Fast Numerical Solvers for Subdiffusion Problems with Spatial Interfaces

IF 1.3 4区数学 Q1 MATHEMATICS

International Journal of Numerical Analysis and Modeling Pub Date : 2024-05-01 DOI:10.4208/ijnam2024-1017

Boyang Yu,Yonghai Li, Jiangguo Liu

引用次数: 0

Abstract

This paper develops novel fast numerical solvers for subdiffusion problems with spatial interfaces. These problems are modeled by partial differential equations that contain both fractional order and conventional first order time derivatives. The former is non-local and approximated by L1 and L2 discretizations along with fast evaluation algorithms based on approximation by sums of exponentials. This results in an effective treatment of the “long-tail” kernel of subdiffusion. The latter is local and hence conventional implicit Euler or Crank-Nicolson discretizations can be used. Finite volumes are utilized for spatial discretization based on consideration of local mass conservation. Interface conditions for mass and fractional fluxes are incorporated into these fast solvers. Computational complexity and implementation procedures are briefly discussed. Numerical experiments demonstrate accuracy and efficiency of these new fast solvers.

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空间界面亚扩散问题的快速数值求解器

本文针对具有空间界面的亚扩散问题开发了新型快速数值求解器。这些问题由包含分数阶和传统一阶时间导数的偏微分方程建模。前者是非局部的，通过 L1 和 L2 离散以及基于指数和近似的快速评估算法进行近似。这样就能有效处理亚扩散的 "长尾 "内核。后者是局部的，因此可以使用传统的隐式欧拉或 Crank-Nicolson 离散方法。在考虑局部质量守恒的基础上，利用有限体积进行空间离散。质量和分数通量的界面条件被纳入这些快速求解器。数值实验证明了这些新型快速求解器的精度和效率。

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

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.