A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation

Xue lei Lin, Xin Lu, Kwok Po NG, Hai Wei Sun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

A fast accurate approximation method with multigrid solver is proposed to solve a two-dimensional fractional sub-diffusion equation. Using the finite difference discretization of fractional time derivative, a block lower triangular Toeplitz matrix is obtained where each main diagonal block contains a two-dimensional matrix for the Laplacian operator. Our idea is to make use of the block ϵ-circulant approximation via fast Fourier transforms, so that the resulting task is to solve a block diagonal system, where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a Laplacian matrix. We show that the accuracy of the approximation scheme is of O(ϵ). Because of the special diagonal block structure, we employ the multigrid method to solve the resulting linear systems. The convergence of the multigrid method is studied. Numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver.

Original languageEnglish
Pages (from-to)204-218
Number of pages15
JournalJournal of Computational Physics
Volume323
DOIs
Publication statusPublished - 15 Oct 2016

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Block lower triangular Toeplitz matrix
  • Block ϵ-circulant approximation
  • Fractional sub-diffusion equations
  • Multigrid method

Fingerprint

Dive into the research topics of 'A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation'. Together they form a unique fingerprint.

Cite this