Domain decomposition methods for space fractional partial differential equations

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/δ), where H is the maximum diameter of subdomains and δ is the overlap size among the subdomains. Numerical results are given to support our theoretical findings.