18 papers
Asymptotic Analysis of the Narrow Escape and Berg-Purcell problems on general three-dimensional domains with reactive boundary patches
A. E. Lindsay, A. J. Bernoff, D. S. Grebenkov +2
We present an asymptotic analysis of two diffusive capture problems in general smooth closed three-dimensional geometries with multiple small reactive boundary patches of arbitrary…
The three-dimensional Neumann Green's function for general surfaces: singular asymptotics and boundary integral methods
Alan E. Lindsay, Andrew J. Bernoff, Tristan Goodwill +1
We present an asymptotic analysis and high-order boundary integral method for the three-dimensional Neumann Green's function in general closed and smooth geometries. The Neumann Gr…
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…
Integral equations for flexural scattering problems with periodic boundaries
Fruzsina Agocs, Tristan Goodwill, Jeremy G. Hoskins +1
We develop a method for computing the scattering of flexural waves off of a periodic wall or a periodic line of scatterers. These waves model the fluctuations of thin plates with p…
A parametrix for the surface Stokes equation
Tristan Goodwill, Jeremy Hoskins, Zydrunas Gimbutas +1
We introduce an integral equation formulation of the surface Stokes equations, constructed using two-dimensional Stokeslets. The resulting integral equations are Fredholm integral…
A Boundary Integral Method for Generalized Impedance Boundary Conditions in 2D
Jacob Linden, Travis Askham, Jeremy Hoskins
Generalized impedance boundary conditions for the Helmholtz equation arise in a number of acoustic and electromagnetic models that approximate boundary effects, including thin coat…
Self-Affine Scaling of Earth's Islands
Matthew Oline, Jeremy Hoskins, David Seekell +2
Earth's relief is approximately self-affine, meaning a zoom-in on a small region looks statistically similar to a large region upon rescaling. Fractional Brownian surfaces give an…
High-order integral methods for the Neumann Green's function: applications to capture and signaling problems in two dimensions
Sanchita Chakraborty, Jeremy Hoskins, Alan E. Lindsay
We present a high order numerical method for the solution of the Neumann Green's function in two dimensions. For a general closed planar curve, our computational method resolves bo…
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…
Complex Scaling for the Junction of Semi-infinite Gratings
Fruzsina J. Agocs, Tristan Goodwill, Jeremy Hoskins
We present and analyze an integral equation method for the scattering of a non-periodic source from a geometry consisting of two semi-infinite, periodic structures glued together 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 […
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…
Boundary Integral Formulations for Flexural Wave Scattering in Thin Plates
Peter Nekrasov, Zhaosen Su, Travis Askham +1
In this paper, we develop second kind integral formulations for flexural wave scattering problems involving the clamped, supported, and free plate boundary conditions. While the cl…
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…
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…