Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations
Analysis of PDEs
2015-10-07 v3 Numerical Analysis
Abstract
We consider three problems for the Helmholtz equation in interior and exterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.
Cite
@article{arxiv.1504.01037,
title = {Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations},
author = {Dean Baskin and Euan Spence and Jared Wunsch},
journal= {arXiv preprint arXiv:1504.01037},
year = {2015}
}
Comments
Version 3: 42 pages; improved exposition in response to referee comments and added several references