11 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…
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…
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…
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…
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…