Linear

Handle linear system solvers with three different attribute features: Direct, Iterative, and Multigrid.

Syntax

sol.feature(fname).create(lname,"Direct")

sol.feature(fname).feature(lname).set(pname,value)

sol.feature(fname).create(lname,"Iterative")

sol.feature(fname).feature(lname).set(pname,value)

sol.feature(fname).feature(lname).create(pcname,PType);

sol.feature(fname).feature(lname).feature(pcname).set(pname,value)

sol.feature(fname).feature(lname).create(pname,"Multigrid")

sol.feature(fname).feature(lname).feature(pname).feature("pr").create(prename,SType)

sol.feature(fname).feature(lname).feature(pname).feature("po").create(postname,SType)

sol.feature(fname).feature(lname).feature(pname).feature("cs").create(cname,CType)

sol.feature(fname).feature(lname).feature(pname).feature("pr").feature(prename).
set(pname,value)

sol.feature(fname).feature(lname).feature(pname).feature("po").feature(postname).
set(pname,value)

sol.feature(fname).feature(lname).feature(pname).feature("cs").feature(cname).
set(pname,value)

PType is any of the allowed preconditioner feature types. These types are Direct preconditioner, Multigrid, Domain decomposition, SCGS, SOR, SOR Gauge, SOR Vector, Vanka, SOR Line, AMS, Incomplete LU, and Krylov preconditioners. SType is any of the allowed smoother types. These are the same as the PType except Domain decomposition, Multigrid, and AMS. CType is any of the allowed coarse grid solver types: Direct and all types listed for PType.

Presmoother, Postsmoother, and Coarse Solver

Specify the Presmoother, Postsmoother, and Coarse Solver via feature("ps"), feature("po"), and feature("cs"), respectively. These features are for administrative purposes only and do not contain any settings themselves.

Description

Three attribute features for linear system solvers.

Examples:

GMRES with ILU as preconditioner:

Code for Use with Java

SolverFeature solver = sol.feature(fname).create("iter1","Iterative");

solver.set("solver","gmres");

solver.create("ilu","IncompleteLU");

Code for Use with MATLAB

solver = sol.feature(fname).create('iter1','Iterative');

solver.set('solver','gmres');

solver.create('ilu','IncompleteLU');

Change the preconditioner to GMG/SORVector/SPOOLES:

Code for Use with Java

solver.create("gmg","Multigrid");

solver("gmg").set("solver","gmg");

solver("gmg").feature("pr").create("p1","SORVector");

solver("gmg").feature("po").create("p1","SORVector");

SolverFeature csolver = solver("gmg").feature("csolver").create("c1","Direct");

csolver.set("solver","spooles");

csolver.set("errorchkd","on");

Code for Use with MATLAB

solver.create('gmg','Multigrid');

solver('gmg').set('solver','gmg');

solver('gmg').feature('pr').create('p1','SORVector');

solver('gmg').feature('po').create('p1','SORVector');

csolver = solver('gmg').feature('csolver').create('c1','Direct');

csolver.set('solver','spooles');

csolver.set('errorchkd','on');

Use Conjugate Gradients instead of GMRES:

Code for Use with Java

solver.set("solver","cg");

Code for Use with MATLAB

solver.set('solver','cg');

Use the sparse approximate inverse (SAI) preconditioner using a sparsity pattern of SAI defined by a power of 3 of the system matrix:

Code for Use with Java

model.sol("sol1").feature("t1").create("i1", "Iterative");

model.sol("sol1").feature("t1").feature("i1").set("linsolver", "cg");

model.sol("sol1").feature("t1").feature("i1").create("sai1", "SAI");

model.sol("sol1").feature("t1").feature("i1").feature("sai1").set("saisymm", "on");

model.sol("sol1").feature("t1").feature("i1").feature("sai1").
set("saipattern","saipowa");

model.sol("sol1").feature("t1").feature("i1").feature("sai1").set("saipowera", "3");

Code for Use with MATLAB

iter = model.sol('sol1').feature('t1').create('i1', 'Iterative');

iter.set('linsolver', 'cg');

iter.create('sai1', 'SAI');

iter.feature('sai1').set('saisymm', 'on');

iter.feature('sai1').set('saipattern','saipowa');

iter.feature('sai1').set('saipowera', '3');

The Prefun Property

The prefun property for the solver (preconditioner) accepts a different set of values depending on the context. In the section below, its possible values and default value is listed for each preconditioner that supports it.

