Multigrid Methods on Semi-Structured Grids

Autores: Carmen Rodrigo Cardiel , Francisco José Gaspar Lorenz , Francisco Javier Lisbona Cortés
Localización: Archives of computational methods in engineering: state of the art reviews, ISSN 1134-3060, Vol. 19, Nº. 4, 2012, págs. 499-538
Idioma: inglés
DOI: 10.1007/s11831-012-9078-9
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Resumen
- 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