基于 RBF 的无网格技术和三角基函数框架下的反考赫问题

IF 8.7 2区 工程技术 Q1 Mathematics
Farzaneh Safari, Yanjun Duan
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引用次数: 0

摘要

本文旨在指出,在规则域和不规则域上评估椭圆偏微分方程(PDEs)的近似解是有可能的,因为在边界域的某些部分没有定义边界条件。在存在三角基函数 (TBF) 的情况下,与径向基函数神经网络 (RBFNN) 相结合的后向替代法 (BSM) 可以非常容易地实现,而且效果良好。因此,边界条件的近似和求解域内 PDE 的近似是分开的。RBFNN 方法完全分析了不均匀边界条件未给定部分的特殊解,并讨论了所开发算法的效率和准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Inverse Cauchy problem in the framework of an RBF-based meshless technique and trigonometric basis functions

Inverse Cauchy problem in the framework of an RBF-based meshless technique and trigonometric basis functions

The purpose of this paper is to point out that it is possible to evaluate the approximation solution of elliptic Partial differential equations (PDEs) on regular and irregular domains where no boundary conditions are defined on some part of the boundary domain. In the presence of trigonometric basis functions (TBFs), the backward substitution method (BSM) coupled with the radial basis functions neural network (RBFNN) is implemented very easily and works well. As a result, the approximation of the boundary conditions and the approximation of the PDE inside the solution domain is separated. The particular solution with an ungiven part of the inhomogeneous boundary condition is completely analyzed by the RBFNN method, and the efficiency and accuracy of the developed algorithms are discussed.

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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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