38 citations · 129 across the 11 of their papers we have counts for
7 papers · 1 filter
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…
Combined field-only boundary integral equations for PEC electromagnetic scattering problem in spherical geometries
Luiz Faria, Carlos Perez-arancibia, Catalin Turc
We analyze the well posedness of certain field-only boundary integral equations (BIE) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting fr…
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…
Windowed Green function method for wave scattering by periodic arrays of 2D obstacles
Thomas Strauszer-Caussade, Luiz M. Faria, Agustín Fernandez-Lado +1
This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional pene…
General-purpose kernel regularization of boundary integral equations via density interpolation
Luiz M. Faria, Carlos Pérez-Arancibia, Marc Bonnet
This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderón calculus associated with linear elliptic PDEs in two…
Planewave density interpolation methods for 3D Helmholtz boundary integral equations
Carlos Pérez-Arancibia, Catalin Turc, Luiz Faria
This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels prese…
Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
Carlos Pérez-Arancibia, Luiz M. Faria, Catalin Turc
We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials…