Multigrid.src File Reference

Data Types
module	multigrid

Functions/Subroutines
recursive function	gmgsweep ()
integer function	pmggetelementdofs (Indexes, UElement, USolver)
recursive function	amgsweep ()
type(matrix_t) function, pointer	interpolatef2cdistance (Fmat, CF, DOFs)
type(matrix_t) function, pointer	complexinterpolatef2c (Fmat, CF)
subroutine	amgtest (direction)
recursive function	cmgsweep ()
subroutine	projectmatrix (A, PermA, P, Q, B, PermB, DOFs)
real(kind=dp) function	mgnorm (n, x)
subroutine	mgmv (A, x, b, Update)
real(kind=dp) function	mgcnorm (n, x)
subroutine	mgcmv (A, x, b, Update)
recursive function	pmgsweep ()
subroutine	compatiblerelaxation (Amat, Solver, CF, CandList, nods, newcands)
subroutine	choosecoarsenodes (Amat, Solver, Projector, Components, CF, InvCF)
subroutine	amgbonds (Amat, Bonds, Cands, Components)
subroutine	amgbondsdirichlet (Amat, Bonds, Cands)
subroutine	amgbondsgeometric (Amat, Bonds, Cands, Components)
subroutine	amgbondscomplex (Amat, Bonds, Cands)
subroutine	amgpositivebonds (Amat, Bonds, Cands, CF)
subroutine	amgcoarse (Amat, Cands, Bonds, CF, CompMat)
type(matrix_t) function, pointer	interpolatef2c (Fmat, CF, DOFs)
subroutine	cr_jacobi (A, x0, x1, f, Rounds)
subroutine	cr_gs (A, x0, x1, f, Rounds)
subroutine	cr_sgs (A, x0, x1, f, Rounds)
subroutine	cr_csgs (n, A, rx0, rx1, f, Rounds)
subroutine	crs_projectvector (PMatrix, u, v, DOFs, Trans)
subroutine	crs_clusterproject (CF, u, v, DOFs, Trans)
subroutine	crs_projectmatrixcreate (A, P, R, B, DOFs)
subroutine	savematrix (A, FileName)
subroutine	crs_clustermatrixcreate (A, CF, B, Components)
subroutine	saveclusters ()

Function/Subroutine Documentation

subroutine amgsolve::amgbonds	(	type(matrix_t), pointer	Amat,
		logical, dimension(:), pointer	Bonds,
		integer, dimension(:), pointer	Cands,
		integer	Components
	)

Create the initial list for measure of importance and make the inverse table for important connections.

References messages::info(), lists::listgetconstreal(), lists::listgetinteger(), and lists::listgetlogical().

Referenced by choosecoarsenodes().

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subroutine amgsolve::amgbondscomplex	(	type(matrix_t), pointer	Amat,
		logical, dimension(:), pointer	Bonds,
		integer, dimension(:), pointer	Cands
	)

Create the initial list for measure of importance for a complex matrix.

References messages::info(), lists::listgetconstreal(), and lists::listgetinteger().

Referenced by choosecoarsenodes().

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subroutine amgsolve::amgbondsdirichlet	(	type(matrix_t), pointer	Amat,
		logical, dimension(:), pointer	Bonds,
		integer, dimension(:), pointer	Cands
	)

Mark the Dirichlet bonds in the AMG target matrix.

References messages::info(), and lists::listgetconstreal().

Referenced by choosecoarsenodes().

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subroutine amgsolve::amgbondsgeometric	(	type(matrix_t), pointer	Amat,
		logical, dimension(:), pointer	Bonds,
		integer, dimension(:), pointer	Cands,
		integer	Components
	)

Create the initial list for measure of importance using geometric distance information and topology information from the matrix..

References messages::info(), lists::listgetconstreal(), lists::listgetinteger(), and solver().

Referenced by choosecoarsenodes().

