1 citations · 1 across the 10 of their papers we have counts for
12 papers
A kernel-independent precorrected-FFT method
Tristan Goodwill, Owen Melia
The precorrected-FFT has been used to rapidly evaluate -body sums arising in electromagnetics and acoustics settings. It has, however, been historically limited to kernels that…
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…
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…
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…
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 […
A numerical method for scattering problems with unbounded interfaces
Tristan Goodwill, Charles L. Epstein
We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computation…
A parametrix method for elliptic surface PDEs
Tristan Goodwill, Michael O'Neil
Elliptic problems along smooth surfaces embedded in three dimensions occur in thin-membrane mechanics, electromagnetics (harmonic vector fields), and computational geometry. In thi…
An interface formulation of the Laplace-Beltrami problem on piecewise smooth surfaces
Tristan Goodwill, Michael O'Neil
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (ha…