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Article Dans Une Revue Journal of Computational and Applied Mathematics Année : 2006

Plane wave decomposition in the unit disc: Convergence estimates and computational aspects

E. Perrey-Debain

Résumé

This paper deals with the numerical simulation of time-harmonic wave fields using progressive plane waves. It is shown that a plane wave travelling in arbitrary direction can be numerically recovered with an accuracy of the order of the machine precision with a collocation formulation and the square root of the machine precision with a least-square formulation. However, strongly evanescent and nearly singular wave fields cannot be properly recovered with standard double-precision floating-point arithmetic. Some of the ideas are applied to the elastic wave equation and a simple optimization algorithm is proposed to find a good compromise between the accuracy and the number of plane waves.

Dates et versions

hal-03212907 , version 1 (30-04-2021)

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E. Perrey-Debain. Plane wave decomposition in the unit disc: Convergence estimates and computational aspects. Journal of Computational and Applied Mathematics, 2006, 193 (1), pp.140-156. ⟨10.1016/j.cam.2005.05.027⟩. ⟨hal-03212907⟩
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