m_octree_mg_1d

Module for implicitly solving diffusion equations Module which contains multigrid procedures for a Laplacian operator

Module for load balancing a tree (that already has been constructed). The load balancing determines which ranks (MPI processes) allocated physical storage for boxes. The tree structure itself is present on all processes. Module which contains multigrid procedures for a variable-coefficient Laplacian operator, assuming the variation is smooth

Uses

- mod_mpi_wrapper
- mpi
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Variables

Type	Visibility	Attributes		Name		Initial
integer,	public,	parameter	::	dp	=	kind(0.0d0)	Type of reals
integer,	public,	parameter	::	i8	=	selected_int_kind(18)	Type for 64-bit integers
integer,	public,	parameter	::	mg_ahelmholtz	=	5	Indicates a anisotropic-coefficient Helmholtz equation
integer,	public,	parameter	::	mg_bc_continuous	=	-12	Value to indicate a continuous boundary condition
integer,	public,	parameter	::	mg_bc_dirichlet	=	-10	Value to indicate a Dirichlet boundary condition
integer,	public,	parameter	::	mg_bc_neumann	=	-11	Value to indicate a Neumann boundary condition
integer,	public,	parameter	::	mg_cartesian	=	1	Cartesian coordinate system
integer,	public,	parameter	::	mg_child_adj_nb(1,2)	=	reshape([1, 2], [1, 2])
integer,	public,	parameter	::	mg_child_dix(1,2)	=	reshape([0, 1], [1, 2])
logical,	public,	parameter	::	mg_child_low(1,2)	=	reshape([.true., .false.], [1, 2])
integer,	public,	parameter	::	mg_child_rev(2,1)	=	reshape([2, 1], [2, 1])
integer,	public,	parameter	::	mg_cylindrical	=	2	Cylindrical coordinate system
integer,	public,	parameter	::	mg_helmholtz	=	3	Indicates a constant-coefficient Helmholtz equation
integer,	public,	parameter	::	mg_iold	=	3	Index of previous solution (used for correction)
integer,	public,	parameter	::	mg_iphi	=	1	Index of solution
integer,	public,	parameter	::	mg_ires	=	4	Index of residual
integer,	public,	parameter	::	mg_irhs	=	2	Index of right-hand side
integer,	public,	parameter	::	mg_iveps	=	5	Index of the variable coefficient (at cell centers)
integer,	public,	parameter	::	mg_iveps1	=	5	Indexes of anisotropic variable coefficients
integer,	public,	parameter	::	mg_laplacian	=	1	Indicates a standard Laplacian
integer,	public,	parameter	::	mg_lvl_hi	=	20	Maximum allowed grid level
integer,	public,	parameter	::	mg_lvl_lo	=	-20	Minimum allowed grid level
integer,	public,	parameter	::	mg_max_num_vars	=	10	Maximum number of variables
integer,	public,	parameter	::	mg_max_timers	=	20	Maximum number of timers to use
integer,	public,	parameter	::	mg_ndim	=	1	Problem dimension
integer,	public,	parameter	::	mg_neighb_dim(2)	=	[1, 1]
integer,	public,	parameter	::	mg_neighb_dix(1,2)	=	reshape([-1, 1], [1, 2])
integer,	public,	parameter	::	mg_neighb_high_pm(2)	=	[-1, 1]
integer,	public,	parameter	::	mg_neighb_highx	=	2
logical,	public,	parameter	::	mg_neighb_low(2)	=	[.true., .false.]
integer,	public,	parameter	::	mg_neighb_lowx	=	1
integer,	public,	parameter	::	mg_neighb_rev(2)	=	[2, 1]
integer,	public,	parameter	::	mg_no_box	=	0	Special value that indicates there is no box
integer,	public,	parameter	::	mg_num_children	=	2
integer,	public,	parameter	::	mg_num_neighbors	=	2
integer,	public,	parameter	::	mg_num_vars	=	4	Number of predefined multigrid variables
integer,	public,	parameter	::	mg_physical_boundary	=	-1	Special value that indicates there is a physical boundary
integer,	public,	parameter	::	mg_smoother_gs	=	1
integer,	public,	parameter	::	mg_smoother_gsrb	=	2
integer,	public,	parameter	::	mg_smoother_jacobi	=	3
integer,	public,	parameter	::	mg_spherical	=	3	Spherical coordinate system
integer,	public,	parameter	::	mg_vhelmholtz	=	4	Indicates a variable-coefficient Helmholtz equation
integer,	public,	parameter	::	mg_vlaplacian	=	2	Indicates a variable-coefficient Laplacian
real(kind=dp),	protected		::	ahelmholtz_lambda	=	0.0_dp	Module which contains multigrid procedures for a Helmholtz operator of the form: div(D grad(phi)) - lambda*phi = f, where D has a smooth spatial variation and a component in each spatial direction The lambda used for the Helmholtz equation (should be >= 0)
real(kind=dp),	protected		::	helmholtz_lambda	=	0.0_dp	Module which contains multigrid procedures for a Helmholtz operator of the form: laplacian(phi) - lambda*phi = f The lambda used for the Helmholtz equation (should be >= 0)
real(kind=dp),	protected		::	vhelmholtz_lambda	=	0.0_dp	Module which contains multigrid procedures for a Helmholtz operator of the form: div(D grad(phi)) - lambda*phi = f, where D has a smooth spatial variation The lambda used for the Helmholtz equation (should be >= 0)
integer,	private,	parameter	::	kdp	=	selected_real_kind(15)
integer,	private		::	timer_coarse	=	-1
integer,	private		::	timer_correct	=	-1
integer,	private		::	timer_smoother	=	-1
integer,	private		::	timer_smoother_gc	=	-1
integer,	private		::	timer_total_fmg	=	-1
integer,	private		::	timer_total_vcycle	=	-1
integer,	private		::	timer_update_coarse	=	-1

