m_af_multigrid Module Reference

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

Functions/Subroutines
subroutine, public	mg_init (tree, mg)
	Check multigrid options or set them to default. More...
subroutine, public	mg_destroy (mg)
subroutine	use_mg (tree, mg)
	Make sure box tags and operators are set. More...
subroutine	done_with_mg (tree)
	To be called at the end of a multigrid solve. More...
subroutine, public	mg_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	mg_fas_vcycle (tree, mg, set_residual, highest_lvl, standalone)
	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	solve_coarse_grid (tree, mg)
subroutine, public	mg_sides_rb (boxes, id, nb, iv)
	Fill ghost cells near refinement boundaries which preserves diffusive fluxes. More...
subroutine	mg_sides_rb_extrap (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	gsrb_boxes (tree, lvl, mg, type_cycle)
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	mg_auto_gsrb (box, redblack_cntr, mg)
	Based on the box type, apply a Gauss-Seidel relaxation scheme. More...
subroutine	mg_store_operator_stencil (box, mg, ix)
	Store operator stencil for a box. More...
subroutine	mg_store_prolongation_stencil (tree, id, mg)
	Store prolongation stencil for a box. More...
subroutine	mg_auto_op (box, i_out, mg)
	Based on the box type, apply the approriate operator. More...
subroutine	mg_auto_rstr (box_c, box_p, iv, mg)
	Restriction operator. More...
subroutine	mg_auto_rb (boxes, id, nb, iv, op_mask)
	Set ghost cells near refinement boundaries. More...
subroutine	mg_auto_corr (box_p, box_c, mg)
	Based on the box type, correct the solution of the children. More...
subroutine	get_possible_lsf_root_mask (box, nc, dmax, mg, root_mask)
	Check where the level-set function could have a root by computing the numerical gradient. More...
subroutine	store_lsf_distance_matrix (box, nc, mg, boundary)
	Check if the level set function could have zeros, and store distances for the neighboring cells. More...
subroutine, public	mg_set_box_tag (tree, id, mg)
	Set tag (box type) for a box in the tree. More...
subroutine, public	mg_set_operators_lvl (tree, mg, lvl)
subroutine, public	mg_update_operator_stencil (tree, mg)
	Update stencil for an operator, because (part of) the coefficients have changed. More...
subroutine, public	mg_set_operators_tree (tree, mg)
subroutine	mg_box_rstr_lpl (box_c, box_p, iv, mg)
	Restriction of child box (box_c) to its parent (box_p) More...
subroutine	mg_box_lpl_stencil (box, mg, ix)
	Store the matrix stencil for each cell of the box. The order of the stencil is (i, j), (i-1, j), (i+1, j), (i, j-1), (i, j+1) (e.g., -4, 1, 1, 1, 1) More...
subroutine	mg_box_prolong_linear_stencil (box, box_p, mg, ix)
	Store linear prolongation stencil for standard Laplacian. More...
subroutine	mg_box_prolong_sparse_stencil (box, box_p, mg, ix)
	Store sparse linear prolongation stencil for standard Laplacian. More...
subroutine	mg_box_prolong_eps_stencil (box, box_p, mg, ix)
	Store prolongation stencil for standard Laplacian with variable coefficient that can jump at cell faces. More...
subroutine	mg_box_prolong_lsf_stencil (box, box_p, mg, ix)
	Store prolongation stencil for standard Laplacian with level set function for internal boundaries. More...
subroutine	mg_box_lpld_stencil (box, mg, ix)
	Store the matrix stencil for each cell of the box. The order of the stencil is (i, j), (i-1, j), (i+1, j), (i, j-1), (i, j+1) (e.g., -4, 1, 1, 1, 1) More...
subroutine	mg_box_lpld_lsf_stencil (box, mg, ix)
	Store stencil for a box with variable coefficient and level set function. More...
real(dp) function, public	mg_lsf_dist_linear (a, b, mg)
	Compute distance to boundary starting at point a going to point b, in the range from [0, 1], with 1 meaning there is no boundary. More...
real(dp) function, public	mg_lsf_dist_gss (a, b, mg)
	Find root of f in the interval [a, b]. If f(a) and f(b) have different signs, apply bisection directly. Else, first find the (assumed to be) unique local minimum/maximum to determine a bracket. Return relative location of root, or 1 if there is no root. More...
real(dp) function, dimension(ndim)	bisection (f, in_a, in_b, tol, max_iter)
	Simple bisection. More...
real(dp) function, dimension(ndim, 2)	gss (f, in_a, in_b, minimization, tol, find_bracket)
	Golden-section search on a line between a and b. Given a function f with a single local minimum/maximum in the interval [a,b], gss returns a subset interval [c,d] that contains the minimum/maximum with d-c <= tol. Adapted from https://en.wikipedia.org/wiki/Golden-section_search. More...
subroutine	mg_box_lsf_stencil (box, mg, ix)
	Store the matrix stencil for each cell of the box. The order of the stencil is (i, j), (i-1, j), (i+1, j), (i, j-1), (i, j+1) (e.g., -4, 1, 1, 1, 1) More...
subroutine, public	mg_compute_phi_gradient (tree, mg, i_fc, fac, i_norm)
	Compute the gradient of the potential and store in face-centered variables. More...
subroutine, public	mg_box_lpl_gradient (tree, id, mg, i_fc, fac)
	Compute the gradient of the potential. More...
subroutine, public	mg_compute_field_norm (tree, i_fc, i_norm)
	Compute norm of face-centered variable. More...
subroutine, public	mg_box_field_norm (tree, id, i_fc, i_norm)
subroutine	mg_box_lpllsf_gradient (tree, id, mg, i_fc, fac)
	Compute the gradient of the potential with a level set function and store in face-centered variables. The gradients are computed from the positive side of the level set function. More...
subroutine	check_coarse_representation_lsf (tree, mg)
	This method checks whether the level set function is properly defined on the coarse grid. More...
real(dp) function, dimension(ndim)	numerical_gradient (f, r)
	Get amplitude of numerical gradient of level set function. More...

