m_a2_multigrid Module Reference

This module contains the geometric multigrid routines that come with Afivo. More...

Data Types
interface	mg2_box_op
	Subroutine that performs A * cc(..., i_in) = cc(..., i_out) More...
type	mg2_t
	Type to store multigrid options in. More...

Functions/Subroutines
subroutine, public	mg2_init_mg (mg)
	Check multigrid options or set them to default. More...
subroutine, public	mg2_fas_fmg (tree, mg, set_residual, have_guess)
	Perform FAS-FMG cycle (full approximation scheme, full multigrid). Note that this routine needs valid ghost cells (for i_phi) on input, and gives back valid ghost cells on output. More...
subroutine, public	mg2_fas_vcycle (tree, mg, set_residual, highest_lvl)
	Perform FAS V-cycle (full approximation scheme). Note that this routine needs valid ghost cells (for i_phi) on input, and gives back valid ghost cells on output. More...
subroutine, public	mg2_sides_rb (boxes, id, nb, iv)
	Fill ghost cells near refinement boundaries which preserves diffusive fluxes. More...
subroutine	mg2_sides_rb_old (boxes, id, nb, iv)
	Fill ghost cells near refinement boundaries which preserves diffusive fluxes. This routine does not do interpolation of coarse grid values. Basically, we extrapolate from the fine cells to a corner point, and then take the average between this corner point and a coarse neighbor to fill ghost cells for the fine cells. More...
subroutine	correct_children (boxes, ids, mg)
subroutine	update_coarse (tree, lvl, mg)
subroutine	set_coarse_phi_rhs (tree, lvl, mg)
	This routine performs the same as update_coarse, but it ignores the tmp variable. More...
subroutine	init_phi_rhs (tree, mg)
	Set the initial guess for phi and restrict the rhs. More...
subroutine	residual_box (box, mg)
subroutine, public	mg2_auto_gsrb (box, redblack_cntr, mg)
	Based on the box type, apply a Gauss-Seidel relaxation scheme. More...
subroutine, public	mg2_auto_op (box, i_out, mg)
	Based on the box type, apply the approriate Laplace operator. More...
subroutine, public	mg2_auto_rstr (box_c, box_p, iv, mg)
	Based on the box type, apply the approriate Laplace operator. More...
subroutine, public	mg2_auto_corr (box_p, box_c, mg)
	Based on the box type, correct the solution of the children. More...
subroutine, public	mg2_set_box_tag (box, mg)
subroutine, public	mg2_box_corr_lpl (box_p, box_c, mg)
subroutine, public	mg2_box_gsrb_lpl (box, redblack_cntr, mg)
	Perform Gauss-Seidel relaxation on box for a Laplacian operator. More...
subroutine, public	mg2_box_lpl (box, i_out, mg)
	Perform Laplacian operator on a box. More...
subroutine, public	mg2_box_rstr_lpl (box_c, box_p, iv, mg)
	Restriction of child box (box_c) to its parent (box_p) More...
subroutine, public	mg2_box_gsrb_lpld (box, redblack_cntr, mg)
	Perform Gauss-Seidel relaxation on a box. Epsilon can have a jump at cell faces. More...
subroutine, public	mg2_box_lpld (box, i_out, mg)
	Perform Laplacian operator on a box where epsilon varies on cell faces. More...
subroutine, public	mg2_box_corr_lpld (box_p, box_c, mg)
	Correct fine grid values based on the change in the coarse grid, in the case of a jump in epsilon. More...
subroutine, public	mg2_box_corr_lpllsf (box_p, box_c, mg)
subroutine, public	mg2_box_gsrb_lpllsf (box, redblack_cntr, mg)
	Perform Gauss-Seidel relaxation on box for a Laplacian operator. More...
subroutine, public	mg2_box_lpllsf (box, i_out, mg)
	Perform Laplacian operator on a box. More...
subroutine, public	mg2_box_rstr_lpllsf (box_c, box_p, iv, mg)
	Restriction of child box (box_c) to its parent (box_p) More...
subroutine, public	mg2_box_gsrb_clpl (box, redblack_cntr, mg)
	Perform Gauss-Seidel relaxation on box for a cylindrical Laplacian operator. More...
subroutine, public	mg2_box_clpl (box, i_out, mg)
	Perform cylindrical Laplacian operator on a box. More...
subroutine, public	mg2_box_clpld (box, i_out, mg)
	Perform cylindrical Laplacian operator on a box with varying eps. More...
subroutine, public	mg2_box_gsrb_clpld (box, redblack_cntr, mg)
	Perform Gauss-Seidel relaxation on box for a cylindrical Laplacian operator with a changing eps. More...

