Solving time-periodic fractional diffusion equations via diagonalization technique and multigrid

Shu Lin Wu*, Hui Zhang, Tao Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


This paper addresses numerical computation of time-periodic diffusion equations with fractional Laplacian. Time-periodic differential equations present fundamental challenges for numerical computation because we have to consider all the discrete solutions once in all instead of one by one. An idea based on the diagonalization technique is proposed, which yields a direct parallel-in-time computation for all the discrete solutions. The major computation cost is therefore reduced to solve a series of independent linear algebraic systems with complex coefficients, for which we apply a multigrid method using the damped Richardson iteration as the smoother. Such a linear solver possesses mesh-independent convergence factor, and we make an optimization for the damping parameter to minimize such a constant convergence factor. Numerical results are provided to support our theoretical analysis.

Original languageEnglish
Article numbere2178
JournalNumerical Linear Algebra with Applications
Issue number5
Publication statusPublished - Oct 2018
Externally publishedYes


  • convergence analysis
  • diagonalization technique
  • fractional diffusion equations
  • multigrid method
  • parameter optimization
  • time-periodic condition


Dive into the research topics of 'Solving time-periodic fractional diffusion equations via diagonalization technique and multigrid'. Together they form a unique fingerprint.

Cite this