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math.NA2021
Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains
Simon N. Chandler-Wilde, Euan A. Spence
It is well known that, with a particular choice of norm, the classical double-layer potential operator has essential norm as an operator on the natural trace space $H^{1…
math.NA2021
A variational interpretation of Restricted Additive Schwarz with impedance transmission condition for the Helmholtz problem
Shihua Gong, Martin J. Gander, Ivan G. Graham +1
In this paper we revisit the Restricted Additive Schwarz method for solving discretized Helmholtz problems, using impedance boundary conditions on subdomains (sometimes called ORAS…
math.AP2021
Eigenvalues of the truncated Helmholtz solution operator under strong trapping
Jeffrey Galkowski, Pierre Marchand, Euan A. Spence
For the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we prove that if there exists a family of quasimodes (as is the case when the exterior of the obstacle has…