Variables
integer, parameter, public	mg_normal_box = 1
	Normal box. More...
integer, parameter, public	mg_lsf_box = 2
	Box with an internal boundary. More...
integer, parameter, public	mg_ceps_box = 3
	Box with constant eps /= 1. More...
integer, parameter, public	mg_veps_box = 4
	Box with varying eps (on face) More...

Detailed Description

This module contains the geometric multigrid routines that come with Afivo.

Function/Subroutine Documentation

mg2_init_mg()

subroutine, public m_a2_multigrid::mg2_init_mg

(

type(mg2_t), intent(inout)

mg

)

Check multigrid options or set them to default.

Parameters

[in,out]

mg

Multigrid options

Definition at line 133 of file m_a2_multigrid.f90.

mg2_fas_fmg()

subroutine, public m_a2_multigrid::mg2_fas_fmg	(	type(a2_t), intent(inout)	tree,
		type(mg2_t), intent(in)	mg,
		logical, intent(in)	set_residual,
		logical, intent(in)	have_guess
	)

Perform FAS-FMG cycle (full approximation scheme, full multigrid). Note that this routine needs valid ghost cells (for i_phi) on input, and gives back valid ghost cells on output.

Parameters

[in,out]	tree	Tree to do multigrid on
[in]	mg	Multigrid options
[in]	set_residual	If true, store residual in i_tmp
[in]	have_guess	If false, start from phi = 0

Definition at line 167 of file m_a2_multigrid.f90.

mg2_fas_vcycle()

subroutine, public m_a2_multigrid::mg2_fas_vcycle	(	type(a2_t), intent(inout)	tree,
		type(mg2_t), intent(in)	mg,
		logical, intent(in)	set_residual,
		integer, intent(in), optional	highest_lvl
	)

Perform FAS V-cycle (full approximation scheme). Note that this routine needs valid ghost cells (for i_phi) on input, and gives back valid ghost cells on output.

Parameters

[in,out]	tree	Tree to do multigrid on
[in]	mg	Multigrid options
[in]	set_residual	If true, store residual in i_tmp
[in]	highest_lvl	Maximum level for V-cycle

Definition at line 213 of file m_a2_multigrid.f90.

mg2_sides_rb()

subroutine, public m_a2_multigrid::mg2_sides_rb	(	type(box2_t), dimension(:), intent(inout)	boxes,
		integer, intent(in)	id,
		integer, intent(in)	nb,
		integer, intent(in)	iv
	)

Fill ghost cells near refinement boundaries which preserves diffusive fluxes.

Parameters

[in,out]	boxes	List of all boxes
[in]	id	Id of box
[in]	nb	Ghost cell direction
[in]	iv	Ghost cell variable

Definition at line 288 of file m_a2_multigrid.f90.

mg2_sides_rb_old()

subroutine m_a2_multigrid::mg2_sides_rb_old	(	type(box2_t), dimension(:), intent(inout)	boxes,
		integer, intent(in)	id,
		integer, intent(in)	nb,
		integer, intent(in)	iv
	)

Fill ghost cells near refinement boundaries which preserves diffusive fluxes. This routine does not do interpolation of coarse grid values. Basically, we extrapolate from the fine cells to a corner point, and then take the average between this corner point and a coarse neighbor to fill ghost cells for the fine cells.