Detailed Description

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

Todo:

How to use box tag with different types of operators?

Function/Subroutine Documentation

mg_init()

subroutine, public m_af_multigrid::mg_init	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(inout)	mg
	)

Check multigrid options or set them to default.

Parameters

[in,out]	tree	Tree to do multigrid on
[in,out]	mg	Multigrid options

Definition at line 43 of file m_af_multigrid.f90.

mg_destroy()

subroutine, public m_af_multigrid::mg_destroy

(

type(mg_t), intent(inout)

mg

)

Parameters

[in,out]

mg

Multigrid options

Definition at line 109 of file m_af_multigrid.f90.

use_mg()

subroutine m_af_multigrid::use_mg ( type(af_t), intent(inout)  tree, type(mg_t), intent(in), target  mg  )

private

Make sure box tags and operators are set.

Parameters

[in]

mg

Multigrid options

Definition at line 116 of file m_af_multigrid.f90.

done_with_mg()

subroutine m_af_multigrid::done_with_mg ( type(af_t), intent(inout)  tree )

private

To be called at the end of a multigrid solve.

Definition at line 127 of file m_af_multigrid.f90.

mg_fas_fmg()

subroutine, public m_af_multigrid::mg_fas_fmg	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(inout)	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,out]	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 135 of file m_af_multigrid.f90.

mg_fas_vcycle()

subroutine, public m_af_multigrid::mg_fas_vcycle	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(in)	mg,
		logical, intent(in)	set_residual,
		integer, intent(in), optional	highest_lvl,
		logical, intent(in), optional	standalone
	)

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
[in]	standalone	False if called by other cycle

Definition at line 183 of file m_af_multigrid.f90.

solve_coarse_grid()

subroutine m_af_multigrid::solve_coarse_grid	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(in)	mg
	)

Parameters

[in,out]	tree	Tree to do multigrid on
[in]	mg	Multigrid options

Definition at line 264 of file m_af_multigrid.f90.

mg_sides_rb()

subroutine, public m_af_multigrid::mg_sides_rb	(	type(box_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 292 of file m_af_multigrid.f90.