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subroutine amgsolve::amgcoarse	(	type(matrix_t), pointer	Amat,
		integer, dimension(:), pointer	Cands,
		logical, dimension(:)	Bonds,
		integer, dimension(:), pointer	CF,
		logical	CompMat
	)

Creates a coarse mesh using the given list of strong connections. Only nodes assigned by the Cands vector may be included in the coarse set - others are ignored. The subroutine returns the vector CF which is nonzero for coarse nodes. The nodes are chosen using a heuristics which takes into account the strength of the coupling.

References messages::info(), and lists::listgetinteger().

Referenced by choosecoarsenodes().

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subroutine amgsolve::amgpositivebonds	(	type(matrix_t), pointer	Amat,
		logical, dimension(:), pointer	Bonds,
		integer, dimension(:), pointer	Cands,
		integer, dimension(:), pointer	CF
	)

Add a posteriori some nodes to be coarse nodes which have strong positive-positive connections.

References messages::info(), lists::listgetconstreal(), and lists::listgetlogical().

Referenced by choosecoarsenodes().

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recursive function amgsolve::amgsweep

(

)

References crsmatrix::crs_complexmatrixvectormultiply(), crsmatrix::crs_matrixvectormultiply(), crs_projectvector(), lists::listgetintegerarray(), smoothers::mgsmooth(), multigrid::multigridsolve(), parallelutils::parallelmatrixvector(), parallelutils::parallelnorm(), and solver().

Referenced by multigrid::amgsolve().

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subroutine amgsolve::amgtest

(

integer

direction)

This subroutine may be used to check that mapping Xf = P Xc is accurate. The list of original nodes for each level is stored in the Cnodes vector. For the momont this only works for cases with one DOF and no permutation!

References crs_projectvector(), messages::info(), lists::listgetinteger(), and solver().

Referenced by multigrid::amgsolve().

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subroutine amgsolve::choosecoarsenodes	(	type(matrix_t), pointer	Amat,
		type(solver_t), target	Solver,
		type(matrix_t), pointer	Projector,
		integer	Components,
		integer, dimension(:), pointer	CF,
		integer, dimension(:), optional, pointer	InvCF
	)

Create a coarse mesh given the fine mesh and the stiffness matrix. The coarse nodes may be selected in a number of ways and after the selection a new mesh is made of them. This mesh is then used to create a projection between the coarse and fine degrees of freedom.

References amgbonds(), amgbondscomplex(), amgbondsdirichlet(), amgbondsgeometric(), amgcoarse(), amgpositivebonds(), compatiblerelaxation(), complexinterpolatef2c(), messages::fatal(), messages::info(), interpolatef2c(), interpolatef2cdistance(), lists::listgetinteger(), lists::listgetlogical(), and solver().

Referenced by multigrid::amgsolve().

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recursive function cmgsolve::cmgsweep

(

)

References crs_clusterproject(), crsmatrix::crs_complexmatrixvectormultiply(), crsmatrix::crs_matrixvectormultiply(), messages::info(), lists::listgetintegerarray(), smoothers::mgsmooth(), multigrid::multigridsolve(), parallelutils::parallelmatrixvector(), parallelutils::parallelnorm(), and solver().

Referenced by multigrid::cmgsolve().

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subroutine amgsolve::compatiblerelaxation	(	type(matrix_t), pointer	Amat,
		type(solver_t), target	Solver,
		integer, dimension(:), pointer	CF,
		integer, dimension(:), pointer	CandList,
		integer	nods,
		integer	newcands
	)

Apply compatible relaxation for the current C/F split and based on the convergence behavior include some of the F nodes to the new candidate list.

References cr_csgs(), cr_gs(), cr_jacobi(), cr_sgs(), messages::info(), lists::listgetconstreal(), lists::listgetinteger(), lists::listgetstring(), and messages::warn().

Referenced by choosecoarsenodes().

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type(matrix_t) function, pointer amgsolve::complexinterpolatef2c	(	type(matrix_t), target	Fmat,
		integer, dimension(:), pointer	CF
	)

As the previous one but expects complex valued equation. The projector is built using only the absolute values.

