Rational Krylov methods for functions of matrices with applications to fractional partial differential equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:396

Article

Aceto, L.¹  Bertaccini, D.^2,3  Durastante, F.⁴  Novati, R.⁵ 

[1] Univ Pisa, Dipartimento Matemat, Via Buonarroti 1-C, Pisa, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Viale Ric Sci 1, Rome, Italy

[3] Natl Res Council CNR, Ist Applicaz Calcolo IAC M Picone, Rome, Italy

[4] Univ Pisa, Dipartimento Informat, Largo Bruno Pontecorvo 3, Pisa, Italy

[5] Univ Trieste, Dept Math & Geosci, Via Valerio 12-1, I-34127 Trieste, Italy

关键词: Fractional Laplacian;    Matrix functions;    Krylov methods;    Gauss-Jacobi rule;   

DOI  :  10.1016/j.jcp.2019.07.009

来源: Elsevier

【 摘 要 】

In this paper we propose a new choice of poles to define reliable rational Krylov methods. These methods are used for approximating function of positive definite matrices. In particular, the fractional power and the fractional resolvent are considered because of their importance in the numerical solution of fractional partial differential equations. The numerical experiments on some fractional partial differential equation models confirm that the proposed approach is promising. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free