Interfaces

interface

public subroutine mg_box_gsrb(mg, id, nc, redblack_cntr)

Subroutine that performs Gauss-Seidel relaxation

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	redblack_cntr

interface

public subroutine mg_box_op(mg, id, nc, i_out)

Subroutine that performs A * cc(..., i_in) = cc(..., i_out)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	i_out

interface

public subroutine mg_box_prolong(mg, p_id, dix, nc, iv, fine)

Subroutine that performs prolongation to a single child

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	p_id	Id of parent
integer,	intent(in)	::	dix(1)	Offset of child in parent grid
integer,	intent(in)	::	nc	Child grid size
integer,	intent(in)	::	iv	Prolong from this variable
real(kind=dp),	intent(out)	::	fine(nc)	Prolonged values

interface

public subroutine mg_subr_bc(box, nc, iv, nb, bc_type, bc)

To fill ghost cells near physical boundaries

Arguments

Type	Intent		Name
type(mg_box_t),	intent(in)	::	box
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv	Index of variable
integer,	intent(in)	::	nb	Direction
integer,	intent(out)	::	bc_type	Type of b.c.
real(kind=dp),	intent(out)	::	bc(1)	Boundary values

interface

public subroutine mg_subr_rb(box, nc, iv, nb, cgc)

To fill ghost cells near refinement boundaries

Arguments

Type	Intent		Name
type(mg_box_t),	intent(inout)	::	box
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv	Index of variable
integer,	intent(in)	::	nb	Direction
real(kind=dp),	intent(in)	::	cgc(1)	Coarse data

public interface mrgrnk

private subroutine I_mrgrnk(XDONT, IRNGT)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in),		Dimension (:)	::	XDONT
integer,	intent(out),		Dimension (:)	::	IRNGT

Derived Types

type, public :: mg_bc_t

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	bc_type	=	mg_bc_dirichlet	Type of boundary condition
real(kind=dp),	public		::	bc_value	=	0.0_dp	Value (for e.g. Dirichlet or Neumann)
procedure(mg_subr_bc),	public,	pointer, nopass	::	boundary_cond	=>	null()	To set user-defined boundary conditions (overrides bc(:))
procedure(mg_subr_rb),	public,	pointer, nopass	::	refinement_bnd	=>	null()	To set a user-defined refinement boundary method

type, public :: mg_box_t

Box data structure

Components

Type	Visibility	Attributes		Name
real(kind=dp),	public,	allocatable	::	cc(:,:)	Cell-centered data
integer,	public		::	children(2**1)	Ids of children
real(kind=dp),	public		::	dr(1)	Grid spacing
integer,	public		::	id	Box id (index in boxes(:) array)
integer,	public		::	ix(1)	Spatial index
integer,	public		::	lvl	Refinement level
integer,	public		::	neighbors(2*1)	Ids of neighbors
integer,	public		::	parent	Id of parent
real(kind=dp),	public		::	r_min(1)	Minimum coordinate
integer,	public		::	rank	Which process owns this box

type, public :: mg_buf_t

Buffer type (one is used for each pair of communicating processes)

Components

Type	Visibility	Attributes		Name
integer,	public		::	i_ix
integer,	public		::	i_recv
integer,	public		::	i_send	Index in send array
integer,	public,	allocatable	::	ix(:)	Will be used to sort the data
real(kind=dp),	public,	allocatable	::	recv(:)
real(kind=dp),	public,	allocatable	::	send(:)

type, public :: mg_comm_t

Components

Type	Visibility	Attributes		Name		Initial
integer,	public,	allocatable	::	n_recv(:,:)
integer,	public,	allocatable	::	n_send(:,:)

type, public :: mg_lvl_t

Lists of blocks per refinement level

Components

Type	Visibility	Attributes		Name
integer,	public,	allocatable	::	ids(:)
integer,	public,	allocatable	::	leaves(:)
integer,	public,	allocatable	::	my_ids(:)
integer,	public,	allocatable	::	my_leaves(:)
integer,	public,	allocatable	::	my_parents(:)
integer,	public,	allocatable	::	my_ref_bnds(:)
integer,	public,	allocatable	::	parents(:)
integer,	public,	allocatable	::	ref_bnds(:)

type, public :: mg_t

Components

Type	Visibility	Attributes		Name		Initial
type(mg_bc_t),	public		::	bc(mg_num_neighbors,mg_max_num_vars)			To store pre-defined boundary conditions per direction per variable
procedure(mg_box_op),	public,	pointer, nopass	::	box_op	=>	null()	Multigrid operator (e.g., Laplacian)
procedure(mg_box_prolong),	public,	pointer, nopass	::	box_prolong	=>	null()	Multigrid prolongation method
integer,	public		::	box_size	=	-1	Size of boxes in cells, be equal for all dimensions
integer,	public		::	box_size_lvl(mg_lvl_lo:mg_lvl_hi)			Size of boxes per level (differs for coarsest levels)
procedure(mg_box_gsrb),	public,	pointer, nopass	::	box_smoother	=>	null()	Multigrid smoother
type(mg_box_t),	public,	allocatable	::	boxes(:)			Array with all boxes in the tree. Only boxes owned by this task are actually allocated
type(mg_buf_t),	public,	allocatable	::	buf(:)			Buffer for communication with each other task
integer,	public		::	coarsest_grid(1)	=	2
integer,	public		::	comm	=	-1	MPI communicator
type(mg_comm_t),	public		::	comm_ghostcell			Communication info for ghost cell filling
type(mg_comm_t),	public		::	comm_prolong			Communication info for prolongation
type(mg_comm_t),	public		::	comm_restrict			Communication info for restriction
integer,	public		::	domain_size_lvl(1,mg_lvl_lo:mg_lvl_hi)			Size of domain per level (if uniformly refined)
real(kind=dp),	public		::	dr(1,mg_lvl_lo:mg_lvl_hi)			Grid spacing per level
integer,	public		::	first_normal_lvl	=	-1	First normal level of the quadtree/octree, at coarser levels parents have only one child
integer,	public		::	geometry_type	=	mg_cartesian	Type of grid geometry
integer,	public		::	highest_lvl	=	-1	Highest grid level in the tree
logical,	public		::	is_allocated	=	.false.	Whether storage has been allocated for boxes
integer,	public		::	lowest_lvl	=	-1	Lowest grid level in the tree
type(mg_lvl_t),	public		::	lvls(mg_lvl_lo:mg_lvl_hi)			List of all levels
integer,	public		::	max_coarse_cycles	=	1000	Maximum number of cycles on the coarse grid
integer,	public		::	my_rank	=	-1	MPI rank of this task
integer,	public		::	n_boxes	=	0	Total number of boxes in the tree (among all processes)
integer,	public		::	n_cpu	=	-1	Number of MPI tasks
integer,	public		::	n_cycle_down	=	2	Number of cycles when doing downwards relaxation
integer,	public		::	n_cycle_up	=	2	Number of cycles when doing upwards relaxation
integer,	public		::	n_extra_vars	=	0	Number of extra cell-centered variable (e.g., for coefficients)
integer,	public		::	n_smoother_substeps	=	1	Number of substeps for the smoother (for GSRB this is 2)
integer,	public		::	n_timers	=	0	Number of timers
integer,	public		::	operator_type	=	mg_laplacian	Type of operator
logical,	public		::	periodic(1)	=	.false.	Whether a dimension is periodic
logical,	public		::	phi_bc_data_stored	=	.false.	Whether boundary condition data has been stored for mg solution
real(kind=dp),	public		::	r_min(1)			Minimum coordinates
real(kind=dp),	public		::	residual_coarse_abs	=	1e-8_dp	Stop coarse grid when max. residual is smaller than this
real(kind=dp),	public		::	residual_coarse_rel	=	1e-8_dp	Stop coarse grid when residual has been reduced by this factor
integer,	public		::	smoother_type	=	mg_smoother_gs	Type of multigrid smoother
logical,	public		::	subtract_mean	=	.false.	Whether the mean has to be subtracted from the multigrid solution
type(mg_timer_t),	public		::	timers(mg_max_timers)			Values for the timers
logical,	public		::	tree_created	=	.false.	Whether the multigrid tree structure has been created