Parameters

[in,out]	boxes	List of all boxes
[in]	id	Id of box
[in]	nb	Ghost cell direction
[in]	iv	Ghost cell variable

Definition at line 365 of file m_a2_multigrid.f90.

correct_children()

subroutine m_a2_multigrid::correct_children	(	type(box2_t), dimension(:), intent(inout)	boxes,
		integer, dimension(:), intent(in)	ids,
		type(mg2_t), intent(in)	mg
	)

Parameters

[in,out]	boxes	List of all boxes
[in]	ids	Operate on these boxes
[in]	mg	Multigrid options

Definition at line 430 of file m_a2_multigrid.f90.

update_coarse()

subroutine m_a2_multigrid::update_coarse	(	type(a2_t), intent(inout)	tree,
		integer, intent(in)	lvl,
		type(mg2_t), intent(in)	mg
	)

Parameters

[in,out]	tree	Tree containing full grid
[in]	lvl	Update coarse values at lvl-1
[in]	mg	Multigrid options

Definition at line 497 of file m_a2_multigrid.f90.

set_coarse_phi_rhs()

subroutine m_a2_multigrid::set_coarse_phi_rhs	(	type(a2_t), intent(inout)	tree,
		integer, intent(in)	lvl,
		type(mg2_t), intent(in)	mg
	)

This routine performs the same as update_coarse, but it ignores the tmp variable.

Parameters

[in,out]	tree	Tree containing full grid
[in]	lvl	Update coarse values at lvl-1
[in]	mg	Multigrid options

Definition at line 550 of file m_a2_multigrid.f90.

init_phi_rhs()

subroutine m_a2_multigrid::init_phi_rhs	(	type(a2_t), intent(inout)	tree,
		type(mg2_t), intent(in)	mg
	)

Set the initial guess for phi and restrict the rhs.

Parameters

[in,out]	tree	Full grid
[in]	mg	Multigrid options

Definition at line 590 of file m_a2_multigrid.f90.

residual_box()

subroutine m_a2_multigrid::residual_box	(	type(box2_t), intent(inout)	box,
		type(mg2_t), intent(in)	mg
	)

Parameters

[in,out]	box	Operate on this box
[in]	mg	Multigrid options

Definition at line 615 of file m_a2_multigrid.f90.

mg2_auto_gsrb()

subroutine, public m_a2_multigrid::mg2_auto_gsrb	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	redblack_cntr,
		type(mg2_t), intent(in)	mg
	)

Based on the box type, apply a Gauss-Seidel relaxation scheme.

Parameters

[in,out]	box	Box to operate on
[in]	redblack_cntr	Iteration count
[in]	mg	Multigrid options

Definition at line 627 of file m_a2_multigrid.f90.

mg2_auto_op()

subroutine, public m_a2_multigrid::mg2_auto_op	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	i_out,
		type(mg2_t), intent(in)	mg
	)

Based on the box type, apply the approriate Laplace operator.

Parameters

[in,out]	box	Operate on this box
[in]	i_out	Index of output variable
[in]	mg	Multigrid options

Definition at line 653 of file m_a2_multigrid.f90.

mg2_auto_rstr()

subroutine, public m_a2_multigrid::mg2_auto_rstr	(	type(box2_t), intent(in)	box_c,
		type(box2_t), intent(inout)	box_p,
		integer, intent(in)	iv,
		type(mg2_t), intent(in)	mg
	)

Based on the box type, apply the approriate Laplace operator.

Parameters

[in]	box_c	Child box
[in,out]	box_p	Parent box
[in]	iv	Index of variable
[in]	mg	Multigrid options

Definition at line 679 of file m_a2_multigrid.f90.

mg2_auto_corr()

subroutine, public m_a2_multigrid::mg2_auto_corr	(	type(box2_t), intent(in)	box_p,
		type(box2_t), intent(inout)	box_c,
		type(mg2_t), intent(in)	mg
	)

Based on the box type, correct the solution of the children.

