0 Finite element discretization library

#include <operator.hpp>

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## Public Member Functions

The TimedependentAdjointOperator extends the TimeDependentOperator class to use features in SUNDIALS CVODESSolver for computing quadratures and solving adjoint problems. More...

Destructor. More...

virtual void QuadratureIntegration (const Vector &y, Vector &qdot) const
Provide the operator integration of a quadrature equation. More...

virtual void AdjointRateMult (const Vector &y, Vector &yB, Vector &yBdot) const =0
Perform the action of the operator: yBdot = k = f(y,@2 yB, t), where. More...

virtual void QuadratureSensitivityMult (const Vector &y, const Vector &yB, Vector &qBdot) const
Provides the sensitivity of the quadrature w.r.t to primal and adjoint solutions. More...

virtual int SUNImplicitSetupB (const double t, const Vector &x, const Vector &xB, const Vector &fxB, int jokB, int *jcurB, double gammaB)
Setup the ODE linear system $$A(x,t) = (I - gamma J)$$ or $$A = (M - gamma J)$$, where $$J(x,t) = \frac{df}{dt(x,t)}$$. More...

virtual int SUNImplicitSolveB (Vector &x, const Vector &b, double tol)
Solve the ODE linear system $$A(x,xB,t) xB = b$$ as setup by the method SUNImplicitSetup(). More...

Returns the size of the adjoint problem state space. More... Public Member Functions inherited from mfem::TimeDependentOperator
TimeDependentOperator (int n=0, double t_=0.0, Type type_=EXPLICIT)
Construct a "square" TimeDependentOperator y = f(x,t), where x and y have the same dimension n. More...

TimeDependentOperator (int h, int w, double t_=0.0, Type type_=EXPLICIT)
Construct a TimeDependentOperator y = f(x,t), where x and y have dimensions w and h, respectively. More...

virtual double GetTime () const
Read the currently set time. More...

virtual void SetTime (const double t_)
Set the current time. More...

bool isExplicit () const
True if type is EXPLICIT. More...

bool isImplicit () const
True if type is IMPLICIT or HOMOGENEOUS. More...

bool isHomogeneous () const
True if type is HOMOGENEOUS. More...

EvalMode GetEvalMode () const
Return the current evaluation mode. See SetEvalMode() for details. More...

virtual void SetEvalMode (const EvalMode new_eval_mode)
Set the evaluation mode of the time-dependent operator. More...

virtual void ExplicitMult (const Vector &x, Vector &y) const
Perform the action of the explicit part of the operator, G: y = G(x, t) where t is the current time. More...

virtual void ImplicitMult (const Vector &x, const Vector &k, Vector &y) const
Perform the action of the implicit part of the operator, F: y = F(x, k, t) where t is the current time. More...

virtual void Mult (const Vector &x, Vector &y) const
Perform the action of the operator: y = k = f(x, t), where k solves the algebraic equation F(x, k, t) = G(x, t) and t is the current time. More...

virtual void ImplicitSolve (const double dt, const Vector &x, Vector &k)
Solve the equation: k = f(x + dt k, t), for the unknown k at the current time t. More...

virtual OperatorGetImplicitGradient (const Vector &x, const Vector &k, double shift) const
Return an Operator representing (dF/dk shift + dF/dx) at the given x, k, and the currently set time. More...

virtual OperatorGetExplicitGradient (const Vector &x) const
Return an Operator representing dG/dx at the given point x and the currently set time. More...

virtual int SUNImplicitSetup (const Vector &x, const Vector &fx, int jok, int *jcur, double gamma)
Setup the ODE linear system $$A(x,t) = (I - gamma J)$$ or $$A = (M - gamma J)$$, where $$J(x,t) = \frac{df}{dt(x,t)}$$. More...

virtual int SUNImplicitSolve (const Vector &b, Vector &x, double tol)
Solve the ODE linear system $$A x = b$$ as setup by the method SUNImplicitSetup(). More...

virtual int SUNMassSetup ()
Setup the mass matrix in the ODE system $$M y' = f(y,t)$$ . More...

virtual int SUNMassSolve (const Vector &b, Vector &x, double tol)
Solve the mass matrix linear system $$M x = b$$ as setup by the method SUNMassSetup(). More...

virtual int SUNMassMult (const Vector &x, Vector &v)
Compute the mass matrix-vector product $$v = M x$$ . More...

virtual ~TimeDependentOperator () 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 OperatorGetGradient (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 OperatorGetProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity. More...

virtual const OperatorGetRestriction () const
Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity. More...

virtual const OperatorGetOutputProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity. More...

virtual const OperatorGetOutputRestrictionTranspose () const
Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators. More...

virtual const OperatorGetOutputRestriction () 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=0, int m=0) const
Prints operator with input size n and output size m in Matlab format. More...

virtual ~Operator ()
Virtual destructor. More...

Type GetType () const
Return the type ID of the Operator class. More...