type, public :: mg_timer_t

Components

Type	Visibility		Name		Initial
character(len=20),	public	::	name
real(kind=dp),	public	::	t	=	0.0_dp
real(kind=dp),	public	::	t0

Functions

public function mg_add_timer(mg, name)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
character(len=*),	intent(in)			::	name

Return Value integer

public pure function mg_get_child_offset(mg, id) result(ix_offset)

Get the offset of a box with respect to its parent (e.g. in 2d, there can be a child at offset 0,0, one at n_cell/2,0, one at 0,n_cell/2 and one at n_cell/2, n_cell/2) n_cell / 2

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(in)			::	mg
integer,	intent(in)			::	id

Return Value integer, (1)

public elemental function mg_has_children(box)

Return .true. if a box has children

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_box_t),	intent(in)			::	box

Return Value logical

public pure function mg_highest_uniform_lvl(mg) result(lvl)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(in)			::	mg

Return Value integer

public function mg_ix_to_ichild(ix)

Compute the child index for a box with spatial index ix. With child index we mean the index in the children(:) array of its parent.

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	ix(1)	Spatial index of the box

Return Value integer

public function mg_number_of_unknowns(mg) result(n_unknowns)

Determine total number of unknowns (on leaves)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(in)			::	mg

Return Value integer(kind=i8)

private function find_neighb(boxes, id, nb) result(nb_id)

Get the id of neighbor nb of boxes(id), through its parent

Arguments

Type	Intent		Name
type(mg_box_t),	intent(in)	::	boxes(:)	List with all the boxes
integer,	intent(in)	::	id	Box whose neighbor we are looking for
integer,	intent(in)	::	nb	Neighbor index

Return Value integer

private function get_sum(mg, iv)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(in)			::	mg
integer,	intent(in)			::	iv

Return Value real(kind=dp)

private function max_residual_lvl(mg, lvl)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in)			::	lvl

Return Value real(kind=dp)

private pure function most_popular(list, work, n_cpu)

Determine most popular rank in the list. In case of ties, assign the rank with the least work.

Arguments

Type	Intent		Name
integer,	intent(in)	::	list(:)	List of MPI ranks
integer,	intent(in)	::	work(0:n_cpu-1)	Existing work per rank
integer,	intent(in)	::	n_cpu

Return Value integer

Subroutines

public subroutine ahelmholtz_set_lambda(lambda)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	lambda

public subroutine ahelmholtz_set_methods(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine diffusion_solve(mg, dt, diffusion_coeff, order, max_res)

Solve a diffusion equation implicitly, assuming a constant diffusion coefficient. The solution at time t should be stored in mg_iphi, which is on output replaced by the solution at time t+dt.

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
real(kind=dp),	intent(in)	::	dt
real(kind=dp),	intent(in)	::	diffusion_coeff
integer,	intent(in)	::	order
real(kind=dp),	intent(in)	::	max_res

public subroutine diffusion_solve_acoeff(mg, dt, order, max_res)

Solve a diffusion equation implicitly, assuming anisotropic diffusion coefficient which has been stored in mg_iveps1, mg_iveps2, mg_iveps3 (also on coarse grids). The solution at time t should be stored in mg_iphi, which is on output replaced by the solution at time t+dt.

