This class is able to do Matrix inversion in parallel with PETSC solvers. More...

Detailed Description

template<>
class petsc_solver< double >

This class is able to do Matrix inversion in parallel with PETSC solvers.

Example of use of this class

    // velocity in the grid is the property 0, pressure is the property 1
    constexpr int velocity = 0;
    constexpr int pressure = 1;
    // Domain, a rectangle
    Box<2,float> domain({0.0,0.0},{3.0,1.0});
    // Ghost (Not important in this case but required)
    Ghost<2,float> g(0.01);
    // Grid points on x=256 and y=64
    long int sz[] = {256,64};
    size_t szu[2];
    szu[0] = (size_t)sz[0];
    szu[1] = (size_t)sz[1];
    // We need one more point on the left and down part of the domain
    // This is given by the boundary conditions that we impose, the
    // reason is mathematical in order to have a well defined system
    // and cannot be discussed here
    Padding<2> pd({1,1},{0,0});
    // Distributed grid that store the solution
    grid_dist_id<2,float,aggregate<float[2],float>,CartDecomposition<2,float>> g_dist(szu,domain,g);
    // It is the maximum extension of the stencil
    Ghost<2,long int> stencil_max(1);
    // Finite difference scheme
    FDScheme<lid_nn> fd(pd, stencil_max, domain,g_dist);
    // Here we impose the equation, we start from the incompressibility Eq imposed in the bulk with the
    // exception of the first point {0,0} and than we set P = 0 in {0,0}, why we are doing this is again
    // mathematical to have a well defined system, an intuitive explanation is that P and P + c are both
    // solution for the incompressibility equation, this produce an ill-posed problem to make it well posed
    // we set one point in this case {0,0} the pressure to a fixed constant for convenience P = 0
    fd.impose(ic_eq(),0.0, EQ_3, {0,0},{sz[0]-2,sz[1]-2},true);
    fd.impose(Prs(),  0.0, EQ_3, {0,0},{0,0});
    // Here we impose the Eq1 and Eq2
    fd.impose(vx_eq(),0.0, EQ_1, {1,0},{sz[0]-2,sz[1]-2});
    fd.impose(vy_eq(),0.0, EQ_2, {0,1},{sz[0]-2,sz[1]-2});
    // v_x and v_y
    // Imposing B1
    fd.impose(v_x(),0.0, EQ_1, {0,0},{0,sz[1]-2});
    fd.impose(avg_vy_f(),0.0, EQ_2 , {-1,0},{-1,sz[1]-1});
    // Imposing B2
    fd.impose(v_x(),0.0, EQ_1, {sz[0]-1,0},{sz[0]-1,sz[1]-2});
    fd.impose(avg_vy(),1.0, EQ_2,    {sz[0]-1,0},{sz[0]-1,sz[1]-1});
    // Imposing B3
    fd.impose(avg_vx_f(),0.0, EQ_1, {0,-1},{sz[0]-1,-1});
    fd.impose(v_y(), 0.0, EQ_2, {0,0},{sz[0]-2,0});
    // Imposing B4
    fd.impose(avg_vx(),0.0, EQ_1,   {0,sz[1]-1},{sz[0]-1,sz[1]-1});
    fd.impose(v_y(), 0.0, EQ_2, {0,sz[1]-1},{sz[0]-2,sz[1]-1});
    // When we pad the grid, there are points of the grid that are not
    // touched by the previous condition. Mathematically this lead
    // to have too many variables for the conditions that we are imposing.
    // Here we are imposing variables that we do not touch to zero
    //
    // Padding pressure
    fd.impose(Prs(), 0.0, EQ_3, {-1,-1},{sz[0]-1,-1});
    fd.impose(Prs(), 0.0, EQ_3, {-1,sz[1]-1},{sz[0]-1,sz[1]-1});
    fd.impose(Prs(), 0.0, EQ_3, {-1,0},{-1,sz[1]-2});
    fd.impose(Prs(), 0.0, EQ_3, {sz[0]-1,0},{sz[0]-1,sz[1]-2});
    // Impose v_x Padding Impose v_y padding
    fd.impose(v_x(), 0.0, EQ_1, {-1,-1},{-1,sz[1]-1});
    fd.impose(v_y(), 0.0, EQ_2, {-1,-1},{sz[0]-1,-1});
    solver_type solver;
    auto x = solver.solve(fd.getA(),fd.getB());

Definition at line 101 of file petsc_solver.hpp.

