Black box multigrid solver for definite and indefinite problems

Abstract

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Multigrid for refined triangle meshes

“…Nevertheless, when multi-level implementations are considered this pattern may be resolved recursively by a similar approach, using some splitting of the next fine grid fc c c derived from c the same way f was derived from c U f . A reasonable choice is to use the above splitting method also for fc; it is recommended to construct the next prolongation and restriction operators Pc : c + c and R, : c + c not from JcRAPJ: but from a modification of it, in which elements which are outside the pattern of the corresponding linear finite element scheme are 'thrown' to the main diagonal (see [9] [lo]). With this implementation, the pattern of the coarse grid coefficient matrix is preserved also for the next coarse level coefficient matrix, which results in an efficient multi-level implementation.…”