References generalutils::allocatematrix(), messages::fatal(), messages::info(), lists::listgetconstreal(), lists::listgetinteger(), and lists::listgetlogical().

Referenced by choosecoarsenodes().

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subroutine amgsolve::cr_csgs	(	integer	n,
		type(matrix_t), pointer	A,
		real(kind=dp), dimension(:)	rx0,
		real(kind=dp), dimension(:)	rx1,
		integer, dimension(:)	f,
		integer	Rounds
	)

References lists::listgetinteger().

Referenced by compatiblerelaxation().

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subroutine amgsolve::cr_gs	(	type(matrix_t), pointer	A,
		real(kind=dp), dimension(:)	x0,
		real(kind=dp), dimension(:)	x1,
		integer, dimension(:)	f,
		integer	Rounds
	)

Referenced by compatiblerelaxation().

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subroutine amgsolve::cr_jacobi	(	type(matrix_t), pointer	A,
		real(kind=dp), dimension(:)	x0,
		real(kind=dp), dimension(:)	x1,
		integer, dimension(:)	f,
		integer	Rounds
	)

The following subroutines are CR (Compatible Relaxation) versions of the simple relaxation schemes. The relaxation speed of equation Ax = 0 to x=0 may be used as a measure of the goodness of the chosen coarse node set.

Referenced by compatiblerelaxation().

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subroutine amgsolve::cr_sgs	(	type(matrix_t), pointer	A,
		real(kind=dp), dimension(:)	x0,
		real(kind=dp), dimension(:)	x1,
		integer, dimension(:)	f,
		integer	Rounds
	)

Referenced by compatiblerelaxation().

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subroutine cmgsolve::crs_clustermatrixcreate	(	type(matrix_t), pointer	A,
		integer, dimension(:), pointer	CF,
		type(matrix_t), pointer	B,
		integer	Components
	)

Project cluster matrix A to B: B = PAR The projector is formed implicitely.

References generalutils::allocatematrix(), messages::info(), lists::listgetconstreal(), and lists::listgetlogical().

Referenced by multigrid::cmgsolve().

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subroutine crs_clusterproject	(	integer, dimension(:), pointer	CF,
		real(kind=dp), dimension(:), pointer	u,
		real(kind=dp), dimension(:), pointer	v,
		integer	DOFs,
		logical, optional	Trans
	)

Project the residuals from coarse to fine and restrict from fine to coarse in the clustering multigrid method.

Referenced by cmgsweep().

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subroutine amgsolve::crs_projectmatrixcreate	(	type(matrix_t), pointer	A,
		type(matrix_t), pointer	P,
		type(matrix_t), pointer	R,
		type(matrix_t), pointer	B,
		integer	DOFs
	)

Project matrix A to B: B = PAR.

References generalutils::allocatematrix(), messages::info(), and lists::listgetconstreal().

Referenced by multigrid::amgsolve().

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subroutine amgsolve::crs_projectvector	(	type(matrix_t), pointer	PMatrix,
		real(kind=dp), dimension(:), pointer	u,
		real(kind=dp), dimension(:), pointer	v,
		integer	DOFs,
		logical, optional	Trans
	)

References messages::fatal().

Referenced by amgsweep(), and amgtest().

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recursive function gmgsolve::gmgsweep

(

)

References crsmatrix::crs_applyprojector(), messages::info(), lists::listgetintegerarray(), smoothers::mgsmooth(), multigrid::multigridsolve(), and solver().

Referenced by multigrid::gmgsolve().

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type(matrix_t) function, pointer amgsolve::interpolatef2c	(	type(matrix_t), target	Fmat,
		integer, dimension(:), pointer	CF,
		integer	DOFs
	)

make a matrix projection such that fine nodes are expressed with coarse nodes Xf = P Xc, with given set of coarse nodes, CF, and the stiffness matrix used in the projection.