#include <petsc_solver.hpp>

Data Structures
struct	itError
	contain the infinity norm of the residual at each iteration More...

struct	solv_bench_info
	It contain the benchmark information for each solver. More...

Public Types
typedef Vector< double, PETSC_BASE >	return_type
	Type of the solution object.

Public Member Functions
void	addTestSolver (std::string &solver)
	Add a test solver. More...

void	removeTestSolver (const std::string &solver)
	Remove a test solver. More...

void	log_monitor ()
	Set the Petsc solver. More...

void	setSolver (KSPType type)
	Set the Petsc solver. More...

void	setRelTol (PetscReal rtol_)
	Set the relative tolerance as stop criteria. More...

void	setAbsTol (PetscReal abstol_)
	Set the absolute tolerance as stop criteria. More...

void	setDivTol (PetscReal dtol_)
	Set the divergence tolerance. More...

void	setMaxIter (PetscInt n)
	Set the maximum number of iteration for Krylov solvers. More...

void	searchDirections (PetscInt l)

void	setRestart (PetscInt n)
	For GMRES based method, the number of Krylov directions to orthogonalize against. More...

void	setPreconditioner (PCType type)
	Set the preconditioner of the linear solver. More...

void	setPreconditionerAMG_nl (int nl)
	Set the number of levels for the algebraic-multigrid preconditioner. More...

void	setPreconditionerAMG_maxit (int nit)
	Set the maximum number of V or W cycle for algebraic-multi-grid. More...

void	setPreconditionerAMG_relax (const std::string &type, int k=REL_ALL)
	Set the relaxation method for the algebraic-multi-grid preconditioner. More...

void	setPreconditionerAMG_cycleType (const std::string &cycle_type, int sweep_up=-1, int sweep_dw=-1, int sweep_crs=-1)
	It set the type of cycle and optionally the number of sweep. More...

void	setPreconditionerAMG_coarsen (const std::string &type)
	Set the coarsening method for the algebraic-multi-grid preconditioner. More...

void	setPreconditionerAMG_interp (const std::string &type)
	Set the interpolation method for the algebraic-multi-grid preconditioner. More...

void	setPreconditionerAMG_coarsenNodalType (int norm)
	Set the block coarsening norm type. More...

void	setPreconditionerAMG_interp_eu_level (int k)
	Indicate the number of levels in the ILU(k) for the Euclid smoother. More...

void	setBlockSize (int block_sz)
	Set how many degree of freedom each node has. More...

Vector< double, PETSC_BASE >	solve (SparseMatrix< double, int, PETSC_BASE > &A, const Vector< double, PETSC_BASE > &b, bool initial_guess=false)
	Here we invert the matrix and solve the system. More...

KSP	getKSP ()
	Return the KSP solver. More...

solError	get_residual_error (SparseMatrix< double, int, PETSC_BASE > &A, const Vector< double, PETSC_BASE > &x, const Vector< double, PETSC_BASE > &b)
	It return the resiual error. More...

solError	get_residual_error (const Vector< double, PETSC_BASE > &x, const Vector< double, PETSC_BASE > &b)
	It return the resiual error. More...

bool	solve (SparseMatrix< double, int, PETSC_BASE > &A, Vector< double, PETSC_BASE > &x, const Vector< double, PETSC_BASE > &b)
	Here we invert the matrix and solve the system. More...

Vector< double, PETSC_BASE >	solve (const Vector< double, PETSC_BASE > &b)
	Here we invert the matrix and solve the system. More...

bool	solve (Vector< double, PETSC_BASE > &x, const Vector< double, PETSC_BASE > &b)
	Here we invert the matrix and solve the system. More...

void	setPetscOption (const char name, const char value)
	this function give you the possibility to set PETSC options More...