mg_sides_rb_extrap()

subroutine m_af_multigrid::mg_sides_rb_extrap ( type(box_t), dimension(:), intent(inout)  boxes, integer, intent(in)  id, integer, intent(in)  nb, integer, intent(in)  iv  )

private

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 466 of file m_af_multigrid.f90.

correct_children()

subroutine m_af_multigrid::correct_children ( type(box_t), dimension(:), intent(inout)  boxes, integer, dimension(:), intent(in)  ids, type(mg_t), intent(in)  mg  )

private

Parameters

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

Definition at line 622 of file m_af_multigrid.f90.

gsrb_boxes()

subroutine m_af_multigrid::gsrb_boxes ( type(af_t), intent(inout)  tree, integer, intent(in)  lvl, type(mg_t), intent(in)  mg, integer, intent(in)  type_cycle  )

private

Parameters

[in,out]	tree	Tree containing full grid
[in]	mg	Multigrid options
[in]	lvl	Operate on this refinement level
[in]	type_cycle	Type of cycle to perform

Definition at line 646 of file m_af_multigrid.f90.

update_coarse()

subroutine m_af_multigrid::update_coarse ( type(af_t), intent(inout)  tree, integer, intent(in)  lvl, type(mg_t), intent(in)  mg  )

private

Parameters

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

Definition at line 689 of file m_af_multigrid.f90.

set_coarse_phi_rhs()

subroutine m_af_multigrid::set_coarse_phi_rhs	(	type(af_t), intent(inout)	tree,
		integer, intent(in)	lvl,
		type(mg_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 740 of file m_af_multigrid.f90.

init_phi_rhs()

subroutine m_af_multigrid::init_phi_rhs	(	type(af_t), intent(inout)	tree,
		type(mg_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 777 of file m_af_multigrid.f90.

residual_box()

subroutine m_af_multigrid::residual_box	(	type(box_t), intent(inout)	box,
		type(mg_t), intent(in)	mg
	)

Parameters

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

Definition at line 799 of file m_af_multigrid.f90.

mg_auto_gsrb()

subroutine m_af_multigrid::mg_auto_gsrb ( type(box_t), intent(inout)  box, integer, intent(in)  redblack_cntr, type(mg_t), intent(in)  mg  )

private

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 811 of file m_af_multigrid.f90.

mg_store_operator_stencil()

subroutine m_af_multigrid::mg_store_operator_stencil ( type(box_t), intent(inout)  box, type(mg_t), intent(in)  mg, integer, intent(inout)  ix  )

private

Store operator stencil for a box.

Parameters

[in,out]

ix

Index of the stencil. If equal to af_stencil_none, store a new stencil

Definition at line 821 of file m_af_multigrid.f90.

mg_store_prolongation_stencil()

subroutine m_af_multigrid::mg_store_prolongation_stencil ( type(af_t), intent(inout)  tree, integer, intent(in)  id, type(mg_t), intent(in)  mg  )

private

Store prolongation stencil for a box.

Parameters

[in]

id

Id of box

Definition at line 860 of file m_af_multigrid.f90.

mg_auto_op()

subroutine m_af_multigrid::mg_auto_op ( type(box_t), intent(inout)  box, integer, intent(in)  i_out, type(mg_t), intent(in)  mg  )

private

Based on the box type, apply the approriate operator.

Parameters

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

Definition at line 904 of file m_af_multigrid.f90.

mg_auto_rstr()

subroutine m_af_multigrid::mg_auto_rstr ( type(box_t), intent(in)  box_c, type(box_t), intent(inout)  box_p, integer, intent(in)  iv, type(mg_t), intent(in)  mg  )

private

Restriction 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 913 of file m_af_multigrid.f90.

mg_auto_rb()

subroutine m_af_multigrid::mg_auto_rb ( type(box_t), dimension(:), intent(inout)  boxes, integer, intent(in)  id, integer, intent(in)  nb, integer, intent(in)  iv, integer, intent(in)  op_mask  )

private

Set ghost cells near refinement boundaries.

