607 citations · 817 across the 43 of their papers we have counts for
46 papers
String kernel representations in elastostatics
Jeremy G. Hoskins, Alan E. Lindsay, Manas Rachh
In this paper we present a new boundary integral equation formulation for the solution of the elastostatic traction boundary value problem in two and three dimensions. The approach…
The peak heat flux conjecture for the first Dirichlet eigenmode of convex planar domains
Zijian Wang, Jeremy G. Hoskins, Manas Rachh +1
In this paper, we study the scale-invariant quantity \[\mathcal{G}(Ω)=\frac{\|\partial_n u_1\|_{L^\infty(\partialΩ)}}{λ_1},\]where is the first -normalized Dirichlet Lap…
Surface layers and linearized water waves: a boundary integral equation framework
Travis Askham, Tristan Goodwill, Jeremy G Hoskins +2
The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important ph…
Fast Multipole Method with Complex Coordinates
Tristan Goodwill, Leslie Greengard, Jeremy Hoskins +2
When solving problems of potential theory in unbounded layered media, recently developed integral equation methods rely on coordinate complexification to permit truncation of the c…
A domain decomposition method for computing the scattering matrix of waveguide circuits
Tristan Goodwill, Shidong Jiang, Manas Rachh +1
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulate…
Helmholtz boundary integral methods and the pollution effect
Jeffrey Galkowski, Manas Rachh, Euan A. Spence
This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber and smooth obstacles using the standard second-kind boundary in…
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…
Integral equations for flexural-gravity waves: analysis and numerical methods
Travis Askham, Jeremy G. Hoskins, Peter Nekrasov +1
In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This prob…
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…
On the construction of scattering matrices for irregular or elongated enclosures using Green's representation formula
Carlos Borges, Leslie Greengard, Michael O'Neil +1
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing…
Integral formulation of Dirac singular waveguides
Guillaume Bal, Jeremy Hoskins, Solomon Quinn +1
This paper concerns a boundary integral formulation for the two-dimensional massive Dirac equation. The mass term is assumed to jump across a one-dimensional interface, which model…
On quadrature for singular integral operators with complex symmetric quadratic forms
Jeremy Hoskins, Manas Rachh, Bowei Wu
This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadra…
Cytoplasmic stirring by active carpets
Brato Chakrabarti, Stanislav Y. Shvartsman, Michael J. Shelley
Large cells often rely on cytoplasmic flows for intracellular transport, maintaining homeostasis, and positioning cellular components. Understanding the mechanisms of these flows i…
Random walks in frequency and the reconstruction of obstacles with cavities from multi-frequency data
Travis Askham, Carlos Borges, Jeremy Hoskins +1
Inverse obstacle scattering is the recovery of an obstacle boundary from the scattering data produced by incident waves. This shape recovery can be done by iteratively solving a PD…
Fast adaptive high-order integral equation methods for electromagnetic scattering from smooth perfect electric conductors
Felipe Vico, Leslie Greengard, Michael O'Neil +1
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise i…
Uniform approximation of common Gaussian process kernels using equispaced Fourier grids
Alex Barnett, Philip Greengard, Manas Rachh
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponential…
A new version of the adaptive fast Gauss transform for discrete and continuous sources
Leslie Greengard, Shidong Jiang, Manas Rachh +1
We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave…
Integral formulation of Klein-Gordon singular waveguides
Guillaume Bal, Jeremy Hoskins, Solomon Quinn +1
We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger equation and the s…
A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem
Mo Zhou, Jiequn Han, Manas Rachh +1
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the…
On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary
Carlos Borges, Manas Rachh, Leslie Greengard
The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (prob…
Equispaced Fourier representations for efficient Gaussian process regression from a billion data points
Philip Greengard, Manas Rachh, Alex Barnett
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials…
Quantum electrodynamics of chiral waveguide arrays
Jeremy Hoskins, Manas Rachh, John C Schotland
We consider the quantum electrodynamics of a binary array of chiral waveguides, each containing many atoms. We show that the one-photon amplitude of a single-excitation state obeys…
FMM-LU: A fast direct solver for multiscale boundary integral equations in three dimensions
Daria Sushnikova, Leslie Greengard, Michael O'Neil +1
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonizati…