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

Authors:
E. Perrey-Debain
Affiliations:
School of Mathematics, University of Manchester, Manchester, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 4
Cited 2

Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem

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Computational aspects of the ultra-weak variational formulation

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The Ultra-Weak Variational Formulation for Elastic Wave Problems

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Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Wavelet based ILU preconditioners for the numerical solution by PUFEM of high frequency elastic wave scattering

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An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

SIAM Journal on Scientific Computing

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Abstract

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.