Vector< double, PETSC_BASE >	try_solve (SparseMatrix< double, int, PETSC_BASE > &A, const Vector< double, PETSC_BASE > &b)
	Try to solve the system using all the solvers and generate a report. More...

Private Member Functions
void	write_bench_report ()
	Here we write the benchmark report. More...

void	pre_solve_impl (const Mat &A_, const Vec &b_, Vec &x_)
	It set up the solver based on the provided options. More...

void	print_progress_bar ()
	Print a progress bar on standard out. More...

void	progress (PetscInt it)
	This function print an "*" showing the progress of the solvers. More...

void	print_stat (solError &err)
	Print statistic about the solution error and method used. More...

std::string	to_string_method (const std::string &solv)
	It convert the KSP type into a human read-able string. More...

void	new_bench (const std::string &str)
	Allocate a new benchmark slot for a method. More...

void	copy_if_better (double res, Vec &sol, double &best_res, Vec &best_sol)
	Copy the solution if better. More...

void	try_solve_simple (const Mat &A_, const Vec &b_, Vec &x_)
	Try to solve the system x=inv(A)*b using all the Krylov solvers with simple Jacobi pre-conditioner. More...

void	bench_solve_simple (const Mat &A_, const Vec &b_, Vec &x_, solv_bench_info &bench)
	Benchmark solve simple solving x=inv(A)*b. More...

void	solve_simple (const Mat &A_, const Vec &b_, Vec &x_)
	solve simple use a Krylov solver + Simple selected Parallel Pre-conditioner More...

void	solve_simple (const Vec &b_, Vec &x_)
	solve simple use a Krylov solver + Simple selected Parallel Pre-conditioner More...

void	initKSP ()
	initialize the KSP object More...

void	initKSPForTest ()
	initialize the KSP object for solver testing More...

void	destroyKSP ()
	Destroy the KSP object. More...

Static Private Member Functions
static double	calculate_it (double t, solv_bench_info &slv)
	Calculate the residual error at time t for one method. More...

static PetscErrorCode	monitor_progress_residual (KSP ksp, PetscInt it, PetscReal res, void *data)
	procedure print the progress of the solver in benchmark mode More...

static solError	statSolutionError (const Mat &A_, const Vec &b_, Vec &x_, KSP ksp)
	Calculate statistic on the error solution. More...

static solError	getSolNormError (const Vec &b_, const Vec &x_, KSP ksp)
	Return the norm error of the solution. More...

static solError	getSolNormError (const Mat &A_, const Vec &b_, const Vec &x_)
	Return the norm error of the solution. More...

Private Attributes
bool	is_preconditioner_set = false
	indicate if the preconditioner is set

PetscInt	maxits
	KSP Maximum number of iterations.

KSP	ksp
	Main parallel solver.

size_t	tmp
	Temporal variable used for calculation of static members.

openfpm::vector< std::string >	solvs
	The full set of solvers.

openfpm::vector< solv_bench_info >	bench
	It contain the solver benchmark results.

AMG_type	atype = NONE_AMG
	Type of the algebraic multi-grid preconditioner.

int	block_sz = 0
	Block size.

Member Function Documentation

void petsc_solver< double >::addTestSolver ( std::string & solver )

inline

Add a test solver.

The try solve function use the most robust solvers in PETSC, if you want to add additionally solver like KSPIBCGS,KSPFBCGSR,KSPPGMRES, use addTestSolver(std::string(KSPIBCGS))

Parameters

solver additional solver solver to test

Definition at line 834 of file petsc_solver.hpp.

void petsc_solver< double >::bench_solve_simple	(	const Mat &	A_,
		const Vec &	b_,
		Vec &	x_,
		solv_bench_info &	bench
	)

inlineprivate

Benchmark solve simple solving x=inv(A)*b.

Parameters

A_	Matrix A
b_	vector b
x_	solution x
bench	structure that store the benchmark information

Definition at line 604 of file petsc_solver.hpp.

static double petsc_solver< double >::calculate_it	(	double	t,
		solv_bench_info &	slv
	)

inlinestaticprivate

Calculate the residual error at time t for one method.