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
real(kind=dp),	intent(in)	::	dt
integer,	intent(in)	::	order
real(kind=dp),	intent(in)	::	max_res

public subroutine diffusion_solve_vcoeff(mg, dt, order, max_res)

Solve a diffusion equation implicitly, assuming a variable diffusion coefficient which has been stored in mg_iveps (also on coarse grids). The solution at time t should be stored in mg_iphi, which is on output replaced by the solution at time t+dt.

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
real(kind=dp),	intent(in)	::	dt
integer,	intent(in)	::	order
real(kind=dp),	intent(in)	::	max_res

public subroutine helmholtz_set_lambda(lambda)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	lambda

public subroutine helmholtz_set_methods(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine laplacian_set_methods(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_add_children(mg, id)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in)			::	id	Id of box that gets children

public subroutine mg_allocate_storage(mg)

Allocate communication buffers and local boxes for a tree that has already been created

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_apply_op(mg, i_out, op)

Apply operator to the tree and store in variable i_out

Arguments

Type	Intent	Optional		Name
type(mg_t),	intent(inout)		::	mg
integer,	intent(in)		::	i_out
procedure(mg_box_op),		optional	::	op

public subroutine mg_build_rectangle(mg, domain_size, box_size, dx, r_min, periodic, n_finer)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	domain_size(1)
integer,	intent(in)	::	box_size
real(kind=dp),	intent(in)	::	dx(1)
real(kind=dp),	intent(in)	::	r_min(1)
logical,	intent(in)	::	periodic(1)
integer,	intent(in)	::	n_finer

public subroutine mg_comm_init(mg, comm)

Prolong from a parent to a child with index offset dix. This method could sometimes work better than the default prolongation, which does not take the variation in epsilon into account Initialize MPI if needed, and store MPI information

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in),	optional		::	comm	MPI communicator (default: MPI_COMM_WORLD)

public subroutine mg_deallocate_storage(mg)

Deallocate all allocatable arrays

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_fas_fmg(mg, have_guess, max_res)

Perform FAS-FMG cycle (full approximation scheme, full multigrid).

Arguments

Type	Intent	Optional		Name
type(mg_t),	intent(inout)		::	mg
logical,	intent(in)		::	have_guess	If false, start from phi = 0
real(kind=dp),	intent(out),	optional	::	max_res	Store max(abs(residual))

public subroutine mg_fas_vcycle(mg, highest_lvl, max_res, standalone)

Perform FAS V-cycle (full approximation scheme).

Arguments

Type	Intent	Optional		Name
type(mg_t),	intent(inout)		::	mg
integer,	intent(in),	optional	::	highest_lvl	Maximum level for V-cycle
real(kind=dp),	intent(out),	optional	::	max_res	Store max(abs(residual))
logical,	intent(in),	optional	::	standalone	Whether the V-cycle is called by itself (default: true)

public subroutine mg_fill_ghost_cells(mg, iv)

Fill ghost cells at all grid levels

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t)				::	mg
integer,	intent(in)			::	iv	Index of variable

public subroutine mg_fill_ghost_cells_lvl(mg, lvl, iv)

Fill ghost cells at a grid level

Arguments

Type	Intent		Name
type(mg_t)		::	mg
integer,	intent(in)	::	lvl
integer,	intent(in)	::	iv	Index of variable

public subroutine mg_get_face_coords(box, nb, nc, x)

Get coordinates at the face of a box

Arguments

Type	Intent		Name
type(mg_box_t),	intent(in)	::	box
integer,	intent(in)	::	nb
integer,	intent(in)	::	nc
real(kind=dp),	intent(out)	::	x(1)

public subroutine mg_ghost_cell_buffer_size(mg, n_send, n_recv, dsize)

Specify minimum buffer size (per process) for communication

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(out)	::	n_send(0:mg%n_cpu-1)
integer,	intent(out)	::	n_recv(0:mg%n_cpu-1)
integer,	intent(out)	::	dsize

public subroutine mg_load_balance(mg)

Load balance all boxes in the multigrid tree. Compared to mg_load_balance_simple, this method does a better job of setting the ranks of parent boxes

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_load_balance_parents(mg)

Load balance the parents (non-leafs). Assign them to the rank that has most children.

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_load_balance_simple(mg)

Load balance all boxes in the multigrid tree, by simply distributing the load per grid level. This method will only work well for uniform grids.

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_phi_bc_store(mg)

Store boundary conditions for the solution variable, this can speed up calculations if the same boundary conditions are re-used.