Direct Properties

Table 6-35: Valid Direct Properties (For All Solver)
Property	Values	Default	Description
errorchk	off \| on \| auto	auto	Check error estimate.
iterrefine	on \| off	on off (eigenvalue solver)	Iterative refinement.
linsolver	mumps \| pardiso \| spooles \| dense	mumps	Method to use.
maxrefinesteps	nonnegative integer	15	Maximum number of iterative refinement steps.
nliniterrefine	on \| off	off	Use iterative refinement in nonlinear solver.
prefun	mumps \| pardiso \| spooles \| dense	mumps	Solver for preconditioner (MUMPS, PARDISO, SPOOLES, or Dense Matrix).
rhob	scalar > 1	400 1 (coarse solver)	Factor in linear error estimate.

Table 6-36: Optional Direct Properties
Property	Values	Default	Description
clusterpardiso	on \| off	off	Use Parallel Direct Sparse Solver for Clusters (PARDISO).
incore	auto \| manual	auto	In-core memory method (PARDISO, MUMPS).
internalmemusage	positive real	3	Internal memory usage factor (PARDISO, MUMPS).
memfracooc	scalar between 0 and 1	0.99	Fraction of memory to store out of core.
minicmemory	positive real	512.0	Minimum in-core memory in MB (PARDISO, MUMPS).
mumpsalloc	scalar at least 1	1.2	MUMPS memory allocation factor (MUMPS).
mumpsreorder	auto \| amd \| amf \| qamd \| nd	auto	Preordering algorithm (MUMPS).
mumpsrreorder	on \| off	on	Row preordering (MUMPS).
ooc	automatic \| on \| off	automatic	Use out-of-core (PARDISO, MUMPS). The automatic option switches to out-of-core storage if needed.
oocmemory	positive real	512.0	In-core memory in MB (PARDISO, MUMPS).
pardmtsolve	on \| off	off	Multithreaded forward and backward solve (PARDISO).
pardreorder	mmd \| nd \| ndmt	nd	Preordering algorithm (PARDISO).
pardrreorder	on \| off	on	Row preordering algorithm (PARDISO).
pardschedule	auto \| one \| two	auto	Scheduling method (PARDISO).
pivotenable	on \| off	on	Use pivoting (MUMPS).
pivotperturb	scalar between 0 and 1	1e-8	Pivot perturbation threshold (PARDISO, MUMPS).
pivotrefines	nonnegative integer	0	Number of forced iterative refinements (PARDISO, MUMPS).
pivotstrategy	on \| off	off	Use 2-by-2 Bunch-Kaufman pivoting (on) or 1-by-1 diagonal pivoting (off) (PARDISO).
preorder	mmd \| nd \| ms \| bestof	nd	Preordering algorithm (SPOOLES).
thresh	scalar between 0 and 1	0.1	Pivot threshold (MUMPS, SPOOLES).
usetotmemory	scalar between 0 and 1	0.8	Used fraction of total memory (PARDISO, MUMPS).

Iterative Properties

Table 6-37: Valid Iterative Properties (for All Solvers)
Property	Values	Default	Description
errorchk	off \| on \| auto	auto	Validate error estimate.
iterrefine	on \| off	on	Iterative refinement.
linsolver	gmres \| fgmres \| bicgstab \| cg \| precond	gmres, ilu (precond)	Method to use.
maxlinit	positive integer	10000 500 (coarse solver)	Maximum number of linear iterations (when used with a tolerance).
maxrefinesteps	nonnegative integer	15	Maximum number of iterative refinement steps.
nliniterrefine	on \| off	off	Use iterative refinement in nonlinear solver.
rhob	scalar > 1	400 1 (coarse solver)	Factor in linear error estimate.