Parameters

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

Definition at line 924 of file m_af_multigrid.f90.

mg_auto_corr()

subroutine m_af_multigrid::mg_auto_corr ( type(box_t), intent(in)  box_p, type(box_t), intent(inout)  box_c, type(mg_t), intent(in)  mg  )

private

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 941 of file m_af_multigrid.f90.

get_possible_lsf_root_mask()

subroutine m_af_multigrid::get_possible_lsf_root_mask ( type(box_t), intent(in)  box, integer, intent(in)  nc, real(dp), intent(in)  dmax, type(mg_t), intent(in)  mg, logical, dimension(dtimes(nc)), intent(out)  root_mask  )

private

Check where the level-set function could have a root by computing the numerical gradient.

Parameters

[in]	box	Box to operate on
[in]	dmax	Maximal distance to consider
[in]	nc	Box size
[in]	mg	Multigrid options
[out]	root_mask	Whether there could be a root

Definition at line 952 of file m_af_multigrid.f90.

store_lsf_distance_matrix()

subroutine m_af_multigrid::store_lsf_distance_matrix ( type(box_t), intent(inout)  box, integer, intent(in)  nc, type(mg_t), intent(in)  mg, logical, intent(out)  boundary  )

private

Check if the level set function could have zeros, and store distances for the neighboring cells.

Parameters

[in,out]	box	Box to operate on
[in]	nc	Box size
[in]	mg	Multigrid options
[out]	boundary	Whether a boundary is found

Definition at line 975 of file m_af_multigrid.f90.

mg_set_box_tag()

subroutine, public m_af_multigrid::mg_set_box_tag	(	type(af_t), intent(inout)	tree,
		integer, intent(in)	id,
		type(mg_t), intent(in)	mg
	)

Set tag (box type) for a box in the tree.

Definition at line 1098 of file m_af_multigrid.f90.

mg_set_operators_lvl()

subroutine, public m_af_multigrid::mg_set_operators_lvl	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(in)	mg,
		integer, intent(in)	lvl
	)

Definition at line 1131 of file m_af_multigrid.f90.

mg_update_operator_stencil()

subroutine, public m_af_multigrid::mg_update_operator_stencil	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(inout)	mg
	)

Update stencil for an operator, because (part of) the coefficients have changed.

Definition at line 1172 of file m_af_multigrid.f90.

mg_set_operators_tree()

subroutine, public m_af_multigrid::mg_set_operators_tree	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(in)	mg
	)

Definition at line 1195 of file m_af_multigrid.f90.

mg_box_rstr_lpl()

subroutine m_af_multigrid::mg_box_rstr_lpl ( type(box_t), intent(in)  box_c, type(box_t), intent(inout)  box_p, integer, intent(in)  iv, type(mg_t), intent(in)  mg  )

private

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 1206 of file m_af_multigrid.f90.

mg_box_lpl_stencil()

subroutine m_af_multigrid::mg_box_lpl_stencil	(	type(box_t), intent(inout)	box,
		type(mg_t), intent(in)	mg,
		integer, intent(in)	ix
	)

Store the matrix stencil for each cell of the box. The order of the stencil is (i, j), (i-1, j), (i+1, j), (i, j-1), (i, j+1) (e.g., -4, 1, 1, 1, 1)

Parameters

[in]

ix

Stencil index

Definition at line 1225 of file m_af_multigrid.f90.

mg_box_prolong_linear_stencil()

subroutine m_af_multigrid::mg_box_prolong_linear_stencil ( type(box_t), intent(inout)  box, type(box_t), intent(in)  box_p, type(mg_t), intent(in)  mg, integer, intent(in)  ix  )

private

Store linear prolongation stencil for standard Laplacian.

Parameters

[in,out]	box	Current box
[in]	box_p	Parent box
[in]	ix	Stencil index

Definition at line 1246 of file m_af_multigrid.f90.

mg_box_prolong_sparse_stencil()

subroutine m_af_multigrid::mg_box_prolong_sparse_stencil ( type(box_t), intent(inout)  box, type(box_t), intent(in)  box_p, type(mg_t), intent(in)  mg, integer, intent(in)  ix  )

private

Store sparse linear prolongation stencil for standard Laplacian.

