Local Multiple Traces Formulation for High-Frequency Scattering Problems by Spectral Elements

Time-Domain Multiple Traces Boundary Integral Formulation for Acoustic Wave Scattering in 2D

“…We recall notation and results for the local MTF for the Helmholtz equation as exposed in [23,26]. Let Ω ⊂ R 2 be a bounded Lipschitz domain composed of M non-overlapping Lipschitz subdomains Ω , = 1, .…”

“…These lead to well-posed problems in such complex materials. The discretization of such MTF-BIEs then may be formulated by the boundary element method (BEM) [23], spectral Galerkin [25,26] or Nyström [24] methods. We chose a spectral variational scheme for the local MTF based on Chebyshev polynomials for the discretization of two-dimensional problems in order to have a high-order solution with a small number of degrees of freedom.…”

“…Lately, CQ schemes have attracted much attention due to their stability and possibility to implement as a blackbox with complex frequency-domain solvers. In particular, we employ the local MTF as it allows easy parallelization and fast solvers, such as [25,26]. Many theoretical aspects of the CQ method along with numerical analysis results are given in the monograph [36].…”

“…In what follows, we set the framework required to apply CQ to solve the time-domain acoustic transmission problem (2) in composite materials via the local MTF [23,25,26]. In Section 2, we present the MTF in frequency domain as described in [23].…”

“…Section 3 recalls the main ideas behind time-domain BIEs. Section 4 describes our numerical scheme including the spectral non-conforming Galerkin discretization for MTF [25,26]. Then, in Sections 5, 5.1 and 5.2 we explain CQ for multistep and multistage linear methods and the corresponding application for the Petrov-Galerkin formulation with spectral elements as convolutional equations in Section 5.3.…”