Table 6-38: Optional Iterative Properties
Property	Values	Default	Description
droptol	scalar between 0 and 1	0.01 when used as preconditioner, 1 when used as presmoother, postsmoother, or coarse solver	Drop tolerance (SPOOLES, Incomplete LU with tolerance element dropping strategy).
droptype	tol \| fill	tol	Element dropping strategy for Incomplete LU (Tolerance, Fill ratio).
fillratio	nonnegative integer	1	Fill ratio (Incomplete LU with Fill ratio element dropping strategy and SAI).
ilutdroptol	scalar between 0 and 1	0.01	Drop tolerance (ILUT).
ilutfillratio	nonnegative integer	1	Fill ratio (ILUT).
iter	nonnegative integer	2 (1 for ILU and ILUT)	Fixed number of iterations (when used as preconditioner, smoother, or coarse solver), for all iterative solvers except direct preconditioner.
iterm	tol \| iter	iter	Termination technique (when Incomplete LU, ILUT, or ILU0 are used as coarse solver).
itrestart	positive integer	50	Number of iterations before restart (gmres, fgmres).
prefun	ilu \| ilut \| ilu0 \| spooles	ilu	Solver (preconditioner) for Incomplete LU, ILUT (Intel MKL), ILU0 (Intel MKL), or SPOOLES).
prefuntype	auto (SAI only) \| left \| right	left (auto for SAI)	Left or right preconditioning (gmres, cg, bicgstab, SAI). For SAI, the default preconditioning type is auto.
relax	scalar between 0 and 2	1	Relaxation factor (Jacobi, SOR-based algorithms, ILU, ILUT, SAI, and Vanka).
respectpattern	on \| off	on	Respect the matrix pattern (ILU).
saisymm	auto \| off \| on \| hermitian	auto	Symmetry characteristics of SAI method corresponding to Automatic, Nonsymmetric, Symmetric, and Hermitian, respectively.
saipattern	sysmat \| saipowa	sysmat	Sparsity pattern of SAI defined by system matrix or power of system matrix.
saipowera	positive integer	2	Power of system matrix for SAI sparsity pattern.
seconditer	nonnegative integer	1	Number of secondary iterations (SOR vector and SOR gauge algorithms), number of SSOR updates (vanka).
sorblocked	on \| off	on	Blocked SOR method.
sorvecdof	vector of strings		Vector element variables (SOR vector and SOR gauge algorithms).
symmetric	on \| off	off	Use symmetric form; ssor instead of sor, and so forth. (SOR, SORVector, SORGauge, SORLine).
thresh	scalar between 0 and 1	1	Pivot threshold (ILU).
transpose	on \| off	off	Use transposed form; soru instead of sor and so forth. (SOR, SORVector, SORGauge, SORLine).
hybridization	single \| multi	single	Use a single preconditioner or multiple preconditioner as a hybrid preconditioner.
hybridvar	vector of strings		Fields/States in step.
hybridvarspec	all \| manual	all	Include all components or specify which manually.
hybridcomp	vector of strings		Field/State components in step if hybridvarspec=manual.
vankablocked	on \| off	on	Blocked Vanka method.
vankarelax	scalar between 0 and 2	0.8	Relaxation factor for Vanka update.
vankarestart	positive integer	100	GMRES restart value (vanka).
vankasolv	gmres \| direct	gmres	Local block solver (vanka).
vankatol	positive scalar	0.02	GMRES tolerance (vanka).
vankavars	vector of strings	{}	Lagrange multiplier variables (vanka).

The property divcleantol is used in the inequality |TTb| < divcleantol · |b| to ensure that the numerical divergence after divergence cleaning is small enough; see SOR Gauge in the COMSOL Multiphysics Reference Manual.

Multigrid Properties

Table 6-39: Valid Multigrid Properties
Property	Values	Default	Description
gmglevels	positive integer	1	Maximum number of geometric multigrid levels.
iter	integer	2	Fixed number of iterations (when used as preconditioner, smoother, or coarse solver).
linsolver	gmg \| amg	gmg	Method to use.
maxlinit	positive integer	500	Maximum number of linear iterations (when used with a tolerance).
mgcycle	v \| w \| f	v	Cycle type.
mglevels	positive integer	5	Maximum number of algebraic multigrid levels.
prefun	gmg \| amg \| saamg	amg if used as Krylov preconditioner. gmg, otherwise.	Solver for preconditioner (Geometric multigrid, Algebraic multigrid, or Smoothed aggregation AMG).
rhob	scalar > 1	400 1 (coarse solver)	Factor in linear error estimate.