Parameters

[in,out]	box	Current box
[in]	box_p	Parent box
[in]	ix	Stencil index

Definition at line 1266 of file m_af_multigrid.f90.

mg_box_prolong_eps_stencil()

subroutine m_af_multigrid::mg_box_prolong_eps_stencil ( type(box_t), intent(inout)  box, type(box_t), intent(in)  box_p, type(mg_t), intent(in)  mg, integer, intent(in)  ix  )

private

Store prolongation stencil for standard Laplacian with variable coefficient that can jump at cell faces.

Parameters

[in,out]	box	Current box
[in]	box_p	Parent box
[in]	ix	Stencil index

Definition at line 1287 of file m_af_multigrid.f90.

mg_box_prolong_lsf_stencil()

subroutine m_af_multigrid::mg_box_prolong_lsf_stencil ( type(box_t), intent(inout)  box, type(box_t), intent(in)  box_p, type(mg_t), intent(in)  mg, integer, intent(in)  ix  )

private

Store prolongation stencil for standard Laplacian with level set function for internal boundaries.

Parameters

[in,out]	box	Current box
[in]	box_p	Parent box
[in]	ix	Stencil index

Definition at line 1371 of file m_af_multigrid.f90.

mg_box_lpld_stencil()

subroutine m_af_multigrid::mg_box_lpld_stencil ( type(box_t), intent(inout)  box, type(mg_t), intent(in)  mg, integer, intent(in)  ix  )

private

Store the matrix stencil for each cell of the box. The order of the stencil is (i, j), (i-1, j), (i+1, j), (i, j-1), (i, j+1) (e.g., -4, 1, 1, 1, 1)

Parameters

[in]

ix

Index of the stencil

Definition at line 1472 of file m_af_multigrid.f90.

mg_box_lpld_lsf_stencil()

subroutine m_af_multigrid::mg_box_lpld_lsf_stencil ( type(box_t), intent(inout)  box, type(mg_t), intent(in)  mg, integer, intent(in)  ix  )

private

Store stencil for a box with variable coefficient and level set function.

Parameters

[in]

ix

Index of the stencil

Todo:

This is not fully accurate when there is both a change in epsilon and a boundary for the same cell

Definition at line 1514 of file m_af_multigrid.f90.

mg_lsf_dist_linear()

real(dp) function, public m_af_multigrid::mg_lsf_dist_linear	(	real(dp), dimension(ndim), intent(in)	a,
		real(dp), dimension(ndim), intent(in)	b,
		type(mg_t), intent(in)	mg
	)

Compute distance to boundary starting at point a going to point b, in the range from [0, 1], with 1 meaning there is no boundary.

Parameters

[in]	a	Start point
[in]	b	End point

Definition at line 1605 of file m_af_multigrid.f90.

mg_lsf_dist_gss()

real(dp) function, public m_af_multigrid::mg_lsf_dist_gss	(	real(dp), dimension(ndim), intent(in)	a,
		real(dp), dimension(ndim), intent(in)	b,
		type(mg_t), intent(in)	mg
	)

Find root of f in the interval [a, b]. If f(a) and f(b) have different signs, apply bisection directly. Else, first find the (assumed to be) unique local minimum/maximum to determine a bracket. Return relative location of root, or 1 if there is no root.

Parameters

[in]	a	Start point
[in]	b	End point

Definition at line 1627 of file m_af_multigrid.f90.

bisection()

real(dp) function, dimension(ndim) m_af_multigrid::bisection ( procedure(mg_func_lsf)  f, real(dp), dimension(ndim), intent(in)  in_a, real(dp), dimension(ndim), intent(in)  in_b, real(dp), intent(in)  tol, integer, intent(in)  max_iter  )

private

Simple bisection.

Definition at line 1665 of file m_af_multigrid.f90.

gss()

real(dp) function, dimension(ndim, 2) m_af_multigrid::gss ( procedure(mg_func_lsf)  f, real(dp), dimension(ndim), intent(in)  in_a, real(dp), dimension(ndim), intent(in)  in_b, logical, intent(in)  minimization, real(dp), intent(in)  tol, logical, intent(in)  find_bracket  )

private

Golden-section search on a line between a and b. Given a function f with a single local minimum/maximum in the interval [a,b], gss returns a subset interval [c,d] that contains the minimum/maximum with d-c <= tol. Adapted from https://en.wikipedia.org/wiki/Golden-section_search.