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_prolong(mg, lvl, iv, iv_to, method, add)

Prolong variable iv from lvl to variable iv_to at lvl+1

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	lvl	Level to prolong from
integer,	intent(in)	::	iv	Source variable
integer,	intent(in)	::	iv_to	Target variable
procedure(mg_box_prolong)		::	method	Prolongation method
logical,	intent(in)	::	add	If true, add to current values

public subroutine mg_prolong_buffer_size(mg, n_send, n_recv, dsize)

Specify minimum buffer size (per process) for communication

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(out)	::	n_send(0:mg%n_cpu-1)
integer,	intent(out)	::	n_recv(0:mg%n_cpu-1)
integer,	intent(out)	::	dsize

public subroutine mg_prolong_sparse(mg, p_id, dix, nc, iv, fine)

Prolong from a parent to a child with index offset dix

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	p_id	Id of parent
integer,	intent(in)	::	dix(1)	Offset of child in parent grid
integer,	intent(in)	::	nc	Child grid size
integer,	intent(in)	::	iv	Prolong from this variable
real(kind=dp),	intent(out)	::	fine(nc)	Prolonged values

public subroutine mg_restrict(mg, iv)

Restrict all levels

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in)			::	iv

public subroutine mg_restrict_buffer_size(mg, n_send, n_recv, dsize)

Specify minimum buffer size (per process) for communication

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(out)	::	n_send(0:mg%n_cpu-1)
integer,	intent(out)	::	n_recv(0:mg%n_cpu-1)
integer,	intent(out)	::	dsize

public subroutine mg_restrict_lvl(mg, iv, lvl)

Restrict from lvl to lvl-1

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	iv
integer,	intent(in)	::	lvl

public subroutine mg_set_leaves_parents(boxes, level)

Create a list of leaves and a list of parents for a level

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_box_t),	intent(in)			::	boxes(:)	List of boxes
type(mg_lvl_t),	intent(inout)			::	level	Level type which contains the indices of boxes

public subroutine mg_set_methods(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine mg_set_neighbors_lvl(mg, lvl)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in)			::	lvl

public subroutine mg_set_next_level_ids(mg, lvl)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in)			::	lvl

public subroutine mg_set_refinement_boundaries(boxes, level)

Create a list of refinement boundaries (from the coarse side)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_box_t),	intent(in)			::	boxes(:)
type(mg_lvl_t),	intent(inout)			::	level

public subroutine mg_timer_end(timer)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_timer_t),	intent(inout)			::	timer

public subroutine mg_timer_start(timer)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_timer_t),	intent(inout)			::	timer

public subroutine mg_timers_show(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(in)			::	mg

public subroutine sort_and_transfer_buffers(mg, dsize)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in)			::	dsize

public subroutine vhelmholtz_set_lambda(lambda)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	lambda

public subroutine vhelmholtz_set_methods(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

public subroutine vlaplacian_set_methods(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

private subroutine I_mrgrnk(XDONT, IRNGT)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in),		Dimension (:)	::	XDONT
integer,	intent(out),		Dimension (:)	::	IRNGT

private subroutine add_single_child(mg, id, n_boxes_lvl)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id	Id of box that gets children
integer,	intent(in)	::	n_boxes_lvl

private subroutine bc_to_gc(mg, id, nc, iv, nb, bc_type)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
integer,	intent(in)	::	nb	Neighbor direction
integer,	intent(in)	::	bc_type	Type of b.c.

private subroutine box_ahelmh(mg, id, nc, i_out)

Perform Helmholtz operator on a box

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	i_out	Index of variable to store Helmholtz in

private subroutine box_gc_for_fine_neighbor(box, nb, di, nc, iv, gc)

Get ghost cells for a fine neighbor

Arguments

Type	Intent		Name
type(mg_box_t),	intent(in)	::	box
integer,	intent(in)	::	nb	Direction of fine neighbor
integer,	intent(in)	::	di(1)	Index offset of fine neighbor
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
real(kind=dp),	intent(out)	::	gc(1)

private subroutine box_gc_for_neighbor(box, nb, nc, iv, gc)

Arguments

Type	Intent		Name
type(mg_box_t),	intent(in)	::	box
integer,	intent(in)	::	nb
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
real(kind=dp),	intent(out)	::	gc(1)

private subroutine box_get_gc(box, nb, nc, iv, gc)

