Year: 2023
Type: preprint
Abstract: We extend the theoretical framework of non-local optimized Schwarz methods as introduced in [Claeys,2021], considering an Helmholtz equation posed in a bounded cavity supplemented with a variety of conditions modeling material boundaries. The problem is reformulated equivalently as an equation posed on the skeleton of a non-overlapping partition of the computational domain, involving an operator of the form "identity + contraction". The analysis covers the possibility of resonance phenomena where the Helmholtz problem is not uniquely solvable. In case of unique solvability, the skeleton formulation is proved coercive, and an explicit bound for the coercivity constant is provided in terms of the inf-sup constant of the primary Helmholtz boundary value problem.
Source: arXiv (Cornell University)
Author: Claeys, Xavier
Institutions: Sorbonne Université, Laboratoire Jacques-Louis Lions
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4315588455