5 papers
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…
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…
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…
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…
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…