A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf{H}$-matrices. The computational model can be thought of as a two-stage alternating iterative method, which well suits to the well-known Hermitian and skew-Hermitian splitting (HSS) approach, with the particularity here of considering only one inner iteration. Experimental parallel performance comparison is conducted between the generalized minimal residual (GMRES) algorithm, the standard HSS and our asynchronous variant, on both real and complex non-Hermitian linear systems, respectively, arising from convection–diffusion and structural dynamics problems. A significant gain on execution time is observed in both cases.

设计了一个通用的异步交替迭代模型，在经典光谱半径界限下，理论上保证收敛，然后，对于经典的矩阵分裂类$\mathsf{H}$-矩阵。计算模型可以被认为是一种两阶段交替迭代方法，非常适合著名的 Hermitian 和 skew-Hermitian 分裂 (HSS) 方法，这里的特殊性是只考虑一次内部迭代。在广义最小残差 (GMRES) 算法、标准 HSS 和我们的异步变体之间分别对由对流扩散和结构动力学问题引起的实数和复数非厄米线性系统进行了实验并行性能比较。在这两种情况下都可以观察到执行时间的显着增加。