Abstract

Various choices of a finite-difference scheme for approximating the heat diffusion equation in solving a three-dimensional coefficient inverse problem were studied. A comparative analysis was conducted for several alternating direction schemes, such as locally one-dimensional, Douglas–Rachford, and Peaceman–Rachford schemes, as applied to nonlinear problems for the three-dimensional heat equation with temperature-dependent coefficients. Each numerical method was used to compute the temperature distribution inside a parallelepiped. The methods were compared in terms of the accuracy of the resulting solution and the computation time required for achieving the prescribed accuracy on a computer.

中文翻译：

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求解系数反问题的有限差分格式的选择

摘要

研究了在求解三维系数逆问题中逼近热扩散方程的有限差分方案的各种选择。对几种交替方向方案进行了比较分析，例如局部一维，Douglas-Rachford和Peaceman-Rachford方案，这些方案应用于具有温度相关系数的三维热方程的非线性问题。每种数值方法都用于计算平行六面体内部的温度分布。根据所得解决方案的精度和在计算机上达到规定精度所需的计算时间对方法进行了比较。