Package FL.GEOMG (Femlisp User Manual)

7.24 Package FL.GEOMG

The FL.GEOMG package contains iterations which depend on geometric information, obtained for example from the discretization. At the moment, these are the geometric multigrid iteration, an AMG-like scheme for preconditioning high-order discretizations with low-order ones, and some block smoothers with overlapping blocks.

Class: <GEOMETRIC-CS>

Geometric multigrid of correction scheme type.

Superclasses: <CORRECTION-SCHEME> <GEOMETRIC-MG>

Class: <GEOMETRIC-FAS>

Brandt’s FAS scheme approximates the unknowns on every level instead of using corrections. This requires slightly more work, but is better suited for handling nonlinear problems and local refinements.

Superclasses: <FAS> <GEOMETRIC-MG>

Class: <GEOMETRIC-PSC>

PSC with geometry-based block choice.

Superclasses: <GEOMETRIC-BLOCKING-MIXIN> <PSC>

Class: <GEOMETRIC-SSC>

SSC with geometry-based block choice.

Superclasses: <GEOMETRIC-BLOCKING-MIXIN> <SSC>

Class: <S1-COARSE-GRID-ITERATOR>

Calls LU directly, if the matrix was not reduced to S1 which may happen if there are only Dirichlet vertices.

Superclasses: <LINEAR-ITERATION>

Class: <S1-REDUCTION>

This class is useful for reducing a higher-order FE discretization to a first-order FE discretization. This can afterwards be treated by ordinary AMG steps. Even if it has the structure of a <selection-amg>, it is far from being a pure algebraic multigrid.

Superclasses: <SELECTION-AMG>

Class: <VANKA>

Vanka-like smoother for Q^{k+1}/Q^k discretizations of Navier-Stokes.

Superclasses: <GEOMETRIC-SSC>

Function: FAS &REST KEY-ARGS: Constructor of a geometric multigrid iteration of FAS type.

Function: GEOMETRIC-CS &REST KEY-ARGS: Constructor of a geometric multigrid iteration of correction scheme type.

Function: GEOMETRIC-PSC &REST REST: Constructor of a geometric parallel subspace correction.

Function: GEOMETRIC-SSC &REST REST: Constructor of a geometric successive subspace correction.

Function: S1-REDUCTION-AMG-SOLVER ORDER &KEY OUTPUT REDUCTION (MAXSTEPS 100): This is an AMG solver which works also for Lagrange fe of order p by reducing them to P^1 first.