论文标题
使用块toeplitz矩阵分析平行施瓦茨算法，用于时间谐波问题
Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices
论文作者
论文摘要
在这项工作中，我们研究了具有罗宾传输条件的一级平行Schwarz方法的收敛性能，该方法应用于一维和二维Helmholtz和Maxwell的方程。通常，一级方法通常不可扩展。但是，最近已经证明，在使用吸收方程的算法中使用阻抗传播条件时，在某些假设下，可以实现可伸缩性，并且不需要粗糙的空间。我们在这里表明，对于该方法在连续级别的迭代版本中，将条带分解为子域中的迭代版本也是如此，通常在解决波浪引导问题时会遇到这些结果。收敛证明依赖于全局迭代矩阵的特定块Toeplitz结构。虽然是非热的，但我们证明其限制频谱与相同结构的赫米尔族矩阵的形式几乎相同。我们通过数值实验说明了结果。
In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not scalable in general. However, it has recently been proven that when impedance transmission conditions are used in the case of the algorithm applied to the equations with absorption, under certain assumptions, scalability can be achieved and no coarse space is required. We show here that this result is also true for the iterative version of the method at the continuous level for strip-wise decompositions into subdomains that can typically be encountered when solving wave-guide problems. The convergence proof relies on the particular block Toeplitz structure of the global iteration matrix. Although non-Hermitian, we prove that its limiting spectrum has a near identical form to that of a Hermitian matrix of the same structure. We illustrate our results with numerical experiments.
