6 papers
A Multilevel Interacting Particle System Method for the estimation of Failure Probabilities
Rubén Aylwin, José Pinto
We propose a novel method that combines a multilevel decomposition with the framework of Interacting Particle Systems to compute the probability that given quantities of interest t…
Integral Formulations for two-dimensional Multi-Arcs
Jose Pinto, Ruben Aylwin
We study the Laplace equation with Dirichlet and Neumann boundary conditions posed on multi-arcs, i.e., collections of open arcs meeting at junction points. We begin by introducing…
Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs
Jose Pinto, Fernando Henríquez, Carlos Jerez-Hanckes
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-d…
Spectral Galerkin method for solving elastic wave scattering problems with multiple open arcs
Carlos Jerez-Hanckes, Jose Pinto, Tao Yin
We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dim…
Fast Galerkin Method for Solving Helmholtz Boundary Integral Equations on Screens
Jose Pinto, Carlos Jerez-Hanckes
We solve first-kind Fredholm boundary integral equations arising from Helmholtz and Laplace problems on bounded, smooth screens in three-dimensions with either Dirichlet or Neumann…
Fast Solver for Quasi-Periodic 2D-Helmholtz Scattering in Layered Media
José Pinto, Rubén Aylwin, Carlos Jerez-Hanckes
We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered perio…