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      Solving the 3D High-Frequency Helmholtz Equation using Contour Integration and Polynomial Preconditioning

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          Abstract

          We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by solving complex-shifted linear systems, resulting in faster GMRES iterations due to the restricted spectrum. The shifted systems are solved by exploiting a polynomial fixed-point iteration, which is a robust scheme even if the magnitude of the shift is small. Numerical tests in 3D indicate that \(O(n^{1/3})\) matrix-vector products are needed to solve a high-frequency problem with a matrix size \(n\) with high accuracy. The method has a small storage requirement, can be applied to both dense and sparse linear systems, and is highly parallelizable.

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          A perfectly matched layer for the absorption of electromagnetic waves

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            Nested Dissection of a Regular Finite Element Mesh

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              ILUT: A dual threshold incomplete LU factorization

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                Author and article information

                Journal
                29 November 2018
                Article
                1811.12378
                8af24513-59a1-4896-87da-763d2e5d1fbe

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.NA

                Numerical & Computational mathematics
                Numerical & Computational mathematics

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