collaborators

5 papers

math.NA2025

Fully discrete analysis of the Galerkin POD neural network approximation with application to 3D acoustic wave scattering

Jürgen Dölz, Fernando Henríquez

In this work, we consider the approximation of parametric maps using the so-called Galerkin POD-NN method. This technique combines the computation of a reduced basis via proper ort…

math.NA2024

Domain Uncertainty Quantification for the Lippmann-Schwinger Volume Integral Equation

Fernando Henríquez, Ignacio Labarca-Figueroa

In this work, we consider the propagation of acoustic waves in unbounded domains characterized by a constant wavenumber, except possibly in a bounded region. The geometry of this i…

math.NA2024

Deep ReLU Neural Network Emulation in High-Frequency Acoustic Scattering

Fernando Henríquez, Christoph Schwab

We obtain wavenumber-robust error bounds for the deep neural network (DNN) emulation of the solution to the time-harmonic, sound-soft acoustic scattering problem in the exterior of…

math.NA2024

Reduced Basis Method for the Elastic Scattering by Multiple Shape-Parametric Open Arcs in Two Dimensions

Fernando Henríquez, José Pinto

We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of…

math.NA2024

Fast Numerical Approximation of Parabolic Problems Using Model Order Reduction and the Laplace Transform

Fernando Henríquez, Jan S. Hesthaven

We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients base…