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Numerical Method for Solving Volume Integral Equations on a Nonuniform Grid
Computational Mathematics and Mathematical Physics ( IF 0.7 ) Pub Date : 2021-07-01 , DOI: 10.1134/s0965542521050158
A. B. Samokhin , E. E. Tyrtyshnikov

Abstract

Numerical methods for solving volume integral equations describing the problems of wave scattering by transparent obstacles are considered. The equations are approximated using the collocation method on a nonuniform grid, and the problem is reduced to solving a system of linear algebraic equations. An efficient method is proposed for the approximate multiplication of the matrix of this system by a vector, which is comparable in complexity to the method used in the case of a uniform grid. An auxiliary uniform grid is introduced, and methods of interpolation of functions and algorithms of the fast discrete Fourier transform are used. It is essential that the number of nodes of the auxiliary uniform grid is comparable to the number of nodes of the original nonuniform grid.



中文翻译:

求解非均匀网格上体积积分方程的数值方法

摘要

考虑了求解描述透明障碍物引起的波散射问题的体积积分方程的数值方法。在非均匀网格上使用搭配方法逼近方程,并将问题简化为求解线性代数方程组。提出了一种有效的方法,用于将该系统的矩阵与向量的近似乘法,其复杂性与在均匀网格情况下使用的方法相当。引入了辅助均匀网格,采用了快速离散傅立叶变换的函数插值方法和算法。辅助均匀网格的节点数必须与原始非均匀网格的节点数相当。

更新日期:2021-07-02
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