Algebraic Multigrid Solvers for Complex-Valued Matrices

In the mathematical modeling of real-life applications, systems of equations with complex coefficients often arise. While many techniques of numerical linear algebra, e.g., Krylovsubspace methods, extend directly to the case of complex-valued matrices, some of the most effective preconditioning techniques and linear solvers are limited to the real-valued case. Here, we consider the extension of the popular algebraic multigrid method to such complex-valued systems. The choices for this generalization are motivated by classical multigrid considerations, evaluated with the tools of local Fourier analysis, and verified on a selection of problems related to real-life applications. Key words. multigrid, algebraic multigrid, complex-valued matrices AMS subject classifications. 65F10, 65N22, 65N55 DOI. 10.1137/070687232

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Scott MacLachlan, Cornelis W. Oosterlee
• Keywords: Algebraic Multigrid, Multigrid, Real-life Applications, SIAMSC 2008