Table 6-40: Optional Multigrid Properties
Property	Values	Default	Description
agglevel	positive integer	2	Multigrid level to start smoothing at, if aggmethod =manual (saamg).
aggmethod	auto \| manual	auto	Smoothing of prolongations if usesmooth=on (saamg).
amgauto	integer from 1 to 10	3	Quality of multigrid hierarchy (amg).
geomuse	vector of strings		Geometries for geometric multigrid hierarchy.
hybridization	single \| multi	single	Use a single preconditioner or multiple preconditioner as a hybrid preconditioner.
hybridvar	vector of strings		Fields/States in step.
hybridvarspec	all \| manual	all	Include all components or specify which manually.
hybridcomp	vector of strings		Field/State components in step if hybridvarspec=manual.
jacdamp	positive scalar	2/3	Jacobi damping facto if usesmooth=on (saamg).
massem	on \| off	on	Assemble on multigrid levels (gmg).
maxcoarsedof	positive integer	5000	Maximum number of DOFs at coarsest level (amg, saamg).
mcaseassem	vector of strings		Multigrid levels where assemble should be performed (gmg, mcasegen=manual).
mcasegen	manual \| all \| any \| coarse \| coarseorder \| refine \| refineany \| refineall	any	Hierarchy generation method (gmg).
mcaseuse	vector of strings		Multigrid levels which should be used (gmg, mcasegen=manual).
mkeep	on \| off	off	Keep generated mesh cases (gmg).
nullspace	constant \| rbm		Null-space vectors: constant or rigid body modes (saamg).
rmethod	regular \| longest	regular	Mesh refinement method (gmg).
saamgcompwise	on \| off	off	Construct the SAAMG prolongators componentwise (saamg).
scale	vector of positive numbers	2	Mesh scale factor (gmg).
strconn	positive scalar	0.01	Strength of connection (saamg).
usefilter	on \| off	on	Use filtering if usesmooth=on (saamg).
usesmooth	on \| off	on	Use prolongation smoothing (saamg).

Th useaggressive property is no longer used from version 5.3. For the geometric multigrid solver/preconditioners, the multigrid hierarchy is controlled in the following way (see also Multigrid in the COMSOL Multiphysics Reference Manual):

•

If mcasegen=all, any, or coarse, coarseorder, then the multigrid hierarchy is automatically constructed starting from the mesh and discretization set by the study. The number of multigrid levels generated is given in the property gmglevels. The method all and any first tries to lower the discretization order for the shape functions used, and secondly coarsens the mesh. The method all lowers the order (by one) if all used shape functions can be lowered. The method any lowers the order (by one) if at least one shape function can be lowered. The method coarse does not lower the order, it only coarsens the mesh. The method coarseorder both lowers the order (for any shape functions that can be lowered by one) and coarsen the mesh, at the same time.

•

If mcasegen=refine, refineany, or refineall then the multigrid hierarchy is automatically constructed by a combination of refining the mesh given by the study and changing the discretization. The number of multigrid levels generated is given in the property gmglevels. The refinement method can be specified using the property rmethod. The originally selected mesh for the study is used, in the case of refining the mesh, in a multigridlevel and the finest multigrid level generated is used for the study (solved for). The generated multigrid levels are kept in the model and the mcasegen property is changed into manual. The method refine only refines the mesh and does not change the shape function order. The method refineany and refineall first tries to lower the order, and secondly refines the mesh. The method refineany constructs a multigrid level by lowering the order (by one) if at least on shape function can be lowered. The method refineall generates multigrid levels by lowering the order (by one) if all used shape function can be lowered.

•

If mcasegen=manual, then the existing multigrid levels (children to the current study) can be used. The subset to use is selected by giving their tags to the mcaseuse property.

The construction of coarse level matrices is controlled by the property massem and mcaseassem. The first property controls if the matrices should be assembled for the automatically generated levels. If set to off, prolongation and restriction matrices are used to project the matrices from the top level in the hierarchy. The second property controls which multigrid levels that should use the assemble technique in the mcasegen=manual case.

When an iterative solver is used as preconditioner, smoother, or coarse solver you can choose whether to solve using a tolerance or to perform a fixed number of iterations. When used as a coarse solver the default is to solve using a tolerance. When used as a preconditioner or smoother the default is to perform a fixed number of iterations. If both properties itol and iter are given, the program solves using a tolerance.

