Fast direct solver for CN-ADI-FV scheme to two-dimensional Riesz space-fractional diffusion equations

Highlights：

• The Gohberg-Semencul formula (GSF) utilizing the preconditioned conjugate gradient (PCG) method is developed for solving the CN-ADI-FV scheme to improve efficiency and save memory, and its computational complexity is discussed.

• The superlinear convergence of the PCG method for solving the symmetric positive definite Toeplitz linear system associated with the GSF is studied, which is rarely mentioned in the literature.

摘要

•A fast direct solver is proposed for solving the Crank-Nicolson alternating direction implicit finite volume (CN-ADI-FV) discretization of two dimensional Riesz space-fractional diffusion equations.•The Gohberg-Semencul formula (GSF) utilizing the preconditioned conjugate gradient (PCG) method is developed for solving the CN-ADI-FV scheme to improve efficiency and save memory, and its computational complexity is discussed.•The superlinear convergence of the PCG method for solving the symmetric positive definite Toeplitz linear system associated with the GSF is studied, which is rarely mentioned in the literature.

论文关键词：Two dimensional Riesz space-fractional diffusion equations,Finite volume method,Alternating direction implicit method,Gohberg-Semencul formula,Strang’s circulant preconditioner,Preconditioned conjugate gradient method

论文评审过程：Received 5 September 2020, Revised 28 December 2020, Accepted 23 January 2021, Available online 26 February 2021, Version of Record 26 February 2021.