9 papers
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…
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…
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
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three di…