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arXiv · 1810.01055

A Fourier-Bessel method with a regularization strategy for the boundary value problems of the Helmholtz equation

Deyue Zhang·Fenglin Sun·Yan Ma·Yukun Guo
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Abstract

This paper is concerned with the Fourier-Bessel method for the boundary value problems of the Helmholtz equation in a smooth simply connected domain. Based on the denseness of Fourier-Bessel functions, the problem can be approximated by determining the unknown coefficients in the linear combination. By the boundary conditions, an operator equation can be obtained. We derive a lower bound for the smallest singular value of the operator, and obtain a stability and convergence result for the regularized solution with a suitable choice of the regularization parameter. Numerical experiments are also presented to show the effectiveness of the proposed method.

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Deyue Zhang, Fenglin Sun, Yan Ma, Yukun Guo. 2018-10-02. A Fourier-Bessel method with a regularization strategy for the boundary value problems of the Helmholtz equation. https://arxiv.org/abs/1810.01055

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