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”.我们实现了多级时空纯乘性施瓦茨（multilevel space-time pure multiplicative Schwarz，简称STPMS）算法以求解线性抛物方程，具体通过在时空维度并行运行的多级乘性施瓦茨预条件广义最小残差（GMRES）方法完成求解。本数据集验证了STPMS算法的最优性与可扩展性：其迭代次数随重叠度"ovlp"的提升而降低，且迭代次数的上界与窗口大小"s"及子域数量"N_p"均无关。