NumLib::NonlinearSystem< NonlinearSolverTag::Picard > Class Reference

Detailed Description

A System of nonlinear equations to be solved with the Picard fixpoint iteration method.

The Picard method will iterate the linearized equation \( \mathtt{A} \cdot x_i = \mathtt{rhs} \).

Definition at line 100 of file NonlinearSystem.h.

#include <NonlinearSystem.h>

Inheritance diagram for NumLib::NonlinearSystem< NonlinearSolverTag::Picard >:

Collaboration diagram for NumLib::NonlinearSystem< NonlinearSolverTag::Picard >:

Public Member Functions
virtual void	assemble (std::vector< GlobalVector * > const &x, std::vector< GlobalVector * > const &x_prev, int const process_id)=0
virtual std::vector< GlobalIndexType >	getIndicesOfResiduumWithoutInitialCompensation () const =0
virtual void	getA (GlobalMatrix &A) const =0
virtual void	getRhs (GlobalVector const &x_prev, GlobalVector &rhs) const =0
virtual void	getAandRhsNormalized (GlobalMatrix &A, GlobalVector &rhs) const =0
virtual void	computeKnownSolutions (GlobalVector const &x, int const process_id)=0
	Pre-compute known solutions and possibly store them internally.
virtual void	applyKnownSolutions (GlobalVector &x) const =0
virtual void	applyKnownSolutionsPicard (GlobalMatrix &A, GlobalVector &rhs, GlobalVector &x) const =0
virtual MathLib::LinearSolverBehaviour	linearSolverNeedsToCompute () const =0
Public Member Functions inherited from NumLib::EquationSystem
virtual bool	isLinear () const =0
virtual bool	requiresNormalization () const =0
virtual void	preIteration (const unsigned iter, GlobalVector const &x)
virtual IterationResult	postIteration (GlobalVector const &x)
virtual MathLib::MatrixSpecifications	getMatrixSpecifications (const int process_id) const =0
virtual	~EquationSystem ()=default

Member Function Documentation

applyKnownSolutions()

virtual void NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::applyKnownSolutions ( GlobalVector & x ) const

pure virtual

Apply known solutions to the solution vector x.

Precondition

computeKnownSolutions() must have been called before.

applyKnownSolutionsPicard()

virtual void NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::applyKnownSolutionsPicard ( GlobalMatrix & A, GlobalVector & rhs, GlobalVector & x ) const

pure virtual

Apply known solutions to the linearized equation system \( A \cdot x = \mathit{rhs} \).

Precondition

computeKnownSolutions() must have been called before.

assemble()

virtual void NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::assemble ( std::vector< GlobalVector * > const & x, std::vector< GlobalVector * > const & x_prev, int const process_id )

pure virtual

Assembles the linearized equation system at the point x. The linearized system is \(J(x) \cdot \Delta x = (x)\). Here the residual vector \(r(x)\) and its Jacobian \(J(x)\) are assembled.

computeKnownSolutions()

virtual void NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::computeKnownSolutions ( GlobalVector const & x, int const process_id )

pure virtual

Pre-compute known solutions and possibly store them internally.

getA()

virtual void NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::getA ( GlobalMatrix & A ) const

pure virtual

Writes the linearized equation system matrix to A.

Precondition

assemble() must have been called before.

getAandRhsNormalized()

virtual void NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::getAandRhsNormalized ( GlobalMatrix & A, GlobalVector & rhs ) const

pure virtual

Writes the A_transposed times A into A and also writes A_transposed times rhs into rhs

Precondition

getA() and getRhs must have been called before.

getIndicesOfResiduumWithoutInitialCompensation()

virtual std::vector< GlobalIndexType > NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::getIndicesOfResiduumWithoutInitialCompensation ( ) const

pure virtual

Returns

The global indices for the entries of the global residuum vector that do not need initial non-equilibrium compensation.

getRhs()

virtual void NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::getRhs ( GlobalVector const & x_prev, GlobalVector & rhs ) const

pure virtual

Writes the linearized equation system right-hand side to rhs.

Precondition

assemble() must have been called before.

linearSolverNeedsToCompute()

virtual MathLib::LinearSolverBehaviour NumLib::NonlinearSystem< NonlinearSolverTag::Picard >::linearSolverNeedsToCompute ( ) const

pure virtual

Returns whether the assembled matrix \(A\) has changed and the linear solver must perform the MathLib::EigenLinearSolver::compute() step.

---

The documentation for this class was generated from the following file:

• NumLib/ODESolver/NonlinearSystem.h