Parameters

t	time
slv	solver

Returns: the residual

Definition at line 168 of file petsc_solver.hpp.

void petsc_solver< double >::copy_if_better	(	double	res,
		Vec &	sol,
		double &	best_res,
		Vec &	best_sol
	)

inlineprivate

Copy the solution if better.

Parameters

res	Residual of the solution
sol	solution
best_res	residual of the best solution
best_sol	best solution

Definition at line 493 of file petsc_solver.hpp.

void petsc_solver< double >::destroyKSP ( )

inlineprivate

Destroy the KSP object.

Definition at line 726 of file petsc_solver.hpp.

solError petsc_solver< double >::get_residual_error	(	SparseMatrix< double, int, PETSC_BASE > &	A,
		const Vector< double, PETSC_BASE > &	x,
		const Vector< double, PETSC_BASE > &	b
	)

inline

It return the resiual error.

Parameters

A	Sparse matrix
x	solution
b	right-hand-side

Returns: the solution error norms

Definition at line 1312 of file petsc_solver.hpp.

solError petsc_solver< double >::get_residual_error	(	const Vector< double, PETSC_BASE > &	x,
		const Vector< double, PETSC_BASE > &	b
	)

inline

It return the resiual error.

Parameters

x	solution
b	right-hand-side

Returns: the solution error norms

Definition at line 1325 of file petsc_solver.hpp.

KSP petsc_solver< double >::getKSP ( )

inline

Return the KSP solver.

In case you want to do fine tuning of the KSP solver before solve your system whith this function you can retrieve the KSP object

Returns: the Krylov solver

Definition at line 1298 of file petsc_solver.hpp.

static solError petsc_solver< double >::getSolNormError	(	const Vec &	b_,
		const Vec &	x_,
		KSP	ksp
	)

inlinestaticprivate

Return the norm error of the solution.

Parameters

x_	the solution
b_	the right-hand-side
ksp	Krylov solver

Returns: the solution error

Definition at line 740 of file petsc_solver.hpp.

static solError petsc_solver< double >::getSolNormError	(	const Mat &	A_,
		const Vec &	b_,
		const Vec &	x_
	)

inlinestaticprivate

Return the norm error of the solution.

Parameters

A_	the matrix that identity the linear system
x_	the solution
b_	the right-hand-side

Returns: the solution error

Definition at line 758 of file petsc_solver.hpp.

void petsc_solver< double >::initKSP ( )

inlineprivate

initialize the KSP object

Definition at line 706 of file petsc_solver.hpp.

void petsc_solver< double >::initKSPForTest ( )

inlineprivate

initialize the KSP object for solver testing

Definition at line 715 of file petsc_solver.hpp.

void petsc_solver< double >::log_monitor ( )

inline

Set the Petsc solver.

See Also: KSPType in PETSC manual for a list of all PETSC solvers

Definition at line 864 of file petsc_solver.hpp.

static PetscErrorCode petsc_solver< double >::monitor_progress_residual	(	KSP	ksp,
		PetscInt	it,
		PetscReal	res,
		void *	data
	)

inlinestaticprivate

procedure print the progress of the solver in benchmark mode

Parameters

ksp	Solver
it	Iteration number
res	resudual
data	custom pointer to data

Returns: always zero

Definition at line 339 of file petsc_solver.hpp.

void petsc_solver< double >::new_bench ( const std::string & str )

inlineprivate

Allocate a new benchmark slot for a method.

Parameters

str	Method name

Definition at line 477 of file petsc_solver.hpp.

void petsc_solver< double >::pre_solve_impl	(	const Mat &	A_,
		const Vec &	b_,
		Vec &	x_
	)

inlineprivate

It set up the solver based on the provided options.

Parameters

A_	Matrix
x_	solution
b_	right-hand-side

Definition at line 300 of file petsc_solver.hpp.

void petsc_solver< double >::print_progress_bar ( )

inlineprivate

Print a progress bar on standard out.

Definition at line 320 of file petsc_solver.hpp.

void petsc_solver< double >::print_stat ( solError & err )

inlineprivate

Print statistic about the solution error and method used.