Parameters

[in,out]	box_c	Child box
[in]	box_p	Parent box
[in]	mg	Multigrid options

Definition at line 697 of file m_a2_multigrid.f90.

mg2_set_box_tag()

subroutine, public m_a2_multigrid::mg2_set_box_tag	(	type(box2_t), intent(inout)	box,
		type(mg2_t), intent(in)	mg
	)

Parameters

[in,out]	box	Box to operate on
[in]	mg	Multigrid options

Definition at line 714 of file m_a2_multigrid.f90.

mg2_box_corr_lpl()

subroutine, public m_a2_multigrid::mg2_box_corr_lpl	(	type(box2_t), intent(in)	box_p,
		type(box2_t), intent(inout)	box_c,
		type(mg2_t), intent(in)	mg
	)

Parameters

[in,out]	box_c	Child box
[in]	box_p	Parent box
[in]	mg	Multigrid options

Definition at line 745 of file m_a2_multigrid.f90.

mg2_box_gsrb_lpl()

subroutine, public m_a2_multigrid::mg2_box_gsrb_lpl	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	redblack_cntr,
		type(mg2_t), intent(in)	mg
	)

Perform Gauss-Seidel relaxation on box for a Laplacian operator.

Parameters

[in,out]	box	Box to operate on
[in]	redblack_cntr	Iteration counter
[in]	mg	Multigrid options

Definition at line 755 of file m_a2_multigrid.f90.

mg2_box_lpl()

subroutine, public m_a2_multigrid::mg2_box_lpl	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	i_out,
		type(mg2_t), intent(in)	mg
	)

Perform Laplacian operator on a box.

Parameters

[in,out]	box	Box to operate on
[in]	i_out	Index of variable to store Laplacian in
[in]	mg	Multigrid options

Definition at line 781 of file m_a2_multigrid.f90.

mg2_box_rstr_lpl()

subroutine, public m_a2_multigrid::mg2_box_rstr_lpl	(	type(box2_t), intent(in)	box_c,
		type(box2_t), intent(inout)	box_p,
		integer, intent(in)	iv,
		type(mg2_t), intent(in)	mg
	)

Restriction of child box (box_c) to its parent (box_p)

Parameters

[in]	box_c	Child box to restrict
[in,out]	box_p	Parent box to restrict to
[in]	iv	Variable to restrict
[in]	mg	Multigrid options

Definition at line 802 of file m_a2_multigrid.f90.

mg2_box_gsrb_lpld()

subroutine, public m_a2_multigrid::mg2_box_gsrb_lpld	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	redblack_cntr,
		type(mg2_t), intent(in)	mg
	)

Perform Gauss-Seidel relaxation on a box. Epsilon can have a jump at cell faces.

Parameters

[in,out]	box	Box to operate on
[in]	redblack_cntr	Iteration counter
[in]	mg	Multigrid options

Definition at line 816 of file m_a2_multigrid.f90.

mg2_box_lpld()

subroutine, public m_a2_multigrid::mg2_box_lpld	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	i_out,
		type(mg2_t), intent(in)	mg
	)

Perform Laplacian operator on a box where epsilon varies on cell faces.

Parameters

[in,out]	box	Box to operate on
[in]	i_out	Index of variable to store Laplacian in
[in]	mg	Multigrid options

Definition at line 848 of file m_a2_multigrid.f90.

mg2_box_corr_lpld()

subroutine, public m_a2_multigrid::mg2_box_corr_lpld	(	type(box2_t), intent(in)	box_p,
		type(box2_t), intent(inout)	box_c,
		type(mg2_t), intent(in)	mg
	)

Correct fine grid values based on the change in the coarse grid, in the case of a jump in epsilon.

Parameters

[in,out]	box_c	Child box
[in]	box_p	Parent box
[in]	mg	Multigrid options

Definition at line 878 of file m_a2_multigrid.f90.

mg2_box_corr_lpllsf()

subroutine, public m_a2_multigrid::mg2_box_corr_lpllsf	(	type(box2_t), intent(in)	box_p,
		type(box2_t), intent(inout)	box_c,
		type(mg2_t), intent(in)	mg
	)

Parameters

[in,out]	box_c	Child box
[in]	box_p	Parent box
[in]	mg	Multigrid options

Definition at line 948 of file m_a2_multigrid.f90.

mg2_box_gsrb_lpllsf()

subroutine, public m_a2_multigrid::mg2_box_gsrb_lpllsf	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	redblack_cntr,
		type(mg2_t), intent(in)	mg
	)

Perform Gauss-Seidel relaxation on box for a Laplacian operator.