Arguments

Type	Intent		Name
type(mg_box_t),	intent(in)	::	box
integer,	intent(in)	::	nb
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
real(kind=dp),	intent(out)	::	gc(1)

private subroutine box_gs_ahelmh(mg, id, nc, redblack_cntr)

Perform Gauss-Seidel relaxation on box for a Helmholtz operator

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	redblack_cntr	Iteration counter

private subroutine box_gs_helmh(mg, id, nc, redblack_cntr)

Perform Gauss-Seidel relaxation on box for a Helmholtz operator

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	redblack_cntr	Iteration counter

private subroutine box_gs_lpl(mg, id, nc, redblack_cntr)

Perform Gauss-Seidel relaxation on box for a Laplacian operator

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	redblack_cntr	Iteration counter

private subroutine box_gs_vhelmh(mg, id, nc, redblack_cntr)

Perform Gauss-Seidel relaxation on box for a Helmholtz operator

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	redblack_cntr	Iteration counter

private subroutine box_gs_vlpl(mg, id, nc, redblack_cntr)

Perform Gauss-Seidel relaxation on box for a Laplacian operator

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	redblack_cntr	Iteration counter

private subroutine box_helmh(mg, id, nc, i_out)

Perform Helmholtz operator on a box

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	i_out	Index of variable to store Helmholtz in

private subroutine box_lpl(mg, id, nc, i_out)

Perform Laplacian operator on a box

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	i_out	Index of variable to store Laplacian in

private subroutine box_set_gc(box, nb, nc, iv, gc)

Arguments

Type	Intent		Name
type(mg_box_t),	intent(inout)	::	box
integer,	intent(in)	::	nb
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
real(kind=dp),	intent(in)	::	gc(1)

private subroutine box_vhelmh(mg, id, nc, i_out)

Perform Helmholtz operator on a box

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	i_out	Index of variable to store Helmholtz in

private subroutine box_vlpl(mg, id, nc, i_out)

Perform Laplacian operator on a box

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	i_out	Index of variable to store Laplacian in

private subroutine buffer_for_fine_nb(mg, box, nc, iv, fine_id, fine_rank, nb, dry_run)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
type(mg_box_t),	intent(inout)	::	box
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
integer,	intent(in)	::	fine_id
integer,	intent(in)	::	fine_rank
integer,	intent(in)	::	nb
logical,	intent(in)	::	dry_run

private subroutine buffer_for_nb(mg, box, nc, iv, nb_id, nb_rank, nb, dry_run)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
type(mg_box_t),	intent(inout)	::	box
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
integer,	intent(in)	::	nb_id
integer,	intent(in)	::	nb_rank
integer,	intent(in)	::	nb
logical,	intent(in)	::	dry_run

private subroutine buffer_ghost_cells(mg, id, nc, iv, dry_run)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
logical,	intent(in)	::	dry_run

private subroutine buffer_refinement_boundaries(mg, id, nc, iv, dry_run)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
logical,	intent(in)	::	dry_run

private subroutine check_methods(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

private subroutine copy_from_nb(box, box_nb, nb, nc, iv)

Arguments

Type	Intent		Name
type(mg_box_t),	intent(inout)	::	box
type(mg_box_t),	intent(in)	::	box_nb
integer,	intent(in)	::	nb
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv

private subroutine correct_children(mg, lvl)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
integer,	intent(in)			::	lvl

private subroutine fill_buffered_nb(mg, box, nb_rank, nb, nc, iv, dry_run)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
type(mg_box_t),	intent(inout)	::	box
integer,	intent(in)	::	nb_rank
integer,	intent(in)	::	nb
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
logical,	intent(in)	::	dry_run

private subroutine fill_refinement_bnd(mg, id, nb, nc, iv, dry_run)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nb
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
logical,	intent(in)	::	dry_run

private subroutine mg_add_timers(mg)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg

private subroutine mg_phi_bc_store_lvl(mg, lvl, nc)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	lvl
integer,	intent(in)	::	nc

private subroutine prolong_onto(mg, id, nc, iv, iv_to, add, method)

Prolong onto a child box

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv	Prolong from this variable
integer,	intent(in)	::	iv_to	Prolong to this variable
logical,	intent(in)	::	add	If true, add to current values
procedure(mg_box_prolong)		::	method

private subroutine prolong_set_buffer(mg, id, nc, iv, method)

In case the fine grid is on a different CPU, perform the prolongation and store the fine-grid values in the send buffer.

