Energetic BEM–FEM coupling for wave propagation in 3D multidomains

Abstract

SUMMARYStarting from a recently developed energetic space–time weak formulation of boundary integral equations for wave propagation problems, a coupling algorithm is presented, which allows a flexible use of FEMs and BEMs as local discretization techniques. Emphasis is given to theoretical and experimental analysis of the stability of the proposed method. Several numerical results on model problems are presented and discussed, showing that both bounded and unbounded three‐dimensional domains can be efficiently addressed. Copyright © 2013 John Wiley & Sons, Ltd.

BEM‐FEM coupling for the 1D Klein–Gordon equation

“…All these difficulties are, at least theoretically, overcome by the BEM-FEM coupling formulation adopted in this article. The continuous problem is set in a space-time weak formulation which couples the initial-boundary value problem for the partial differential equation in the bounded interval 1 with two retarded integro-differential equations at the interface point x = L, whose unknowns are u L (t) = u(L, t) and p L (t) = −c 2 2 u x (L, t), (see (17), (19), and Section IIC for details on their derivation): u L (t) = 2(Vp L )(t), p L (t) = 2(−Du L )(t).…”

Time domain boundary elements for dynamic contact problems

“…As in Cooper [15], we start with a regularized contact problem with parameter σ > 0. The analysis lets σ → 0 + at the end, to recover the existence of weak solutions to the contact problem (2). We let w σ = e −σt w and h σ = e −σt h. Using appropriate units, we may also assume c s = 1.…”

“…Our approach also relates to the recent interest in coupled and nonlinear interface problems for wave propagation, solved by time domain boundary element methods. In particular, we refer to the fundamental articles [1,6] for the coupling of FEM and BEM, as well as [2] for an energetic Galerkin formulation of the coupling. Reference [7] considers a nonlinear boundary value problem.…”

On the discretization and application of two space–time boundary integral equations for 3D wave propagation problems in unbounded domains

“…In the last decades, space-time Boundary Integral Equations (BIE) have been successfully applied to wave propagation problems defined in the exterior of a bounded domain (see, for example, [9], [24], [3], [19], [26], [15], [10], [2], [27], [16], [5], [4], [25], [18], [17], [22], [12]).…”