基于傅里叶扩展和过采样技术的任意域双调和求解器

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-08-16 DOI:10.1016/j.apnum.2025.08.005

Wenbin Li, Tinggang Zhao, Zhenyu Zhao

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引用次数: 0

摘要

双调和方程在弹性理论、流体动力学和图像处理等各个领域都经常遇到。在不规则域上求解这一问题是一个重大的挑战。本文采用傅里叶扩展法求解任意域上的双调和方程。该方法将过采样配置技术与截断奇异值分解正则化相结合，得到光滑解的谱收敛速率。该方法只使用等距节点上的函数值，具有计算量少、通用性强、精度高等特点。各种数值实验证明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A biharmonic solver based on Fourier extension with oversampling technique for arbitrary domain

The biharmonic equation is commonly encountered in various fields such as elasticity theory, fluid dynamics, and image processing. Solving it on irregular domain presents a significant challenge. In this paper, Fourier extension method is used to solve the biharmonic equation on arbitrary domain. The method involves the oversampling collocation technique with the truncated singular value decomposition regularization, which comes out a spectral convergence rate for the smooth solution. This method only uses the function values on equidistant nodes and has the characteristics of less computation, strong universality and better accuracy. The effectiveness of the proposed method is demonstrated by a variety of numerical experiments.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.