38 citations · 129 across the 11 of their papers we have counts for
15 papers
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 the EFIE on simple and composite surfaces
Carlos Pérez-Arancibia, Catalin Turc, Luiz Faria +1
This paper presents an extension of the recently introduced planewave density interpolation (PWDI) method to the electric field integral equation (EFIE) formulation of problems of…
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…
Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces
Ignacio Labarca, Luiz M. Faria, Carlos Pérez-Arancibia
This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbo…
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…
Anomalous chained turbulence in actively driven flows on spheres
Oscar Mickelin, Jonasz Słomka, Keaton J. Burns +4
Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for non-equ…
A model for Faraday pilot waves over variable topography
Luiz M. Faria
Couder and Fort discovered that droplets walking on a vibrating bath possess certain features previously thought to be exclusive to quantum systems. These millimetric droplets sync…
Qualitative modeling of the dynamics of detonations with losses
Luiz M. Faria, Aslan R. Kasimov
We consider a simplified model for the dynamics of one-dimensional detonations with generic losses. It consists of a single partial differential equation that reproduces, at a qual…
Theory of weakly nonlinear self sustained detonations
Luiz M. Faria, Aslan R. Kasimov, Rodolfo R. Rosales
We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that…
Study of a model equation in detonation theory
Luiz M. Faria, Aslan R. Kasimov, Rodolfo R. Rosales
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales. Model for s…
A model for shock wave chaos
Aslan Kasimov, Luiz Faria, Rodolfo R. Rosales
We propose the following model equation: \[u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}), \] that predicts chaotic shock waves. It is given on the half-line and the shock is located…