Parameters

	f	Function to minimize/maximize
[in]	in_a	Start coordinate
[in]	in_b	End coordinate
[in]	minimization	Whether to perform minimization or maximization
[in]	tol	Absolute tolerance
[in]	find_bracket	Whether to search for a bracket

Definition at line 1692 of file m_af_multigrid.f90.

mg_box_lsf_stencil()

subroutine m_af_multigrid::mg_box_lsf_stencil ( type(box_t), intent(inout)  box, type(mg_t), intent(in)  mg, integer, intent(in)  ix  )

private

Store the matrix stencil for each cell of the box. The order of the stencil is (i, j), (i-1, j), (i+1, j), (i, j-1), (i, j+1) (e.g., -4, 1, 1, 1, 1)

Parameters

[in]

ix

Index of stencil

Definition at line 1760 of file m_af_multigrid.f90.

mg_compute_phi_gradient()

subroutine, public m_af_multigrid::mg_compute_phi_gradient	(	type(af_t), intent(inout)	tree,
		type(mg_t), intent(in)	mg,
		integer, intent(in)	i_fc,
		real(dp), intent(in)	fac,
		integer, intent(in), optional	i_norm
	)

Compute the gradient of the potential and store in face-centered variables.

Parameters

[in]	i_fc	Face-centered indices
[in]	fac	Multiply with this factor
[in]	i_norm	If present, store norm in this cell-centered variable

Todo:

Solution on coarse grid can lead to large gradient due to inconsistencies with level set function

Definition at line 1835 of file m_af_multigrid.f90.

mg_box_lpl_gradient()

subroutine, public m_af_multigrid::mg_box_lpl_gradient	(	type(af_t), intent(inout)	tree,
		integer, intent(in)	id,
		type(mg_t), intent(in)	mg,
		integer, intent(in)	i_fc,
		real(dp), intent(in)	fac
	)

Compute the gradient of the potential.

Parameters

[in]	i_fc	Face-centered indices
[in]	fac	Multiply with this factor

Definition at line 1880 of file m_af_multigrid.f90.

mg_compute_field_norm()

subroutine, public m_af_multigrid::mg_compute_field_norm	(	type(af_t), intent(inout)	tree,
		integer, intent(in)	i_fc,
		integer, intent(in)	i_norm
	)

Compute norm of face-centered variable.

Parameters

[in]	i_fc	Index of face-centered variable
[in]	i_norm	Index of cell-centered variable

Definition at line 1975 of file m_af_multigrid.f90.

mg_box_field_norm()

subroutine, public m_af_multigrid::mg_box_field_norm	(	type(af_t), intent(inout)	tree,
		integer, intent(in)	id,
		integer, intent(in)	i_fc,
		integer, intent(in)	i_norm
	)

Parameters

[in]	i_fc	Face-centered indices
[in]	i_norm	Store norm in this cell-centered variable

Definition at line 1993 of file m_af_multigrid.f90.

mg_box_lpllsf_gradient()

subroutine m_af_multigrid::mg_box_lpllsf_gradient ( type(af_t), intent(inout)  tree, integer, intent(in)  id, type(mg_t), intent(in)  mg, integer, intent(in)  i_fc, real(dp), intent(in)  fac  )

private

Compute the gradient of the potential with a level set function and store in face-centered variables. The gradients are computed from the positive side of the level set function.

Parameters

[in]	i_fc	Face-centered indices
[in]	fac	Multiply with this factor

Definition at line 2028 of file m_af_multigrid.f90.

check_coarse_representation_lsf()

subroutine m_af_multigrid::check_coarse_representation_lsf ( type(af_t), intent(in)  tree, type(mg_t), intent(in)  mg  )

private

This method checks whether the level set function is properly defined on the coarse grid.

Definition at line 2122 of file m_af_multigrid.f90.

numerical_gradient()

real(dp) function, dimension(ndim) m_af_multigrid::numerical_gradient ( procedure(mg_func_lsf)  f, real(dp), dimension(ndim), intent(in)  r  )

private

Get amplitude of numerical gradient of level set function.

Definition at line 2142 of file m_af_multigrid.f90.