Domain Decomposition Methods for Space Fractional Partial Differential Equations

TL;DR

This paper introduces a two-level additive Schwarz preconditioner for efficiently solving algebraic systems from finite element approximations of space fractional PDEs, with theoretical bounds and numerical validation.

Contribution

It presents a novel preconditioning technique specifically designed for space fractional PDEs, improving solution efficiency and providing theoretical condition number bounds.

Findings

Condition number bounded by C(1+H/δ)

Numerical results support theoretical bounds

Preconditioner enhances computational efficiency

Abstract

In this paper, a two-level additive Schwarz preconditioner is proposed for solving the algebraic systems resulting from the finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that the condition number of the preconditioned system is bounded by C(1+H/\delta), where H is the maximum diameter of subdomains and \delta is the overlap size among the subdomains. Numerical results are given to support our theoretical findings.