Influence of outer boundary conditions on Schwarz methods for a scalar PDE
Applicationes Mathematicae
MSC: Primary 65N55
DOI: 10.4064/am2551-3-2025
Published online: 27 August 2025
Abstract
In this article we concern ourselves with the study of the parallel Schwarz algorithms employed for solving advection-diffusion type partial differential equations. Schwarz algorithms, very popular in the literature as efficient methods for solving partial differential equations, were pioneered by the mathematical analyst Hermann Schwarz back in 1870. The technology behind these algorithms is that they divide the global problem into a collection of smaller subproblems, and these local problems are solved in an iterative fashion. In this study we use Fourier analysis techniques to obtain the contraction factor of the algorithms for two overlapping unbounded subdomains, by modifying the outer boundary conditions of the global domain.
