Work

Schwarz Methods for Nonlocal Problems

Year: 2025

Type: article

Abstract: The first domain decomposition methods for partial differential equations were already developed in 1870 by H. A. Schwarz. Here we consider a nonlocal Dirichlet problem with variable coefficients, where a nonlocal diffusion operator is used. We find that domain decomposition methods like the so-called Schwarz methods seem to be a natural way to solve these nonlocal problems. In this work, we show the convergence for nonlocal problems, where specific symmetric kernels are employed, and present the implementation of the multiplicative and additive Schwarz algorithms in the above-mentioned nonlocal setting.

Source: Journal of Peridynamics and Nonlocal Modeling

DOI: 10.1007/s42102-025-00133-7

Authors: Matthias Schuster, Christian Vollmann, Volker Schulz

Institution: Universität Trier

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Universität Trier, Deutsche Forschungsgemeinschaft