High-frequency asymptotics for the numerical solution of the Helmholtz equation |
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Affiliation: | 1. Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA;2. School of Civil, Urban & Geosystem Engineering, Seoul National University, 56-1 Shinlim-Dong, Kwanak-Gu, Seoul 151-742, South Korea;3. Department of Mathematics, Stanford University, Stanford, CA 94305, USA |
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Abstract: | It is often noted that the Helmholtz equation is extremely difficult to solve, in particular, for high-frequency solutions for heterogeneous media. Since stability for second-order discretization methods requires one to choose at least 10–12 grid points per wavelength, the discrete problem on the possible coarsest mesh is huge. In a realistic simulation, one is required to choose 20–30 points per wavelength to achieve a reasonable accuracy; this problem is hard to solve. This article is concerned with the high-frequency asymptotic decomposition of the wavefield for an efficient and accurate simulation for the high-frequency numerical solution of the Helmholtz equation. It has been numerically verified that the new method is accurate enough even when one chooses 4–5 grid points per wavelength. |
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