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math.NA2026
Robust Hierarchical Matrix Compression of Acoustic Volume and Boundary Integral Operators
Alberto Almuna-Morales, Danilo Aballay, Ignacio Labarca-Figueroa +1
Discretizing integral formulations of the Helmholtz equation yields dense linear systems. Hence, simulating acoustic models at larger scales or higher frequencies is typically cons…
math.NA2026
Nested Volume-Surface Integral Equations for Acoustics
Danilo Aballay, Elwin van 't Wout
The simulation of high-frequency acoustic wave propagation in unbounded domains with local heterogeneous materials and high-contrast interfaces poses significant challenges to nume…
math.NA2025
An -adaptive finite element method using neural networks for parametric self-adjoint elliptic problem
Danilo Aballay, Federico Fuentes, Vicente Iligaray +5
This work proposes an -adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting i…