3D Helmholtz Krylov Solver Preconditioned by a Shifted Laplace Multigrid Method on Multi-GPUs

GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method

Delft University of Technology Report 11-01 a Scalable Helmholtz Solver Combining the Shifted Laplace Preconditioner with Multigrid Deflation

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 mu...

Multilevel Krylov Method for the Helmholtz Equation

In the first part of the talks on multilevel Krylov methods, Reinhard Nabben discussed the underlying concept of the method and showed by some numerical examples the effectiveness of the method. In this talk, we extend the application of the multilevel Krylov method to the indefinite, high wavenumber Helmholtz equation. In this case, we consider the preconditioned Helmholtz system, where the pr...

On a Multilevel Krylov Method for the Helmholtz Equation Preconditioned by Shifted Laplacian

In Erlangga and Nabben [SIAM J. Sci. Comput., 30 (2008), pp. 1572–1595], a multilevel Krylov method is proposed to solve linear systems with symmetric and nonsymmetric matrices of coefficients. This multilevel method is based on an operator which shifts some small eigenvalues to the largest eigenvalue, leading to a spectrum which is favorable for convergence acceleration of a Krylov subspace me...

On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning

This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not only the coordinates in the absorbing layer have an imaginary part, but also the coordinates in the interior region. This results into a preconditioner problem ...