球面有限差分法的高度局部化 RBF 拉格朗日函数

IF 1.6 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

BIT Numerical Mathematics Pub Date : 2024-03-15 DOI:10.1007/s10543-024-01016-x

W. Erb, T. Hangelbroek, F. J. Narcowich, C. Rieger, J. D. Ward

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引用次数: 0

摘要

本文旨在展示如何利用球面上快速衰减的 RBF 拉格朗日函数来创建一种基于径向基函数的数值可行、稳定的有限差分方法（类 RBF-FD 方法）。对于某些类别的 PDEs，这种方法可为随着离散化精细度的增加而适度增长的模板带来严格的收敛估计值。

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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Highly localized RBF Lagrange functions for finite difference methods on spheres

The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the sphere can be used to create a numerically feasible, stable finite difference method based on radial basis functions (an RBF-FD-like method). For certain classes of PDEs this approach leads to rigorous convergence estimates for stencils which grow moderately with increasing discretization fineness.

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来源期刊

BIT Numerical Mathematics 数学-计算机：软件工程

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The journal BIT has been published since 1961. BIT publishes original research papers in the rapidly developing field of numerical analysis. The essential areas covered by BIT are development and analysis of numerical methods as well as the design and use of algorithms for scientific computing. Topics emphasized by BIT include numerical methods in approximation, linear algebra, and ordinary and partial differential equations.