A Positive and Moment-Preserving Fourier Spectral Method

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-01-25 DOI:10.1137/23m1563918

Zhenning Cai, Bo Lin, Meixia Lin

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 273-294, February 2024.
Abstract. This paper presents a novel Fourier spectral method that utilizes optimization techniques to ensure the positivity and conservation of moments in the space of trigonometric polynomials. We rigorously analyze the accuracy of the new method and prove that it maintains spectral accuracy. To solve the optimization problem, we propose an efficient Newton solver that has a quadratic convergence rate. Numerical examples are provided to demonstrate the high accuracy of the proposed method. Our method is also integrated into the spectral solver of the Boltzmann equation, showing the benefit of our approach in applications.

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正向和保时傅立叶谱方法

SIAM 数值分析期刊》第 62 卷第 1 期第 273-294 页，2024 年 2 月。摘要本文提出了一种新的傅立叶谱方法，利用优化技术确保三角多项式空间中矩的正性和守恒性。我们对新方法的精度进行了严格分析，并证明它保持了频谱精度。为了解决优化问题，我们提出了一种具有二次收敛率的高效牛顿求解器。我们提供了数值示例来证明所提方法的高精度。我们的方法还被集成到了玻尔兹曼方程的光谱求解器中，显示了我们的方法在应用中的优势。

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.