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
procedure(mg_box_prolong)		::	method

private subroutine residual_box(mg, id, nc)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc

private subroutine restrict_onto(mg, id, nc, iv)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv

private subroutine restrict_set_buffer(mg, id, iv)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	iv

private subroutine set_ghost_cells(mg, id, nc, iv, dry_run)

The routine that actually fills the ghost cells

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	id
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
logical,	intent(in)	::	dry_run

private subroutine set_neighbs(boxes, id)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_box_t),	intent(inout)			::	boxes(:)
integer,	intent(in)			::	id

private subroutine set_rhs(mg, f1, f2)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
real(kind=dp),	intent(in)	::	f1
real(kind=dp),	intent(in)	::	f2

private subroutine sides_rb(box, nc, iv, nb, gc)

Fill ghost cells near refinement boundaries which preserves diffusive fluxes.

Arguments

Type	Intent		Name
type(mg_box_t),	intent(inout)	::	box
integer,	intent(in)	::	nc
integer,	intent(in)	::	iv
integer,	intent(in)	::	nb	Ghost cell direction
real(kind=dp),	intent(in)	::	gc(1)	Interpolated coarse grid ghost cell data (but not yet in the nb direction)

private subroutine smooth_boxes(mg, lvl, n_cycle)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	lvl
integer,	intent(in)	::	n_cycle	Number of cycles to perform

private subroutine sort_sendbuf(gc, dsize)

Sort send buffers according to the idbuf array

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_buf_t),	intent(inout)			::	gc
integer,	intent(in)			::	dsize	Size of send buffer elements

private subroutine subtract_mean(mg, iv, include_ghostcells)

Arguments

Type	Intent		Name
type(mg_t),	intent(inout)	::	mg
integer,	intent(in)	::	iv
logical,	intent(in)	::	include_ghostcells

private subroutine update_coarse(mg, lvl)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg	Tree containing full grid
integer,	intent(in)			::	lvl	Update coarse values at lvl-1

private subroutine update_lvl_info(mg, lvl)

Arguments

Type	Intent	Optional	Attributes		Name
type(mg_t),	intent(inout)			::	mg
type(mg_lvl_t),	intent(inout)			::	lvl

m_octree_mg_1d Module

Contents

Variables

Interfaces

Derived Types

Functions

Subroutines

Uses

Variables

Interfaces

interface

public subroutine mg_box_gsrb(mg, id, nc, redblack_cntr)

Arguments

interface

public subroutine mg_box_op(mg, id, nc, i_out)

Arguments

interface

public subroutine mg_box_prolong(mg, p_id, dix, nc, iv, fine)

Arguments

interface

public subroutine mg_subr_bc(box, nc, iv, nb, bc_type, bc)

Arguments

interface

public subroutine mg_subr_rb(box, nc, iv, nb, cgc)

Arguments

public interface mrgrnk

private subroutine I_mrgrnk(XDONT, IRNGT)

Arguments

Derived Types

type, public :: mg_bc_t

Components

type, public :: mg_box_t

Components

type, public :: mg_buf_t

Components

type, public :: mg_comm_t

Components

type, public :: mg_lvl_t

Components

type, public :: mg_t

Components

type, public :: mg_timer_t

Components

Functions

public function mg_add_timer(mg, name)

Arguments

Return Value integer

public pure function mg_get_child_offset(mg, id) result(ix_offset)

Arguments

Return Value integer, (1)

public elemental function mg_has_children(box)

Arguments

Return Value logical

public pure function mg_highest_uniform_lvl(mg) result(lvl)

Arguments

Return Value integer

public function mg_ix_to_ichild(ix)

Arguments

Return Value integer

public function mg_number_of_unknowns(mg) result(n_unknowns)

Arguments

Return Value integer(kind=i8)

private function find_neighb(boxes, id, nb) result(nb_id)

Arguments

Return Value integer

private function get_sum(mg, iv)

Arguments

Return Value real(kind=dp)

private function max_residual_lvl(mg, lvl)

Arguments

Return Value real(kind=dp)

private pure function most_popular(list, work, n_cpu)

Arguments

Return Value integer

Subroutines

public subroutine ahelmholtz_set_lambda(lambda)

Arguments

public subroutine ahelmholtz_set_methods(mg)

Arguments

public subroutine diffusion_solve(mg, dt, diffusion_coeff, order, max_res)