References generalutils::allocatematrix(), messages::fatal(), messages::info(), lists::listgetconstreal(), lists::listgetinteger(), and lists::listgetlogical().

Referenced by choosecoarsenodes().

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type(matrix_t) function, pointer amgsolve::interpolatef2cdistance	(	type(matrix_t), target	Fmat,
		integer, dimension(:), pointer	CF,
		integer	DOFs
	)

A pseudo geometric version of the previous Here the stregth of connections is assumed to be inversily proportional to the distance between nodes.

References generalutils::allocatematrix(), messages::info(), lists::listgetconstreal(), lists::listgetinteger(), lists::listgetlogical(), solver(), and generalutils::sortf().

Referenced by choosecoarsenodes().

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subroutine mgcmv	(	type(matrix_t), pointer	A,
		complex(kind=dp), dimension(:)	x,
		complex(kind=dp), dimension(:)	b,
		logical, optional	Update
	)

References crsmatrix::crs_complexmatrixvectormultiply().

Referenced by ccg(), and cjacobi().

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real(kind=dp) function gmgsolve::mgcnorm	(	integer	n,
		complex(kind=dp), dimension(:)	x
	)

subroutine mgmv	(	type(matrix_t), pointer	A,
		real(kind=dp), dimension(:)	x,
		real(kind=dp), dimension(:)	b,
		logical, optional	Update
	)

References crsmatrix::crs_matrixvectormultiply(), and parallelutils::parallelmatrixvector().

Referenced by multigrid::amgsolve(), bicg(), paralleleigensolve::bicgpareigen(), cg(), paralleleigensolve::cgpareigen(), multigrid::cmgsolve(), direct1dsmoother(), multigrid::gmgsolve(), jacobi(), paralleleigensolve::jacobi(), smoothers::mgsmooth(), paralleleigensolve::parallelarpackeigensolve(), multigrid::pmgsolve(), smoothedjacobi(), and uzawa().

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real(kind=dp) function gmgsolve::mgnorm	(	integer	n,
		real(kind=dp), dimension(:)	x
	)

References parallelutils::parallelnorm().

Referenced by multigrid::amgsolve(), paralleleigensolve::bicgpareigen(), paralleleigensolve::cgpareigen(), smoothers::mgsmooth(), and multigrid::pmgsolve().

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integer function pmgsolve::pmggetelementdofs	(	integer, dimension(:)	Indexes,
		type(element_t), optional, target	UElement,
		type(solver_t), optional, target	USolver
	)

References pelementmaps::ispelement(), lists::listgetlogical(), and solver().

Referenced by multigrid::pmgsolve().

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recursive function pmgsolve::pmgsweep

(

)

References crsmatrix::crs_matrixvectormultiply(), smoothers::mgsmooth(), multigrid::multigridsolve(), parallelutils::parallelmatrixvector(), parallelutils::parallelnorm(), and solver().

Referenced by multigrid::pmgsolve().

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subroutine gmgsolve::projectmatrix	(	type(matrix_t), pointer	A,
		integer, dimension(:), pointer	PermA,
		type(matrix_t), pointer	P,
		type(matrix_t), pointer	Q,
		type(matrix_t), pointer	B,
		integer, dimension(:), pointer	PermB,
		integer	DOFs
	)

Project matrix A to B: B = PAQ^T.

The code is a little complicated by the fact that there might be three different numbering schemes for the DOFs: one for both matrices and the nodal numbering of the projectors.

Referenced by multigrid::gmgsolve().

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subroutine cmgsolve::saveclusters

(

)

References messages::fatal(), lists::listgetinteger(), solver(), and lists::variableadd().

Referenced by multigrid::cmgsolve().

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subroutine amgsolve::savematrix	(	type(matrix_t)	A,
		character(len=*)	FileName
	)

Referenced by mainutils::addequationsolution(), multigrid::amgsolve(), multigrid::gmgsolve(), parallelutils::parallelmatrixvector(), multigrid::pmgsolve(), and sparitersolve::solve().

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