Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

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 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.

Application of Energetic BEM to 2D Elastodynamic Soft Scattering Problems

“…This weak formulation is called energetic, because it takes advantage of some properties of the energy of the system ( [20], [21]). The Energetic BEM has been applied so far to many models: interior and exterior 2D ( [21], [22], [23]) and 3D ( [24], [25]) scalar wave propagation problems and, more recently, 2D exterior damped wave propagation problems ( [26], [27]). Obtained numerical results are very interesting in comparison with other ones found in literature ( [28]).…”