15 papers · 1 filter
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…