Parameters

err	structure that contain the solution errors

Definition at line 405 of file petsc_solver.hpp.

void petsc_solver< double >::progress ( PetscInt it )

inlineprivate

This function print an "*" showing the progress of the solvers.

Parameters

it	iteration number

Definition at line 380 of file petsc_solver.hpp.

void petsc_solver< double >::removeTestSolver ( const std::string & solver )

inline

Remove a test solver.

The try solve function use the most robust solvers in PETSC, if you want to remove a solver like use removeTestSolver(std::string(KSPIBCGS))

Parameters

solver remove solver to test

Definition at line 847 of file petsc_solver.hpp.

void petsc_solver< double >::searchDirections ( PetscInt l )

inline

For the BiCGStab(L) it define the number of search directions

BiCG Methods can fail for base break-down (or near break-down). BiCGStab(L) try to avoid this problem. Such method has a parameter L (2 by default) Bigger is L more the system will try to avoid the breakdown

Parameters

l	Increasing L should reduce the probability of failure of the solver because of break-down of the base

Definition at line 963 of file petsc_solver.hpp.

void petsc_solver< double >::setAbsTol ( PetscReal abstol_ )

inline

Set the absolute tolerance as stop criteria.

See Also: PETSC manual KSPSetTolerances for an explanation

Parameters

abstol_ Absolute tolerance

Definition at line 907 of file petsc_solver.hpp.

void petsc_solver< double >::setBlockSize ( int block_sz )

inline

Set how many degree of freedom each node has.

In case you are solving a system of equations this function, help in setting the degree of freedom each grid point has. Setting this parameter to the number of variables for each grid point it should improve the convergenve of the solvers in particular using algebraic-multi-grid

Parameters

block_sz number of degree of freedom

Definition at line 1243 of file petsc_solver.hpp.

void petsc_solver< double >::setDivTol ( PetscReal dtol_ )

inline

Set the divergence tolerance.

See Also: PETSC manual KSPSetTolerances for an explanation

Parameters

dtol_ tolerance

Definition at line 925 of file petsc_solver.hpp.

void petsc_solver< double >::setMaxIter ( PetscInt n )

inline

Set the maximum number of iteration for Krylov solvers.

Parameters

n	maximum number of iterations

Definition at line 941 of file petsc_solver.hpp.

void petsc_solver< double >::setPetscOption	(	const char *	name,
		const char *	value
	)

inline

this function give you the possibility to set PETSC options

this function call PetscOptionsSetValue

Parameters

name	the name of the option
value	the value of the option

Definition at line 1415 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditioner ( PCType type )

inline

Set the preconditioner of the linear solver.

The preconditoner that can be set are the same as PETSC

For a full list please visit Please visit: http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCType.html#PCType

An exception is PCHYPRE with BOOMERAMG in this case use PCHYPRE_BOOMERAMG. Many preconditioners has default values, but many times the default values are not good. Here we list some interesting case

Algebraic-multi-grid based preconditioners

Parameters for this type of preconditioner can be set using setPreconditionerAMG_* functions.

Number of levels set by setPreconditionerAMG_nl
Maximum number of cycles setPreconditionerAMG_maxit
Smooth or relax method setPreconditionerAMG_smooth,setPreconditionerAMG_relax
Cycle type and number of sweep (relaxation steps) when going up or down setPreconditionerAMG_cycleType
Coarsening method setPreconditionerAMG_coarsen
interpolation schemes setPreconditionerAMG_interp

Parameters

type	of the preconditioner

Definition at line 1005 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_coarsen ( const std::string & type )

inline

Set the coarsening method for the algebraic-multi-grid preconditioner.

Possible values can be "CLJP","Ruge-Stueben","modifiedRuge-Stueben","Falgout", "PMIS", "HMIS"

Warning: in case of big problem use PMIS or HMIS otherwise the AMG can hang (take a lot of time) in setup

Parameters

type	of the preconditioner smoothing operator

Definition at line 1150 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_coarsenNodalType ( int norm )

inline

Set the block coarsening norm type.

