COMSOL Multiphysics™

femsolver
scalar Shapechg, and the number of multigrid levels (including the finest level) is
given in the property Mglevels (default 2).
• If Mgauto=explicit, then the multigrid hierarchy is automatically constructed
starting from the mesh case given in the property Mcase. The properties
Meshscale and Shapechg should be vectors of the same length (however if one
is scalar, it is expanded to the same length as the other). A number of coarse levels
are constructed, where level i has a mesh that is coarsened with the factor
Meshscale(i), and shape functions orders incremented with Shapechg(i)
relative to mesh case Mcase. Shapechg(i) should be negative or zero.
• If Mgauto=meshrefine, then the multigrid hierarchy is automatically
constructed by refining the mesh in mesh case Mcase repeatedly. The number of
multigrid levels (including the original, coarsest level) is given in the property
Mglevels (default 2). The refinement method can be specified using the
property Rmethod, see meshrefine.
• If Mgauto=off, then only existing mesh cases are used in the hierarchy. If the
property Mcase is a scalar, then all mesh cases that have fewer degrees of freedom
than the mesh case Mcase are used as coarse levels. If Mcase is a vector with more
than one component, the mesh cases in that vector are used. However, if the
property Mglevels is given, no more than Mglevels levels are used. The solver
sorts the list of mesh cases according to decreasing number of DOFs, and the
solution is delivered for the mesh case with the largest number of DOFs. This
corresponds to the Manual option in the COMSOL Multiphysics user interface.
The default for Mgauto is as follows: If the FEM structure has several mesh cases,
then Mgauto=off, otherwise Mgauto is the same as the default in meshcaseadd.
The construction of coarse level matrices is controlled by the property Mgassem. If
Mgassem is a vector, Mgassem(i) should be a 0 or 1. Mgassem(i)=1 means that
matrices should be assembled in mesh case Mcase(i), rather than being projected
from the next finer level. The length of Mgassem should be (at least) the number of
mesh cases used, including the finest level. The value of Mgassem(i) for the finest
level i is ignored, because matrices are always assembled on the finest level. A scalar
Mgassem applies to all coarse mesh cases.
Four Examples How to Construct the Geometric Multigrid Hierarchy
Assume that fem only contains the mesh case 0, and no xmesh.
Alternative 1:
fem.xmesh = meshextend(fem);
fem.sol = femstatic(fem,'linsolver','gmg');
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