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- W4295138948 abstract "The Helmholtz equation arises in many applications, such as seismic and medical imaging. These application are characterized by the need to propagate many wavelengths through an inhomogeneous medium. The typical size of the problems in 3D applications precludes the use of direct factorization to solve the equation and hence iterative methods are used in practice. For higher wavenumbers, the system becomes increasingly indefinite and thus good preconditioners need to be constructed. In this note we consider an accelerated Kazcmarz method (CGMN) and present an expression for the resulting iteration matrix. This iteration matrix can be used to analyze the convergence of the CGMN method. In particular, we present a Fourier analysis for the method applied to the 1D Helmholtz equation. This analysis suggests an optimal choice of the relaxation parameter. Finally, we present some numerical experiments." @default.
- W4295138948 created "2022-09-11" @default.
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- W4295138948 date "2012-10-09" @default.
- W4295138948 modified "2023-09-26" @default.
- W4295138948 title "Fourier analysis of the CGMN method for solving the Helmholtz equation" @default.
- W4295138948 doi "https://doi.org/10.48550/arxiv.1210.2644" @default.
- W4295138948 hasPublicationYear "2012" @default.
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