Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices
نویسندگان
چکیده
In this work we study the convergence properties of one-level parallel Schwarz method with Robin transmission conditions applied to one-dimensional and two-dimensional Helmholtz Maxwell's equations. One-level methods are not scalable in general. However, it has recently been proven that when impedance used case algorithm being equations absorption, then, under certain assumptions, scalability can be achieved no coarse space is required. We show here result also true for iterative version at continuous level strip-wise decompositions into subdomains typically encountered solving wave-guide problems. The proof relies on particular block Toeplitz structure global iteration matrix. Although non-Hermitian, prove its limiting spectrum a near identical form Hermitian matrix same structure. illustrate our results numerical experiments.
منابع مشابه
High Performance Algorithms for Toeplitz and block Toeplitz matrices
High Performance Algorithms for Toeplitz and block Toeplitz matrices
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ژورنال
عنوان ژورنال: Electronic Transactions on Numerical Analysis
سال: 2021
ISSN: ['1068-9613', '1097-4067']
DOI: https://doi.org/10.1553/etna_vol55s112