12 citations · 13 across the 6 of their papers we have counts for
8 papers
Fresnel scattering for open waveguide networks
Solomon Quinn, Charles L. Epstein
This paper concerns the Helmholtz scattering problem for open waveguide networks, extending the analysis from [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674] to plane-wave i…
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 […
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…
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…
Debye Sources, Beltrami Fields, and a Complex Structure on Maxwell Fields
Charles L. Epstein, Leslie Greengard, Michael O'Neil
The Debye source representation for solutions to the time harmonic Maxwell equations is extended to bounded domains with finitely many smooth boundary components. A strong uniquene…
A consistency condition for the vector potential in multiply-connected domains
Charles L. Epstein, Zydrunas Gimbutas, Leslie Greengard +2
A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental ro…
Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations, II
Charles L. Epstein, Leslie Greengard, Michael O'Neil
In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magneti…
Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations
Charles L. Epstein, Leslie Greengard
In this paper, we develop a new representation for outgoing solutions to the time harmonic Maxwell equations in unbounded domains in This representation leads to a Fredho…