Domain Decomposition Properties

Table 6-41: Valid Domain decomposition Properties
Property	Value	Default	Description
prefun	ddadd \| ddmul \| ddhyb \| ddsym	ddmul	Domain decomposition solver (Additive Schwarz/Multiplicative Schwarz/Hybrid Schwarz/ Symmetric Schwarz).
iter	integer	1	Number of iterations.
ndom	integer	2	Number of subdomains.
ddreordermethod	none \| space	space	Element reordering method: none or using a space-filling curve.
domdofmax	integer	1	Maximum number of nodes per subdomain.
domnodesmax	integer	100000	Maximum number of DOFs per subdomain.
overlap	integer	1	Additional overlap.
overlapmethod	auto \| matrix \| mesh	auto	Overlap method.
prefermatfree	on \| off	off	Automatically choose matrix free format.
usecoloring	on \| off	on	Use coloring (for prefun = ddmul \| ddsym).
userac	on \| off	off	Recompute and clear subdomain data.
domgeom	vector of strings		Partition geometries.
usecoarse	on \| algebraic \| aggregation \| off	on	Use coarse level: geometric (on), algebraic multigrid (algebraic), aggregations AMG (aggregation), or off.
mcasegen	coarseorder \| all \| any \| coarse \| refineall \| refineany \| refine \| manual	any	Coarse level generation method.
scale	scalar > 0	2.0	Mesh coarsening factor (for mcasegen = coarseorder \| any \| all \| coarse).
rmethod	longest \| regular	longest	Mesh refinement method (for mcasegen = refineall \| refineany \| refine).
geomuse	vector of strings		Use coarse level in geometries (for mcasegen = coarseorder \| all \| any \| coarse \| refineall \| refineany \| refine).
massem	on \| off	on	Assemble on coarse level (for mcasegen = coarseorder \| all \| any \| coarse \| refineall \| refineany \| refine \| manual).
mkeep	on \| off	on	Keep generated coarse level (for mcasegen = all \| any \| coarse).
mcaseuse	vector of strings		Coarse level that should be used (for mcasegen = manual).
mglevels	positive integer	5	Maximum number of algebraic multigrid levels (algebraic, aggregation).
maxcoarsedofs active	on \| off	off	Enable setting the maximum number of DOFs at coarsest level
maxcoarsedof	positive integer	5000	Maximum number of DOFs at coarsest level (algebraic, aggregation) if maxcoarsedofsactive is on.
amgauto	integer from 1 to 10	3	Quality of multigrid hierarchy (algebraic).
agglevel	positive integer	2	Multigrid level to start smoothing at, if aggmethod =manual (aggregation).
aggmethod	auto \| manual	auto	Postpone prolongation smoothing (aggregation).
amgauto	integer from 1 to 10	3	Quality of multigrid hierarchy (algebraic).
jacdamp	positive scalar	2/3	Jacobi damping factor (aggregation).
strconn	positive scalar	0.01	Strength of connection (aggregation).
useaggressive	on \| off	on	Use aggressive coarsening (aggregation).
usefilter	on \| off	on	Use filtering (aggregation).
hybridization	single \| multi	single	Use a single preconditioner or multiple preconditioner as a hybrid preconditioner.
hybridvar	vector of strings		Fields/states in step / Preconditioner variables (for hybridization = multi).
hybridvarspec	all \| manual	all	Include all components or specify which manually (for hybridization = multi).
hybridcomp	vector of strings		Field/state components in step / Preconditioner selection (for hybridvarspec= manual).

Example Code for Use With Java

model.sol("sol1").feature("s1").create("i1", "Iterative");

model.sol("sol1").feature("s1").feature("i1").create("dd1","DomainDecomposition");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").feature("ds").
create("mg1","Multigrid");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").set("prefun","ddadd");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").set("mcasegen","refine");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").set("domnodesmax","2");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").
set("overlapmethod","mesh");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").set("ndom", "16");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").
set("domgeom", new String[]{"geom1"});

model.sol("sol1").feature("s1").feature("i1").feature("dd1").feature("cs").
feature("dDef").set("linsolver","pardiso");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").feature("ds").

feature("mg1").set("gmglevels","5");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").
set("hybridization","multi");

model.sol("sol1").feature("s1").feature("i1").feature("dd1").
set("hybridcomp", new String[]{"comp1.u"});

SOR Prefun Property

Table 6-42: SOR prefun Property
Property	Value	Default	Description
prefun	ssor \| sor \| soru	ssor	Solver (SSOR, SOR, or SORU).

SSOR Gauge Prefun Property

Table 6-43: SSOR Gauge prefun Property
Property	Value	Default	Description
prefun	ssorgauge \| sorgauge \| sorugauge	sorgauge when used as presmoother; sorugauge when used as postsmoother; ssorgauge otherwise.	Solver (SSOR gauge, SOR gauge, or SORU gauge).

SOR Vector Prefun Property

Table 6-44: SOR Vector prefun Property
Property	Value	Default	Description
prefun	ssorvec \| sorvec \| soruvec	sorvec when used as presmoother; soruvec when used as postsmoother; ssorvec otherwise.	Solver (SSOR vector, SOR vector, or SORU vector).