The use of this function make sanse if you specify the degree of freedom for each node using setBlockSize

0 (default each variable treat independently)
1 Frobenius norm
2 sum of absolute values of elements in each block
3 largest element in each block (not absolute value)
4 row-sum norm
6 sum of all values in each block

In case the matrix represent a system of equations in general

Parameters

norm type

Definition at line 1201 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_cycleType	(	const std::string &	cycle_type,
		int	sweep_up = `-1`,
		int	sweep_dw = `-1`,
		int	sweep_crs = `-1`
	)

inline

It set the type of cycle and optionally the number of sweep.

This function set the cycle type for the multigrid methods. Possible values are:

V cycle
W cycle

Optionally you can set the number of sweep or relaxation steps on each grid when going up and when going down

Parameters

cycle_type	cycle type
sweep_up
sweep_dw
sweep_crs	speep at the coarse level

Definition at line 1119 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_interp ( const std::string & type )

inline

Set the interpolation method for the algebraic-multi-grid preconditioner.

Possible values can be "classical", "direct", "multipass", "multipass-wts", "ext+i", "ext+i-cc", "standard", "standard-wts", "FF", "FF1"

Parameters

type	of the interpolation scheme

Definition at line 1172 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_interp_eu_level ( int k )

inline

Indicate the number of levels in the ILU(k) for the Euclid smoother.

Parameters

k	number of levels for the Euclid smoother

Definition at line 1218 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_maxit ( int nit )

inline

Set the maximum number of V or W cycle for algebraic-multi-grid.

Parameters

nit	number of levels

Definition at line 1054 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_nl ( int nl )

inline

Set the number of levels for the algebraic-multigrid preconditioner.

In case you select an algebraic preconditioner like PCHYPRE or PCGAMG you can set the number of levels using this function

Parameters

nl	number of levels

Definition at line 1037 of file petsc_solver.hpp.

void petsc_solver< double >::setPreconditionerAMG_relax	(	const std::string &	type,
		int	k = `REL_ALL`
	)

inline

Set the relaxation method for the algebraic-multi-grid preconditioner.

Possible values for relazation can be "Jacobi","sequential-Gauss-Seidel","seqboundary-Gauss-Seidel", "SOR/Jacobi","backward-SOR/Jacobi",hybrid chaotic Gauss-Seidel (works only with OpenMP), "symmetric-SOR/Jacobi","l1scaled-SOR/Jacobi","Gaussian-elimination","CG","Chebyshev", "FCF-Jacobi","l1scaled-Jacobi"

Every smooth operator can have additional parameters to be set in order to correctly work.

Parameters

type	of relax method
k	where is applied REL_UP,REL_DOWN,REL_ALL (default is all)

Definition at line 1086 of file petsc_solver.hpp.

void petsc_solver< double >::setRelTol ( PetscReal rtol_ )

inline

Set the relative tolerance as stop criteria.

See Also: PETSC manual KSPSetTolerances for an explanation

Parameters

rtol_ Relative tolerance

Definition at line 889 of file petsc_solver.hpp.

void petsc_solver< double >::setRestart ( PetscInt n )

inline

For GMRES based method, the number of Krylov directions to orthogonalize against.

Parameters

n	number of directions

Definition at line 973 of file petsc_solver.hpp.

void petsc_solver< double >::setSolver ( KSPType type )

inline

Set the Petsc solver.

See Also: KSPType in PETSC manual for a list of all PETSC solvers

Parameters

type	petsc solver type

Definition at line 877 of file petsc_solver.hpp.

Vector<double,PETSC_BASE> petsc_solver< double >::solve	(	SparseMatrix< double, int, PETSC_BASE > &	A,
		const Vector< double, PETSC_BASE > &	b,
		bool	initial_guess = `false`
	)

inline

Here we invert the matrix and solve the system.

Warning: umfpack is not a parallel solver, this function work only with one processor

Note: if you want to use umfpack in a NON parallel, but on a distributed data, use solve with triplet

Template Parameters

impl	Implementation of the SparseMatrix

Parameters

A	sparse matrix
b	vector
initial_guess	true if x has the initial guess

Returns: the solution

Definition at line 1263 of file petsc_solver.hpp.

bool petsc_solver< double >::solve	(	SparseMatrix< double, int, PETSC_BASE > &	A,
		Vector< double, PETSC_BASE > &	x,
		const Vector< double, PETSC_BASE > &	b
	)

inline

Here we invert the matrix and solve the system.

