A numerical study of energetic BEM-FEM applied to wave propagation in 2D multidomains

Abstract

Starting from a recently developed energetic space-time weak formulation of boundary integral equations related to wave propagation problems defined on single and multidomains, a coupling algorithm is presented, which allows a flexible use of finite and boundary element methods as local discretization techniques, in order to efficiently treat unbounded multilayered media. Partial differential equations associated to boundary integral equations will be weakly reformulated by the energetic approach and a particular emphasis will be given to theoretical and experimental analysis of the stability of the proposed method.

Application of Energetic BEM to 2D Elastodynamic Soft Scattering Problems

“…Remark. The marching-on-time scheme is implicit and unconditionally stable, as proved for scalar problems in [30], [31], [32] in the more general framework of Energetic BEM-FEM coupling.…”

“…For what concerns the overall computational cost of the Energetic BEM, it is due to three phases: (i) construction of E ( ) blocks; (ii) numerical solution of linear systems ( 29); (iii) post-processing evaluation of displacements by representation formula ( 14), once the unknown φ is recovered. The first step is the heaviest, since it involves the evaluation of double boundary integrals (31) with the suitable quadrature schemes just cited. Anyway, since matrices E ( ) are independent of each other, this phase can be speeded up using concurrent processors doing blocks evaluation in parallel.…”

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

“…These data can be obtained directly from the solution of BIEs, whereas it is well known that boundary values obtained with low order finite element method (FEM) solutions are in general not so accurate. Sometimes, however, BEM-FEM coupling proves to be highly useful [6][7][8].…”