On the role of relaxation and acceleration in the non-overlapping Schwarz alternating method for coupling

Fuente: arXiv
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Main Authors: Sambataro, Giulia, Tezaur, Irina
Format: Preprint
Published: 2026
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author Sambataro, Giulia
Tezaur, Irina
author_facet Sambataro, Giulia
Tezaur, Irina
contents The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of domain decomposition- (DD-) based coupling. After demonstrating that the multiplicative Schwarz scheme can be formulated as a fixed-point iteration, we explore, both theoretically and numerically, two promising techniques for speeding up the method: (i) Aitken acceleration and (ii) Anderson acceleration. In the process, we derive a robust and efficient adaptive variant of Anderson acceleration, termed "Anderson with memory adaptation". We compare the proposed acceleration strategies to the well-known classical relaxed Dirichlet-Neumann Schwarz alternating method. Our results suggest that, while Aitken-accelerated Schwarz is the best approach in terms efficiency and robustness when considering two sub-domain DDs, Anderson-accelerated Schwarz is the method of choice in larger multi-domain setting.
format Preprint
id arxiv_https___arxiv_org_abs_2603_17143
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the role of relaxation and acceleration in the non-overlapping Schwarz alternating method for coupling
Sambataro, Giulia
Tezaur, Irina
Numerical Analysis
The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of domain decomposition- (DD-) based coupling. After demonstrating that the multiplicative Schwarz scheme can be formulated as a fixed-point iteration, we explore, both theoretically and numerically, two promising techniques for speeding up the method: (i) Aitken acceleration and (ii) Anderson acceleration. In the process, we derive a robust and efficient adaptive variant of Anderson acceleration, termed "Anderson with memory adaptation". We compare the proposed acceleration strategies to the well-known classical relaxed Dirichlet-Neumann Schwarz alternating method. Our results suggest that, while Aitken-accelerated Schwarz is the best approach in terms efficiency and robustness when considering two sub-domain DDs, Anderson-accelerated Schwarz is the method of choice in larger multi-domain setting.
title On the role of relaxation and acceleration in the non-overlapping Schwarz alternating method for coupling
topic Numerical Analysis
url https://arxiv.org/abs/2603.17143