基于 POD 的降阶局部 RBF 搭配方法，用于解决随时间变化的非局部扩散问题

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED Applied Mathematics Letters Pub Date : 2024-09-30 DOI:10.1016/j.aml.2024.109328

Jiashu Lu, Lei Zhang, Xuncheng Guo, Qiong Qi

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引用次数: 0

摘要

针对非稳态非局部扩散模型，提出了一种基于降阶模型（ROM）的快速算法。它结合了适当正交分解（POD）方法和局部径向基函数（RBFs）的配位方法，从而使使用 ROM 求解非局部模型成为可能。一些数值实验表明，这种方法大大降低了非局部模型的计算成本，同时与 RBF 配准方法相比保持了相似的收敛性。

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A POD based reduced-order local RBF collocation approach for time-dependent nonlocal diffusion problems

A fast algorithm based on reduced-order model (ROM) is proposed for unsteady nonlocal diffusion models. It combines proper orthogonal decomposition (POD) approach and collocation method with local radial basis functions (RBFs), which makes it possible for using ROM to solve nonlocal models. Several numerical experiments showed that this approach significantly reduce the computational cost of nonlocal models while keep the similar convergent behavior compared with the RBF collocation methods.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.