A P-Version of Convolution Quadrature in Wave Propagation

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-08-14 DOI:10.1137/24m1642524

Alexander Rieder

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1729-1756, August 2025.
Abstract. We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the time step size ([math]-method), we achieve accuracy by increasing the order of the method ([math]-method). We base this method on discontinuous Galerkin time stepping and use the Z-transform. We show that for a certain class of incident waves, the resulting schemes observe a (root)-exponential convergence rate with respect to the number of boundary integral operators that need to be applied. Numerical experiments confirm the finding.

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波传播中卷积正交的p型

SIAM数值分析杂志，第63卷，第4期，第1729-1756页，2025年8月。摘要。我们考虑了一种利用卷积正交的一般形式来离散波散射问题的新方法，但我们不是减少时间步长（[math]-方法），而是通过增加方法的阶数（[math]-方法）来达到精度。该方法基于不连续伽辽金时间步进，并采用z变换。我们证明，对于某类入射波，所得到的格式相对于需要应用的边界积分算子的数量观察到（根）指数收敛率。数值实验证实了这一发现。

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

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.