Energetic Bem for the Numerical Solution of Damped Wave Propagation Exterior Problems

The analysis of damping phenomena that occur in many physics and engineering problems, such as fluid dynamics, kinetic theory and semiconductors, is of particular interest. For this kind of problems, one needs accurate and stable approximate solutions even on large time intervals. These latter can be obtained reformulating time-dependent problems modeled by partial differential equations (PDEs) of hyperbolic type in terms of boundary integral equations (BIEs) solved via boundary element methods (BEMs). In this context, starting from a recently developed energetic weak formulation of the space-time BIE modeling, in particular, classical wave propagation exterior problems [2, 3], we consider here an extension for the damped wave equation in 2D space dimension, based on successful simulations for the 1D case [6, 7]. In fact, the related energetic BEM reveals a robust time stability property, which is crucial in guaranteeing accurate numerical solutions on large time intervals. Several benchmarks will be presented and discussed.