Multigrid Methods on Semi-Structured Grids

ISSN： 1134-3060

Source： Archives of Computational Methods in Engineering, Vol.19, Iss.4, 2012-12, pp. : 499-538

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Abstract

In this work, efficient block-wise multigrid solvers on semi-structured triangular grids are presented for two-dimensional problems. They take advantage of the flexibility of triangular grids as well as the efficiency of block-structured grids, yielding very promising solvers on nowadays hardware. Semi-structured grids offer many advantages for the stencil-wise implementation of geometric multigrid, as well as for an efficient implementation of finite element methods without assembling the global matrix. The semi-structured character of the grids enables us to develop the multigrid algorithm on a block-wise manner, by choosing different components on the structured patches of the mesh. In order to select appropriate components for the different grid geometries of the blocks, a local Fourier analysis is presented as a very useful tool. Finally, the practical utility of this approach is demonstrated with some numerical experiments.