A boundary-precise method of numerical integration over implicitly defined regions

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-03-21 DOI:10.1016/j.cam.2025.116637

Xuejing Zhang , Huanhuan Ma , Xinyu Wu , Jiansong Deng

引用次数: 0

Abstract

In this paper, we introduce a boundary-precise method of numerical integration over implicitly defined regions using the idea of isogeometry. This method ensures precise boundary representations during the integration process by establishing proper local parameterizations near these boundaries based on the implicit representations. We establish an adaptive algorithm for the method, and provide two examples for integration over different types of regions. We also calculate the error while integrating by this method and provide detailed error estimates. When solving partial differential equations (PDEs) using weighted extended B-spline (WEB) method, the augmented matrix in the linear system of Galerkin framework is derived through integration, where this boundary-precise method can be applied. Three different types of examples are displayed and the results demonstrate the convergence of error and the stability of order.

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隐式定义区域数值积分的边界精确方法

本文利用等几何的思想，提出了隐式区域数值积分的边界精确方法。该方法基于隐式表示，在边界附近建立适当的局部参数化，保证了积分过程中边界的精确表示。建立了该方法的自适应算法，并给出了两个不同类型区域的积分实例。我们还计算了用这种方法积分时的误差，并给出了详细的误差估计。在用加权扩展b样条法求解偏微分方程时，通过积分得到了Galerkin框架线性系统中的增广矩阵，可以应用这种边界精确方法。给出了三种不同类型的算例，结果证明了误差的收敛性和阶序的稳定性。

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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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.