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pro vyhledávání: '"Henríquez, Fernando"'
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 inhomogeneity is assumed to be uncertain, and we are particularly inter
Externí odkaz:
http://arxiv.org/abs/2407.11512
We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the construction of a
Externí odkaz:
http://arxiv.org/abs/2406.13567
Autor:
Henriquez, Fernando, Hesthaven, Jan S.
We extend our previous work [F. Henr\'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique, referred to as the Laplace Transform Reduced Basis (LT-RB) method, uses two widely
Externí odkaz:
http://arxiv.org/abs/2405.19896
Autor:
Henríquez, Fernando, Schwab, Christoph
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 a smooth, convex obstacle in two physical dimensions. The error bound
Externí odkaz:
http://arxiv.org/abs/2405.12624
Autor:
Henríquez, Fernando, Pinto, José
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 each arc's shape, which is controlled by a potentially high-dimensiona
Externí odkaz:
http://arxiv.org/abs/2403.10933
Autor:
Henríquez, Fernando, Hesthaven, Jan S.
We introduce a novel, fast method for the numerical approximation of parabolic partial differential equations (PDEs for short) based on model order reduction techniques and the Laplace transform. We start by applying said transform to the evolution p
Externí odkaz:
http://arxiv.org/abs/2403.02847
Autor:
Dölz, Jürgen, Henríquez, Fernando
We consider a family of boundary integral operators supported on a collection of parametrically defined bounded Lipschitz boundaries. Consequently, the boundary integral operators themselves also depend on the parametric variables, thus leading to a
Externí odkaz:
http://arxiv.org/abs/2305.19853
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recast
Externí odkaz:
http://arxiv.org/abs/2305.12202
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