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 6-36: Valid Direct Properties (For All Solvers)
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
 1
Factor in linear error estimate.
 
Table 6-37: 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).
mumpsblr
 on | off
off
Block low rank factorization (MUMPS).
mumpsblrtol
scalar between 0 and 1
1e-8
Block low rank factorization tolerance (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).
reusereorder
true | false
true
Reuse preordering (PARDISO, MUMPS).
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 6-38: Valid Iterative Properties (for All Solvers)
Property
Values
Default
Description
errorchk
off | on | auto
auto
Validate error estimate.
linsolver
gmres | fgmres | bicgstab | tfqmr | cg | precond
gmres, ilu (precond)
Method to use.
maxilinit
positive integer
100
Maximum number of intermediate iteration for the iterative solver in error checking. Available when errorchk is auto.
maxlinit
positive integer
10000
500 (coarse solver)
Maximum number of linear iterations (when used with a tolerance).
rhob
scalar > 1
 1
Factor in linear error estimate.
 
Table 6-39: 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; 0.001 for Hierarchical LU
Drop tolerance (SPOOLES, Hierarchical LU, Incomplete LU with tolerance element dropping strategy).
droptype
tol | fill
tol
Element dropping strategy for Incomplete LU (Tolerance, Fill ratio).
elimtol
scalar between 0 and 1
1
Elimination tolerance (Hierarchical LU).
fillratio
nonnegative integer
1
Fill ratio (Incomplete LU with Fill ratio element dropping strategy and SAI).
hybridcomp
vector of strings
 
Field/State components in step if hybridvarspec=manual.
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.
irestol
scalar between 0 and 1
0.01
Residual tolerance when prefuntype is left (gmres, cg, bicgstab, tfqmr).
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, tfqmr, 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, Vanka, and Hierarchical LU).
respectpattern
on | off
on
Respect the matrix pattern (ILU).
reuselines
on | off
on
Reuse lines of nodes (SOR line).
reuseprolongations
on | off
on
Reuse blocks of data (SCGS, SOR line, Vanka).
saicolmaxfactor
positive integer
5
Limit the maximum number of nonzero elements of each column in the SAI preconditioner matrix.
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).
usenlweights
true | false
true
Terminate using nonlinear scales (GMRES with left preconditioning).
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 6-40: 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
 1
Factor in linear error estimate.
 
Table 6-41: 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).
compactaggregation
on | off
on
Use an aggregation algorithm that leads to a less rapid coarsening (saamg).
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).
reuseprolongators
on | off
on
Reuse prolongators when possible (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 6-42: 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).
compactaggregation
on | off
on
Use an aggregation algorithm that leads to a less rapid coarsening (aggregation).
jacdamp
positive scalar
2/3
Jacobi damping factor (aggregation).
reuseprolongators
on | off
on
Reuse prolongators when possible (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 6-43: SOR prefun Property
Property
Value
Default
Description
prefun
ssor | sor | soru
ssor
Solver (SSOR, SOR, or SORU).
SSOR Gauge Prefun Property
Table 6-44: 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 6-45: 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).