3 papers
math.NA2025
Complex scaling for open waveguides
Charles L. Epstein, Tristan Goodwill, Jeremy Hoskins +2
In this work we analyze the complex scaling method applied to the problem of time-harmonic scalar wave propagation in junctions between `leaky,' or open dielectric waveguides. In […
math.AP2025
Type-I Superconductors in the Limit as the London Penetration Depth Goes to 0
Charles L. Epstein, Manas Rachh, Yuguan Wang
This paper provides an explicit formula for the approximate solution of the static London equations. These equations describe the currents and magnetic fields in a Type-I supercond…
math.NA2024
Coordinate complexification for the Helmholtz equation with Dirichlet boundary conditions in a perturbed half-space
Charles L. Epstein, Leslie Greengard, Jeremy Hoskins +2
We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly pe…