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A spectral boundary integral equation method for the 2D Helmholtz equation. (English) Zbl 0840.65115
The paper is devoted to the numerical solution of the integral equations occurring in the direct boundary integral method for the Helmholtz equation in a two-dimensional domain with smooth boundary. The boundary integral equation is transformed into a system of algebraic equations using a discrete trigonometric collocation method. Aspects of efficient implementation using FFT are also discussed, and numerical examples of wave scattering are given which demonstrate exponential convergence of the method.
Reviewer’s remark: For the theoretical justification (including stability and convergence analysis) of trigonometric approximation methods for boundary integral equations on smooth closed contours, the reader should consult O. Kelle and G. Vainikko [Z. Anal. Anwend. 14, No. 3, 593-622 (1995; Zbl 0832.65128)] and the references therein.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
65R20 Numerical methods for integral equations
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