Space-time domain decomposition preconditioned GMRES algorithm for linear parabolic equations

We implement the multilevel space-time pure multiplicative Schwarz (STPMS) algorithm to solve the linear parabolic equations, i.e., the linear parabolic equations are solved by the multilevel multiplicative Schwarz preconditioned GMRES method in parallel on both space and time dimensions. The data shows the optimality and scalability of STPMS algorithm, i.e., it shows that the iteration counts of STPMS decrease with the increase of the overlap “ovlp”, and are bounded independently of the window size “s” and the number of subdomains “N_p”.