Related papers: Linearly scalable fast direct solver based on prox…
This manuscript presents a fast direct solution technique for solving two dimensional wave scattering problems from quasi-periodic multilayered structures. When the interface geometries are complex, the dominant term in the computational…
This manuscript is the second in a series presenting fast direct solution techniques for solving two-dimensional wave scattering problems from quasi-periodic multilayered structures. The fast direct solvers presented in the series are for…
This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous…
This paper describes a fast direct boundary element method for elastodynamic transmission problems in two dimensions, which can be used for analyzing elastic wave scattering by an inclusion. We develop an efficient solver based on a…
We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…
As a follow up to \cite{Causley2013}, we provide a detailed description of the numerical implementation of an O(N), A-stable, second order accurate solution of the wave equation, constructed from semi-discrete boundary value problems. We…
A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The…
We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincar\'e-Steklov method. The method takes as input an unstructured, high-order quadrilateral mesh of…
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…
A butterfly-based fast direct integral equation solver for analyzing high-frequency scattering from two-dimensional objects is presented. The solver leverages a randomized butterfly scheme to compress blocks corresponding to near- and…
This paper presents a fast wavefield evaluation method for two-dimensional wave scattering problems. The proposed method is based on a modified version of proxy-surface-accelerated interpolative decomposition, making it effective even if…
We present a fast direct solver for the simulation of electromagnetic scattering from an arbitrarily-shaped, large, empty cavity embedded in an infinite perfectly conducting half space. The governing Maxwell equations are reformulated as a…
A numerical method for variable coefficient elliptic problems on two dimensional domains is described. The method is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system of…
An efficient direct solver for solving the Lippmann-Schwinger integral equation modeling acoustic scattering in the plane is presented. For a problem with $N$ degrees of freedom, the solver constructs an approximate inverse in…
We present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing…
An algorithm for the direct inversion of the linear systems arising from Nystrom discretization of integral equations on one-dimensional domains is described. The method typically has O(N) complexity when applied to boundary integral…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…