Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation. (September 2019)

• Record Type: Journal Article
• Authors: Bertaccini, D.; Durastante, F.
• Is Part Of: Applied mathematics letters. Volume 95(2019)
• Page Start: 92
• Page End: 97
• Publication Date: 2019-09
• Subjects: Structured preconditioners in tensor form -- Tensor trains -- Fractional diffusion equations -- Finite volumes; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.03.028
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We propose a tensor structured preconditioner for the tensor train GMRES algorithm (or TT-GMRES for short) to approximate the solution of the all-at-once formulation of time-dependent fractional partial differential equations discretized in time by linear multistep formulas used in boundary value form and in space by finite volumes. Numerical experiments show that the proposed preconditioner is efficient for very large problems and is competitive, in particular with respect to the AMEn algorithm.