2023/01/07 by Xavier Claeys, Claeys, Xavier
Engineering · Mathematics · #65N38 (31B10 65N55) #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2301.02921
openalex publication_date 2023/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.