4 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…
High-order kernel regularization of singular and hypersingular Helmholtz boundary integral operators
Luiz M. Faria, Carlos Perez-Arancibia, Svetlana Tlupova
This paper extends and analyzes the high-order kernel regularization framework of Beale & Tlupova (arXiv:2510.13639) to all four on-surface boundary integral operators of the Helmh…
A complex-scaled boundary integral equation for time-harmonic water waves
Anne-Sophie Bonnet-Ben Dhia, Luiz M. Faria, Carlos Pérez-Arancibia
This paper presents a novel boundary integral equation (BIE) formulation for the two-dimensional time-harmonic water-waves problem. It utilizes a complex-scaled Laplace's free-spac…