Parameters

[in,out]	box	Box to operate on
[in]	redblack_cntr	Iteration counter
[in]	mg	Multigrid options

Definition at line 992 of file m_a2_multigrid.f90.

mg2_box_lpllsf()

subroutine, public m_a2_multigrid::mg2_box_lpllsf	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	i_out,
		type(mg2_t), intent(in)	mg
	)

Perform Laplacian operator on a box.

Parameters

[in,out]	box	Box to operate on
[in]	i_out	Index of variable to store Laplacian in
[in]	mg	Multigrid options

Definition at line 1034 of file m_a2_multigrid.f90.

mg2_box_rstr_lpllsf()

subroutine, public m_a2_multigrid::mg2_box_rstr_lpllsf	(	type(box2_t), intent(in)	box_c,
		type(box2_t), intent(inout)	box_p,
		integer, intent(in)	iv,
		type(mg2_t), intent(in)	mg
	)

Restriction of child box (box_c) to its parent (box_p)

Parameters

[in]	box_c	Child box to restrict
[in,out]	box_p	Parent box to restrict to
[in]	iv	Variable to restrict
[in]	mg	Multigrid options

Definition at line 1072 of file m_a2_multigrid.f90.

mg2_box_gsrb_clpl()

subroutine, public m_a2_multigrid::mg2_box_gsrb_clpl	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	redblack_cntr,
		type(mg2_t), intent(in)	mg
	)

Perform Gauss-Seidel relaxation on box for a cylindrical Laplacian operator.

Parameters

[in,out]	box	Box to operate on
[in]	redblack_cntr	Iteration counter
[in]	mg	Multigrid options

Definition at line 1107 of file m_a2_multigrid.f90.

mg2_box_clpl()

subroutine, public m_a2_multigrid::mg2_box_clpl	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	i_out,
		type(mg2_t), intent(in)	mg
	)

Perform cylindrical Laplacian operator on a box.

Parameters

[in,out]	box	Box to operate on
[in]	i_out	Index of variable to store Laplacian in
[in]	mg	Multigrid options

Definition at line 1136 of file m_a2_multigrid.f90.

mg2_box_clpld()

subroutine, public m_a2_multigrid::mg2_box_clpld	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	i_out,
		type(mg2_t), intent(in)	mg
	)

Perform cylindrical Laplacian operator on a box with varying eps.

Parameters

[in,out]	box	Box to operate on
[in]	i_out	Index of variable to store Laplacian in
[in]	mg	Multigrid options

Definition at line 1161 of file m_a2_multigrid.f90.

mg2_box_gsrb_clpld()

subroutine, public m_a2_multigrid::mg2_box_gsrb_clpld	(	type(box2_t), intent(inout)	box,
		integer, intent(in)	redblack_cntr,
		type(mg2_t), intent(in)	mg
	)

Perform Gauss-Seidel relaxation on box for a cylindrical Laplacian operator with a changing eps.

Parameters

[in,out]	box	Box to operate on
[in]	redblack_cntr	Iteration counter
[in]	mg	Multigrid options

Definition at line 1193 of file m_a2_multigrid.f90.

Variable Documentation

mg_normal_box

integer, parameter, public m_a2_multigrid::mg_normal_box = 1

Normal box.

Definition at line 11 of file m_a2_multigrid.f90.

mg_lsf_box

integer, parameter, public m_a2_multigrid::mg_lsf_box = 2

Box with an internal boundary.

Definition at line 12 of file m_a2_multigrid.f90.

mg_ceps_box

integer, parameter, public m_a2_multigrid::mg_ceps_box = 3

Box with constant eps /= 1.

Definition at line 13 of file m_a2_multigrid.f90.

mg_veps_box

integer, parameter, public m_a2_multigrid::mg_veps_box = 4

Box with varying eps (on face)

Definition at line 14 of file m_a2_multigrid.f90.