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Extending the applicability of multigrid methods

2006; IOP Publishing; Volume: 46; Linguagem: Inglês

10.1088/1742-6596/46/1/061

1742-6596

James Brannick, Marian Brezina, Robert D. Falgout, Thomas A. Manteuffel, Steve McCormick, J. Ruge, Brendan Sheehan, Jinchao Xu, Ludmil Zikatanov,

Computational Fluid Dynamics and Aerodynamics

Multigrid methods are ideal for solving the increasingly large-scale problems that arise in numerical simulations of physical phenomena because of their potential for computational costs and memory requirements that scale linearly with the degrees of freedom. Unfortunately, they have been historically limited by their applicability to elliptic-type problems and the need for special handling in their implementation. In this paper, we present an overview of several recent theoretical and algorithmic advances made by the TOPS multigrid partners and their collaborators in extending applicability of multigrid methods. specific examples that are presented include quantum chromodynamics, radiation transport, and electromagnetics.