A GPU-accelerated Lagrangian method for solving the Liouville equation in random differential equation systems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.09.021

V.J. Bevia, S. Blanes, J.C. Cortés, N. Kopylov, R.J. Villanueva

引用次数: 0

Abstract

This work presents and analyzes a numerical approach to efficiently solve the Liouville equation in the context of random ODEs using GPGPUs. Our method combines wavelet compression-based adaptive mesh refinement, Lagrangian particle methods, and radial basis function interpolation to create a versatile algorithm applicable in multiple dimensions. We discuss the advantages and limitations of this algorithm. To demonstrate its effectiveness, we compute the probability density function for various 2D and 3D random ODE systems with applications in physics and epidemiology.

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随机微分方程系统中求解Liouville方程的gpu加速拉格朗日方法

本文提出并分析了一种利用gpgpu在随机ode环境下有效求解Liouville方程的数值方法。该方法将基于小波压缩的自适应网格细化、拉格朗日粒子法和径向基函数插值相结合，形成了一种适用于多个维度的通用算法。讨论了该算法的优点和局限性。为了证明其有效性，我们计算了具有物理和流行病学应用的各种二维和三维随机ODE系统的概率密度函数。

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.