Communicated by M. DaugeWe investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant properties of anisotropic Sobolev spaces and the boundary integral operators between them.

This work investigates a time domain boundary element method for the acoustic wave equation in an exterior domain in the half-space R 3 +. The Neumann problem is formulated as a boundary integral equation of the second kind, and the convergence and stability of conforming Galerkin approximations is studied in the complex geometry of a car or truck tire above a street. After a validation experiment, numerical results are presented in time or frequency domain for realistic benchmarks in traffic noise: the sound emission of vibrating tires, noise amplification in the horn-like geometry between the tire and the road, as well as the Doppler effect of a moving tire. The results are compared with calculations in frequency domain.

We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments.

Uncertainty quantification and variability analysis are two domains of interest when looking at the efficiency of HPEM sources. Vircator is known to be a low efficiency high power microwave source subject to several generally volatile phenomena such as plasma expansion and shot-to-shot variability. In this study, a computationally low cost framework combining the Extreme Value Theory (EVT) and the Generalised Design of Experiments is proposed in order to study the peak power distribution of a Vircator obtained with a surrogate model. Following the pre-screening of random variables, the optimised parameters are introduced in 2.5D and 3D simulation tools, namely XOOPIC and CST-PS. It has been confirmed that the peak power output can reach a 40% increase. This shows that the EVT proves to be successful in classifying and quantifying random variables to influence the distribution tails.