sdc.hh File Reference

#include <boost/timer/timer.hpp>
#include "dune/grid/config.h"
#include "dune/istl/operators.hh"
#include "dune/istl/solvers.hh"
#include "dune/common/dynvector.hh"
#include "linalg/dynamicMatrix.hh"
#include "utilities/timing.hh"
#include <cassert>

Go to the source code of this file.

Classes
class	Kaskade::SDCTimeGrid
	Abstract base class of time grids for (block) spectral defect correction methods. More...
class	Kaskade::SDCGridImplementationBase
	A convenience class simplifying the implementation of different SDCTimeGrid derived classes. More...
class	Kaskade::LobattoTimeGrid
	spectral time grid for defect correction methods with Lobatto points on \( [a,b]\) More...
class	Kaskade::RadauTimeGrid
	spectral time grid for defect correction methods with Radau points on \( [a,b]\). More...
class	Kaskade::GaussTimeGrid
	spectral time grid for defect correction methods with Gauss points More...
class	Kaskade::Sdc< Vector >
	Encapsulates the state of an SDC fixed point iteration and provides stepping. More...

Namespaces
namespace	Kaskade

Functions
template<class Matrix , class Vectors , class ReactionDerivatives , class Solver >
Matrix::field_type	Kaskade::sdcIterationStep (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix const &Shat, Solver const &solve, Matrix const &M, Matrix const &A, Vectors const &r, ReactionDerivatives const &f_u, Vectors const &u, Vectors &du)
	A single spectral defect correction iteration sweep. More...
template<class Matrix , class Vectors , class Solver >
Matrix::field_type	Kaskade::sdcIMEXStep (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix const &Shat, Solver const &solve, Matrix const &M, Matrix const &A, Vectors const &r, Vectors const &u, Vectors &du)
	A single IMEX SDIRK spectral deferred correction sweep. More...
template<class Matrix , class Vectors , class ReactionDerivatives , class Solver >
Matrix::field_type	Kaskade::sdcIterationStep2 (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix const &Shat, Solver const &solve, Matrix const &M, Matrix const &A, Vectors const &rUi, ReactionDerivatives const &f_u, Vectors const &Mdu, Vectors &du)
	A single spectral defect correction iteration sweep. More...
template<class Matrix , class Vectors , class ReactionDerivatives >
double	Kaskade::waveformRelaxationStep2 (SDCTimeGrid const &grid, Matrix const &M, Matrix const &A, Vectors const &rUi, ReactionDerivatives const &f_u, Vectors &du)
	A single waveform relaxation iteration. More...
Approximate integration matrices
The convergence properties of SDC are essentially defined by the selection of an approximate integration matrix \( \hat S \) acting as a lower triangular preconditioner for the spectral integration matrix \( S \). We provide several choices.
void	Kaskade::eulerIntegrationMatrix (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix &Shat)
	Triangular approximate integration matrix \( \hat S \) corresponding to the implicit Euler integrator. More...
SDCTimeGrid::RealMatrix	Kaskade::eulerIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to the implicit Euler integrator. More...
void	Kaskade::luIntegrationMatrix (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix &Shat)
	Triangular approximate integration matrix \( \hat S \) corresponding to a specialized DIRK sweep. More...
SDCTimeGrid::RealMatrix	Kaskade::luIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to a specialized DIRK sweep. More...
SDCTimeGrid::RealMatrix	Kaskade::singleEulerIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to an Euler sweep with constant "step size". More...
SDCTimeGrid::RealMatrix	Kaskade::SDIRKIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to an SDIRK sweep (i.e. with constant "step size"). More...