## Protected Attributes Protected Attributes inherited from mfem::TimeDependentOperator
double t
Current time. More...

Type type
Describes the form of the TimeDependentOperator. More...

EvalMode eval_mode
Current evaluation mode. 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... Public Types inherited from mfem::TimeDependentOperator
enum  Type { EXPLICIT, IMPLICIT, HOMOGENEOUS }

Evaluation mode. See SetEvalMode() for details. More... 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
}
Enumeration defining IDs for some classes derived from Operator. 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...

OperatorSetupRAP (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...

## Detailed Description

TimeDependentAdjointOperator is a TimeDependentOperator with Adjoint rate equations to be used with CVODESSolver.

Definition at line 471 of file operator.hpp.

## Constructor & Destructor Documentation

 mfem::TimeDependentAdjointOperator::TimeDependentAdjointOperator ( int dim, int adjdim, double t = 0., Type type = EXPLICIT )
inline

The TimedependentAdjointOperator extends the TimeDependentOperator class to use features in SUNDIALS CVODESSolver for computing quadratures and solving adjoint problems.

To solve adjoint problems one needs to implement the AdjointRateMult method to tell CVODES what the adjoint rate equation is.

QuadratureIntegration (optional) can be used to compute values over the forward problem

QuadratureSensitivityMult (optional) can be used to find the sensitivity of the quadrature using the adjoint solution in part.

SUNImplicitSetupB (optional) can be used to setup custom solvers for the newton solve for the adjoint problem.

SUNImplicitSolveB (optional) actually uses the solvers from SUNImplicitSetupB to solve the adjoint problem.

See SUNDIALS user manuals for specifics.

Parameters
 [in] dim Dimension of the forward operator [in] adjdim Dimension of the adjoint operator. Typically it is the same size as dim. However, SUNDIALS allows users to specify the size if one wants to perform custom operations. [in] t Starting time to set [in] type The TimeDependentOperator type

Definition at line 504 of file operator.hpp.

inlinevirtual

Destructor.

Definition at line 511 of file operator.hpp.

## Member Function Documentation

 virtual void mfem::TimeDependentAdjointOperator::AdjointRateMult ( const Vector & y, Vector & yB, Vector & yBdot ) const
pure virtual

Perform the action of the operator: yBdot = k = f(y,@2 yB, t), where.

Parameters
 [in] y The primal solution at time t [in] yB The adjoint solution at time t [out] yBdot the rate at time t
inline

Returns the size of the adjoint problem state space.

Definition at line 587 of file operator.hpp.

 virtual void mfem::TimeDependentAdjointOperator::QuadratureIntegration ( const Vector & y, Vector & qdot ) const
inlinevirtual

Provide the operator integration of a quadrature equation.

Parameters
 [in] y The current value at time t [out] qdot The current quadrature rate value at t

Definition at line 519 of file operator.hpp.

 virtual void mfem::TimeDependentAdjointOperator::QuadratureSensitivityMult ( const Vector & y, const Vector & yB, Vector & qBdot ) const
inlinevirtual

Provides the sensitivity of the quadrature w.r.t to primal and adjoint solutions.

Parameters
 [in] y the value of the primal solution at time t [in] yB the value of the adjoint solution at time t [out] qBdot the value of the sensitivity of the quadrature rate at time t

Definition at line 540 of file operator.hpp.

 virtual int mfem::TimeDependentAdjointOperator::SUNImplicitSetupB ( const double t, const Vector & x, const Vector & xB, const Vector & fxB, int jokB, int * jcurB, double gammaB )
inlinevirtual

Setup the ODE linear system $$A(x,t) = (I - gamma J)$$ or $$A = (M - gamma J)$$, where $$J(x,t) = \frac{df}{dt(x,t)}$$.

Parameters
 [in] t The current time [in] x The state at which $$A(x,xB,t)$$ should be evaluated. [in] xB The state at which $$A(x,xB,t)$$ should be evaluated. [in] fxB The current value of the ODE rhs function, $$f(x,t)$$. [in] jokB Flag indicating if the Jacobian should be updated. [out] jcurB Flag to signal if the Jacobian was updated. [in] gammaB The scaled time step value.

If not re-implemented, this method simply generates an error.

Presently, this method is used by SUNDIALS ODE solvers, for more details, see the SUNDIALS User Guides.

Definition at line 559 of file operator.hpp.

 virtual int mfem::TimeDependentAdjointOperator::SUNImplicitSolveB ( Vector & x, const Vector & b, double tol )
inlinevirtual

Solve the ODE linear system $$A(x,xB,t) xB = b$$ as setup by the method SUNImplicitSetup().

Parameters
 [in] b The linear system right-hand side. [in,out] x On input, the initial guess. On output, the solution. [in] tol Linear solve tolerance.

If not re-implemented, this method simply generates an error.

Presently, this method is used by SUNDIALS ODE solvers, for more details, see the SUNDIALS User Guides.

Definition at line 579 of file operator.hpp.