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6.27 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.