21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
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  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Craig C. Douglas, Wed, 15.00-15.30 Previous Contents Next  
  A Robust Abstract Multigrid Solver Goes Algebraic
Craig C. Douglas (Univ. of Kentucky)

(joint work with Ryan McKenzie and Adam Zornes, Univ. Kentucky, Lexington)

Abstract multigrid is a term coined by the author some years ago to describe multigrid methods that are defined strictly in terms of matrix operations. For example, on each level Ax = b is the system of linear equations that must be solved. Level transfers are described in terms of matrix-vector operations, e.g., fine to coarse is just c = Rf and coarse to fine is just f = Pc. While the matrices may or may not have a matrix multiply relation in abstract multigrid (though usually they do), in algebraic multigrid there is a relation, namely the Galerkin relation B = RAP to define a coarse level's matrix from a finer level's matrix.

Abstract multigrid leads to quite general solvers for problems in which there is traditional theory leading to convergence results. The Madpack solvers are really general sparse matrix solvers in an abstract multigrid setting. Madpack has recently been extended to algebraic multigrid. Memory cache usage is also an issue that is being addressed.


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28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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