Parameters

A	sparse matrix
b	vector
x	solution and initial guess

Returns: true if succeed

Definition at line 1339 of file petsc_solver.hpp.

Vector<double,PETSC_BASE> petsc_solver< double >::solve ( const Vector< double, PETSC_BASE > & b )

inline

Here we invert the matrix and solve the system.

Parameters

b vector

Returns: true if succeed

Definition at line 1361 of file petsc_solver.hpp.

bool petsc_solver< double >::solve	(	Vector< double, PETSC_BASE > &	x,
		const Vector< double, PETSC_BASE > &	b
	)

inline

Here we invert the matrix and solve the system.

In this call we are interested in solving the system with multiple right-hand-side and the same Matrix. We do not set the Matrix again and this give us the possibility to-skip the preconditioning setting that in some case like Algebraic-multi-grid can be expensive

Parameters

b	vector
x	solution and initial guess

Returns: true if succeed

Definition at line 1396 of file petsc_solver.hpp.

void petsc_solver< double >::solve_simple	(	const Mat &	A_,
		const Vec &	b_,
		Vec &	x_
	)

inlineprivate

solve simple use a Krylov solver + Simple selected Parallel Pre-conditioner

Parameters

A_	SparseMatrix
b_	right-hand-side
x_	solution

Definition at line 641 of file petsc_solver.hpp.

void petsc_solver< double >::solve_simple	(	const Vec &	b_,
		Vec &	x_
	)

inlineprivate

solve simple use a Krylov solver + Simple selected Parallel Pre-conditioner

Parameters

b_	right hand side
x_	solution

Definition at line 672 of file petsc_solver.hpp.

static solError petsc_solver< double >::statSolutionError	(	const Mat &	A_,
		const Vec &	b_,
		Vec &	x_,
		KSP	ksp
	)

inlinestaticprivate

Calculate statistic on the error solution.

Parameters

A_	Matrix of the system
b_	Right hand side of the matrix
x_	Solution
ksp	Krylov solver

Returns: the solution error

Definition at line 688 of file petsc_solver.hpp.

std::string petsc_solver< double >::to_string_method ( const std::string & solv )

inlineprivate

It convert the KSP type into a human read-able string.

Parameters

solv	solver (short form)

Returns: the name of the solver in long form

Definition at line 426 of file petsc_solver.hpp.

Vector<double,PETSC_BASE> petsc_solver< double >::try_solve	(	SparseMatrix< double, int, PETSC_BASE > &	A,
		const Vector< double, PETSC_BASE > &	b
	)

inline

Try to solve the system using all the solvers and generate a report.

In this mode the system will try different Solvers, Preconditioner and combination of solvers in order to find the best solver in speed, and precision. As output it will produce a performance report

Parameters

A	Matrix to invert
b	right hand side

Returns: the solution

Definition at line 1431 of file petsc_solver.hpp.

void petsc_solver< double >::try_solve_simple	(	const Mat &	A_,
		const Vec &	b_,
		Vec &	x_
	)

inlineprivate

Try to solve the system x=inv(A)*b using all the Krylov solvers with simple Jacobi pre-conditioner.

It try to solve the system using JACOBI pre-conditioner and all the Krylov solvers available at the end it write a report

Parameters

A_	Matrix
b_	vector of coefficents
x_	solution

Definition at line 512 of file petsc_solver.hpp.

void petsc_solver< double >::write_bench_report ( )

inlineprivate

Here we write the benchmark report.

Definition at line 185 of file petsc_solver.hpp.

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

openfpm_numerics/src/Solvers/petsc_solver.hpp

Detailed Description

template<> class petsc_solver< double >

Example of use of this class

Data Structures

Public Types

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Member Function Documentation

Algebraic-multi-grid based preconditioners

template<>
class petsc_solver< double >