15 citations · 31 across the 20 of their papers we have counts for
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Fast and stable computation of highly oscillatory and/or exponentially decaying integrals using a Clenshaw-Curtis product-integration rule
Victor Dominguez
We propose, analyze, and implement a quadrature method for evaluating integrals of the form , where is a complex number with a possibly large…
Practical Introduction to FEM with GMSH: A MATLAB/Octave Perspective
Victor Dominguez, Alejandro Duque
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are wi…
Robust boundary integral equations for the solution of elastic scattering problems via Helmholtz decompositions
V. Dominguez, C. Turc
Helmholtz decompositions of the elastic fields open up new avenues for the solution of linear elastic scattering problems via boundary integral equations (BIE) [Dong, Lai, Li, Math…
Nystrom discretizations of boundary integral equations for the solution of 2D elastic scattering problems
Victor Dominguez, Catalin Turc
We present three high-order Nystrom discretization strategies of various boundary integral equation formulations of the impenetrable time-harmonic Navier equations in two dimension…
Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems
Victor Dominguez, Catalin Turc
We introduce and analyze various Regularized Combined Field Integral Equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material pro…
Analysis and application of an overlapped FEM-BEM for wave propagation in unbounded and heterogeneous media
V. Domínguez, M. Ganesh
An overlapped continuous model framework, for the Helmholtz wave propagation problem in unbounded regions comprising bounded heterogeneous media, was recently introduced and analyz…
An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: Formulation, analysis, algorithm, and simulation
Victor Dominguez, Mahadevan Ganesh, Francisco-Javier Sayas
A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medi…
High order Nyström methods for transmission problems for Helmholtz equation
V. Dominguez, C. Turc
We present superalgebraic compatible Nyström discretizations for the four Helmholtz boundary operators of Calderón's calculus on smooth closed curves in 2D. These discretizations a…
Well-posed boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz transmission problems in two-dimensional Lipschitz domains
Victor Dominguez, Mark Lyon, Catalin Turc
We present a comparison between the performance of solvers based on Nyström discretizations of several well-posed boundary integral equation formulations of Helmholtz transmission…
A fully discrete Calderon Calculus for the two-dimensional elastic wave equation
Victor Dominguez, Tonatiuh Sanchez-Vizuet, Francisco-Javier Sayas
In this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the…
High-order Nyström discretizations for the solution of integral equation formulations of two-dimensional Helmholtz transmission problems
Y. Boubendir, V. Dominguez, C. Turc
We present and analyze fully discrete Nyström methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scatteri…
On the discontinuous Galerkin method for solving boundary value problems for the Helmholtz equation: A priori and a posteriori error analyses
T. P. Barrios, R. Bustinza, V. Dominguez
We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some a…
Filon-Clenshaw-Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities
Victor Dominguez
In this work we propose and analyse a numerical method for computing a family of highly oscillatory integrals with logarithmic singularities. For these quadrature rules we derive e…
A Nystrom flavored Calderón Calculus of order three for two dimensional waves
V. Dominguez, S. L. Lu, F. -J. Sayas
In this paper we present and test a full discretization of all elements of the Calderón Calculus (layer potentials and integral operators) for the Helmholtz equation in smooth clos…
A fully discrete Calderon Calculus for two dimensional time harmonic waves
Victor Dominguez, Sijiang L. Lu, Francisco-Javier Sayas
In this paper, we present a fully discretized Calderón Calculus for the two dimensional Helmholtz equation. This full discretization can be understood as highly non-conforming Petr…
A Nystrom method for the two dimensional Helmholtz hypersingular equation
Victor Dominguez, Sijiang L. Lu, Francisco-Javier Sayas
In this paper we propose and analyze a class of simple Nyström discretizations of the hypersingular integral equation for the Helmholtz problem on domains of the plane with smooth…
Filon-Clenshaw-Curtis rules for highly-oscillatory integrals with algebraic singularities and stationary points
V. Dominguez, I. G. Graham, T. Kim
In this paper we propose and analyse composite Filon-Clenshaw-Curtis quadrature rules for integrals of the form $I_{k}^{[a,b]}(f,g) := \int_a^b f(x) \exp(\mathrm{i}kg(x)) \rd x $,…
Interpolation and cubature approximations and analysis for a class of wideband integrals on the sphere
V. Dominguez, M. Ganesh
We propose, analyze, and implement interpolatory approximations and Filon-type cubature for efficient and accurate evaluation of a class of wideband generalized Fourier integrals o…
Convergence analysis of a high-order Nystrom integral-equation method for surface scattering problems
Oscar P. Bruno, Victor Dominguez, Francisco-Javier Sayas
In this paper we present a convergence analysis for the Nystrom method proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of the combined boundary integral…