解决有奇点的椭圆问题的富集多节点谢泼德配位法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-07-20 DOI:10.1016/j.apnum.2024.07.005

Francesco Dell'Accio , Filomena Di Tommaso , Elisa Francomano

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引用次数: 0

摘要

本文首次采用多节点 Shepard 方法对边界不连续的微分问题进行数值求解。从以往对椭圆边界值问题的研究出发，本文采用 Shepard 方法来捕捉边界上的奇点。为了克服所遇到的困难，我们提出了对多节点心形 Shepard 基函数所跨函数空间的富集。莫兹问题被视为评估该方法的数值基准。数值结果显示了所提方法的有效性。

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The enriched multinode Shepard collocation method for solving elliptic problems with singularities

In this paper, the multinode Shepard method is adopted for the first time to numerically solve a differential problem with a discontinuity in the boundary. Starting from previous studies on elliptic boundary value problems, here the Shepard method is employed to catch the singularity on the boundary. Enrichments of the functional space spanned by the multinode cardinal Shepard basis functions are proposed to overcome the difficulties encountered. The Motz's problem is considered as numerical benchmark to assess the method. Numerical results are presented to show the effectiveness of the proposed approach.

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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.