Domínguez Baguena, Víctor
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Domínguez Baguena
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Víctor
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Estadística, Informática y Matemáticas
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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas
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Publication Open Access An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation(Elsevier, 2020) Domínguez Baguena, Víctor; Ganesh, M.; Sayas, Francisco Javier; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasA natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation, include a faraway decay radiation condition (RC). It is desirable to develop algorithms that incorporate the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid an approximation of the RC. In this work we first present and analyze an overlapping decomposition framework that is equivalent to the full-space heterogeneous-homogenous continuous model, governed by the Helmholtz equation with a spatially dependent refractive index and the RC. Our novel overlapping framework allows the user to choose two free boundaries, and gain the advantage of applying established high-order finite and boundary element methods (FEM and BEM) to simulate an equivalent coupled model. The coupled model comprises auxiliary interior bounded heterogeneous and exterior unbounded homogeneous Helmholtz problems. A smooth boundary can be chosen for simulating the exterior problem using a spectrally accurate BEM, and a simple boundary can be used to develop a high-order FEM for the interior problem. Thanks to the spectral accuracy of the exterior computational model, the resulting coupled system in the overlapping region is relatively very small. Using the decomposed equivalent framework, we develop a novel overlapping FEM-BEM algorithm for simulating the acoustic or electromagnetic wave propagation in two dimensions. Our FEM-BEM algorithm for the full-space model incorporates the RC exactly. Numerical experiments demonstrate the efficiency of the FEM-BEM approach for simulating smooth and non-smooth wave fields, with the latter induced by a complex heterogeneous medium and a discontinuous refractive index.Publication Open Access A fully discrete Calderón calculus for the two-dimensional elastic wave equation(Elsevier, 2015) Domínguez Baguena, Víctor; Sánchez Vizuet, Tonatiuh; Sayas, Francisco Javier; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaIn this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the plane. The method can be understood as a non-conforming Petrov–Galerkin discretization, with a very precise choice of testing functions by symmetrically combining elements on two staggered grids, and using a look-around quadrature formula. Unlike in the acoustic counterpart of this work, the kernel of the elastic double layer operator includes a periodic Hilbert transform that requires a particular choice of the mixing parameters. We give mathematical justification of this fact. Finally, we test the method on some frequency domain and time domain problems, and demonstrate its applicability on smooth open arcs.