18 citations · 30 across the 7 of their papers we have counts for
8 papers
Fast high-order solvers for the Lippmann--Schwinger equation in piecewise-smooth heterogeneous media
Thomas G. Anderson, Juan Burbano-Gallegos, Luiz M. Faria +1
This article presents a fast, high-order Nyström solver for the two-dimensional Lippmann--Schwinger equation arising from time-harmonic scattering by penetrable, piecewise-smooth h…
A general-purpose global regularization method for 3D volume integral operators
Thomas G. Anderson, Marc Bonnet, Luiz M. Faria +1
Singular volume integral operators associated with constant-coefficient partial differential operators extend the applicability of potential theory to inhomogeneous problems, for e…
Construction of polynomial particular solutions of linear constant-coefficient partial differential equations
Thomas G. Anderson, Marc Bonnet, Luiz M. Faria +1
This paper introduces general methodologies for constructing closed-form solutions to linear constant-coefficient partial differential equations (PDEs) with polynomial right-hand s…
Fast, high-order numerical evaluation of volume potentials via polynomial density interpolation
Thomas G. Anderson, Marc Bonnet, Luiz M. Faria +1
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poiss…
A fast, high-order scheme for evaluating volume potentials on complex 2D geometries via area-to-line integral conversion and domain mappings
Thomas G. Anderson, Hai Zhu, Shravan Veerapaneni
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a conv…
"Bootstrap Domain of Dependence": Bounds and Time Decay of Solutions of the Wave Equation
Thomas G. Anderson, Oscar P. Bruno
This article introduces a novel "bootstrap domain-of-dependence" concept, according to which, for all time following a given illumination period of arbitrary duration, the wave fie…
High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: Sampling Cost via Incident-Field Windowing and Recentering
Thomas G. Anderson, Oscar P. Bruno, Mark Lyon
This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transform…
Stability analysis of degenerately-damped oscillations
Thomas Anderson, George Avalos, Elizabeth Galvin +4
Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish a…