This modules provides the routines for solving Ax=b using the V-shaped multigrid method. More...

Detailed Description

This modules provides the routines for solving Ax=b using the V-shaped multigrid method.

Data Types
type	mg_solver_t

Functions/Subroutines
subroutine, public	multigrid_solver_init (this, namespace, space, mesh, thr)

recursive subroutine, public	multigrid_solver_v_cycle (this, der, op, sol, rhs)
	Performs one cycle of a V-shaped multigrid solver. More...

recursive subroutine, public	multigrid_solver_w_cycle (this, der, op, sol, rhs)
	Performs one cycle of a W-shaped multigrid solver. More...

subroutine, public	multigrid_iterative_solver (this, namespace, der, op, sol, rhs, multigrid_shape)
	An iterative multigrid solver. More...

recursive subroutine, public	multigrid_fmg_solver (this, namespace, der, op, sol, rhs)
	Full multigrid (FMG) solver. More...

subroutine	multigrid_solver_solve_coarsest (this, der, op, sol, rhs, residue)
	Computes the solution on the coarsest grid. More...

subroutine	get_residual (op, der, sol, rhs, residue)
	Computes the residual. More...

subroutine	multigrid_relax (this, mesh, der, op, sol, rhs, steps)
	Given a nonlocal operator op, perform the relaxation operator. More...

Variables
integer, parameter	gauss_seidel = 1

integer, parameter	weighted_jacobi = 2

integer, parameter, public	mg_v_shape = 1

integer, parameter, public	mg_w_shape = 2

integer, parameter, public	mg_fmg = 3

Function/Subroutine Documentation

◆ multigrid_solver_init()

subroutine, public multigrid_solver_oct_m::multigrid_solver_init	(	type(mg_solver_t), intent(out)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(mesh_t), intent(inout)	mesh,
		real(real64), intent(in)	thr
	)

Definition at line 172 of file multigrid_solver.F90.

◆ multigrid_solver_v_cycle()

recursive subroutine, public multigrid_solver_oct_m::multigrid_solver_v_cycle	(	type(mg_solver_t), intent(in)	this,
		type(derivatives_t), intent(in)	der,
		type(nl_operator_t), intent(in)	op,
		real(real64), dimension(:), intent(inout), contiguous	sol,
		real(real64), dimension(:), intent(in), contiguous	rhs
	)

Performs one cycle of a V-shaped multigrid solver.

This method is called recursively from the finest grid to the coarsest and then back to the finest grid

Parameters

[in]	op	Linear operator
[in,out]	sol	Solution to the problem
[in]	rhs	Right-hand side of the linear problem

Definition at line 273 of file multigrid_solver.F90.

◆ multigrid_solver_w_cycle()

recursive subroutine, public multigrid_solver_oct_m::multigrid_solver_w_cycle	(	type(mg_solver_t), intent(in)	this,
		type(derivatives_t), intent(in)	der,
		type(nl_operator_t), intent(in)	op,
		real(real64), dimension(:), intent(inout), contiguous	sol,
		real(real64), dimension(:), intent(in), contiguous	rhs
	)

Performs one cycle of a W-shaped multigrid solver.

This method is called recursively from the finest grid to the coarsest and then back to the finest grid

Parameters

[in]	op	Linear operator
[in,out]	sol	Solution to the problem
[in]	rhs	Right-hand side of the linear problem

Definition at line 343 of file multigrid_solver.F90.

◆ multigrid_iterative_solver()

subroutine, public multigrid_solver_oct_m::multigrid_iterative_solver	(	type(mg_solver_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		type(derivatives_t), intent(in)	der,
		type(nl_operator_t), intent(in)	op,
		real(real64), dimension(:), intent(inout), contiguous	sol,
		real(real64), dimension(:), intent(inout), contiguous	rhs,
		integer, intent(in)	multigrid_shape
	)

An iterative multigrid solver.

It performs multiple V- or W-cycles up to convergence

Parameters

[in]	op	Linear operator
[in,out]	sol	Solution to the problem
[in,out]	rhs	Right-hand side of the linear problem
[in]	multigrid_shape	The shape of each cycle

Definition at line 442 of file multigrid_solver.F90.

