On the effect of boundary conditions on the scalability of Schwarz methods

2021/03/27 by Gabriele Ciaramella, Ciaramella, Gabriele, Luca Mechelli +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2103.14848

openalex publication_date 2021/03/27 · openalex created_date 2023/03/16 · openalex updated_date 2026/07/28

Abstract

In contrast with classical Schwarz theory, recent results have shown that for special domain geometries, one-level Schwarz methods can be scalable. This property has been proved for the Laplace equation and external Dirichlet boundary conditions. Much less is known if mixed boundary conditions are considered. This short manuscript focuses on the convergence and scalability analysis of one-level parallel Schwarz method and optimized Schwarz method for several different external configurations of boundary conditions, i.e., mixed Dirichlet, Neumann and Robin conditions.

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