Premium
Analysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensions
Author(s) -
Liu Huan,
Zheng Xiangcheng,
Fu Hongfei,
Wang Hong
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22554
Subject(s) - mathematics , finite volume method , norm (philosophy) , conjugate gradient method , space (punctuation) , alternating direction implicit method , stability (learning theory) , convergence (economics) , mathematical analysis , mathematical optimization , finite difference method , computer science , physics , machine learning , political science , mechanics , law , economics , economic growth , operating system
In this article, we develop a Crank–Nicolson alternating direction implicit finite volume method for time‐dependent Riesz space‐fractional diffusion equation in two space dimensions. Norm‐based stability and convergence analysis are given to show that the developed method is unconditionally stable and of second‐order accuracy both in space and time. Furthermore, we develop a lossless matrix‐free fast conjugate gradient method for the implementation of the numerical scheme, which only has O ( N )memory requirement and O ( N log N )computational complexity per iteration with N being the total number of spatial unknowns. Several numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed scheme for large‐scale modeling and simulations.