Print Email Facebook Twitter A scalable Helmholtz solver combining the shifted Laplace preconditioner with multigrid deflation Title A scalable Helmholtz solver combining the shifted Laplace preconditioner with multigrid deflation Author Sheikh, A.H. Lahaye, D. Vuik, C. Faculty Electrical Engineering, Mathematics and Computer Science Date 2011-01-31 Abstract A Helmholtz solver whose convergence is parameter independent can be obtained by combining the shifted Laplace preconditioner with multigrid deflation. To proof this claim, we develop a Fourier analysis of a two-level variant of the algorithm proposed in [1]. In this algorithm those eigenvalues that prevent the shifted Laplace preconditioner from being scalable are removed by deflation using multigrid vectors. Our analysis shows that the spectrum of the two-grid operator consists of a cluster surrounded by a few outliers, yielding a number of outer Krylov subspace iterations that remains constant as the wave number increases. Our analysis furthermore shows that the imaginary part of the shift in the two-grid operator can be made arbitrarily large without affecting the convergence. This opens promising perspectives on obtaining a very good preconditioner at very low cost. Numerical tests for problems with constant and non-constant wave number illustrate our convergence theory. To reference this document use: http://resolver.tudelft.nl/uuid:5cd1678a-4ac8-4490-aa3c-c91584c16be9 Publisher Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics ISSN 1389-6520 Source Reports of the Department of Applied Mathematical Analysis, 11-01 Part of collection Institutional Repository Document type report Rights (c)2011 Sheikh, A.H., Lahaye, D., Vuik, C. Files PDF 11-01_Abdul__2_.pdf 360.65 KB Close viewer /islandora/object/uuid:5cd1678a-4ac8-4490-aa3c-c91584c16be9/datastream/OBJ/view