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Energetic BEM-FEM coupling for the numerical solution of the damped wave equation

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Abstract

Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for the coupling of boundary integral equations and hyperbolic partial differential equations related to wave propagation problems, we consider here an extension for the damped wave equation in layered media. A coupling algorithm is presented, which allows a flexible use of finite element method and boundary element method as local discretization techniques. Stability and convergence, proved by energy arguments, are crucial in guaranteeing accurate solutions for simulations on large time intervals. Several numerical benchmarks, whose numerical results confirm theoretical ones, are illustrated and discussed.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Parma, Parco Area delle Scienze 53/A, 43124, Parma, Italy

    A. Aimi, M. Diligenti & C. Guardasoni

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  1. A. Aimi
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  2. M. Diligenti
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  3. C. Guardasoni
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Correspondence to C. Guardasoni.

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Communicated by: Enrique Zuazua

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Aimi, A., Diligenti, M. & Guardasoni, C. Energetic BEM-FEM coupling for the numerical solution of the damped wave equation. Adv Comput Math 43, 627–651 (2017). https://doi.org/10.1007/s10444-016-9500-1

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  • DOI: https://doi.org/10.1007/s10444-016-9500-1

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