Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities
Abstract
In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave condition). Such problems are heavily impacted by back-propagating waves which are often neglected when devising optimized transmission operators for the Schwarz method. This work explores new operators taking into account those back-propagating waves and compares them with well-established operators neglecting these contributions. Notably, this paper focuses on the case of rectangular cavities, as the optimal (non-local) transmission operator can be easily determined. Nonetheless, deviations from this ideal geometry are considered as well. In particular, computations of the acoustic noise in a three-dimensional model of the helium vessel of a beamline cryostat with optimized Schwarz schemes are discussed. Those computations show a reduction of 46% in the iteration count, when comparing an operator optimized for cavities with those optimized for unbounded problems.
Keywords
Cite
@article{arxiv.2205.06518,
title = {Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities},
author = {Nicolas Marsic and Christophe Geuzaine and Herbert De Gersem},
journal= {arXiv preprint arXiv:2205.06518},
year = {2023}
}
Comments
37 pages, 23 figures. Changes with respect to the previous version: i) one more reference (original GMRES paper) and ii) fixing more typos. This version is published in Computers & Mathematics with Applications