◆ multigrid_fmg_solver()

recursive subroutine, public multigrid_solver_oct_m::multigrid_fmg_solver	(	type(mg_solver_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		type(derivatives_t), intent(in)	der,
		type(nl_operator_t), intent(in)	op,
		real(real64), dimension(:), intent(inout), contiguous	sol,
		real(real64), dimension(:), intent(inout), contiguous	rhs
	)

Full multigrid (FMG) solver.

There is no starting point needed in this case. The code does N V cycles at each level of the full multigrid, in order to reach convergence at each level

Parameters

[in]	op	Linear operator
[in,out]	sol	Solution to the problem
[in,out]	rhs	Right-hand side of the linear problem

Definition at line 505 of file multigrid_solver.F90.

◆ multigrid_solver_solve_coarsest()

subroutine multigrid_solver_oct_m::multigrid_solver_solve_coarsest	(	type(mg_solver_t), intent(in)	this,
		type(derivatives_t), intent(in)	der,
		type(nl_operator_t), intent(in)	op,
		real(real64), dimension(:), intent(inout), contiguous	sol,
		real(real64), dimension(:), intent(in), contiguous	rhs,
		real(real64), dimension(:), intent(inout), contiguous	residue
	)

private

Computes the solution on the coarsest grid.

Parameters

[in]	op	Linear operator
[in,out]	sol	Solution to the problem
[in]	rhs	Right-hand side of the linear problem
[in,out]	residue	A work array for the residue

Definition at line 561 of file multigrid_solver.F90.

◆ get_residual()

subroutine multigrid_solver_oct_m::get_residual	(	type(nl_operator_t), intent(in)	op,
		type(derivatives_t), intent(in)	der,
		real(real64), dimension(:), intent(inout), contiguous	sol,
		real(real64), dimension(:), intent(in), contiguous	rhs,
		real(real64), dimension(:), intent(inout), contiguous	residue
	)

private

Computes the residual.

Definition at line 596 of file multigrid_solver.F90.

◆ multigrid_relax()

subroutine multigrid_solver_oct_m::multigrid_relax	(	type(mg_solver_t), intent(in)	this,
		type(mesh_t), intent(in)	mesh,
		type(derivatives_t), intent(in)	der,
		type(nl_operator_t), intent(in)	op,
		real(real64), dimension(:), intent(inout), contiguous	sol,
		real(real64), dimension(:), intent(in), contiguous	rhs,
		integer, intent(in)	steps
	)

private

Given a nonlocal operator op, perform the relaxation operator.

This is needed to solve the linear problem Op sol = rhs steps times

Parameters

[in]	op	Linear operator
[in,out]	sol	Solution to the problem
[in]	rhs	Right-hand side of the linear problem
[in]	steps	Number of steps to be performed

Definition at line 618 of file multigrid_solver.F90.

Variable Documentation

◆ gauss_seidel

integer, parameter multigrid_solver_oct_m::gauss_seidel = 1

Definition at line 138 of file multigrid_solver.F90.

◆ weighted_jacobi

integer, parameter multigrid_solver_oct_m::weighted_jacobi = 2

Definition at line 138 of file multigrid_solver.F90.

◆ mg_v_shape

integer, parameter, public multigrid_solver_oct_m::mg_v_shape = 1

Definition at line 164 of file multigrid_solver.F90.

◆ mg_w_shape

integer, parameter, public multigrid_solver_oct_m::mg_w_shape = 2

Definition at line 164 of file multigrid_solver.F90.

◆ mg_fmg

integer, parameter, public multigrid_solver_oct_m::mg_fmg = 3

Definition at line 164 of file multigrid_solver.F90.

Detailed Description

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ multigrid_solver_init()

◆ multigrid_solver_v_cycle()

◆ multigrid_solver_w_cycle()

◆ multigrid_iterative_solver()

◆ multigrid_fmg_solver()

◆ multigrid_solver_solve_coarsest()

◆ get_residual()

◆ multigrid_relax()

Variable Documentation

◆ gauss_seidel

◆ weighted_jacobi

◆ mg_v_shape

◆ mg_w_shape

◆ mg_fmg