In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved by a combination of a domain-based method and a boundary-integral method.Our reformulation is aimed at a situation where we have a collection of compact scattering objects located in an otherwise homogeneous unbounded space. The domain-based method is used to propagate the equations governing the wave field inside the scattering objects forward in time. The boundary integral method is used to supply the domain-based method with the required boundary values for the wave field. In this way the best features of both methods come into play; the response inside the scattering objects, which can be caused by both material inhomogeneity and nonlinearities, is easily taken into account using the domain-based method, and the boundary conditions supplied by the boundary integral method makes it possible to confine the domain based method to the inside of each scattering object.
An integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions
Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle
Université de Rennes 1（雷恩第一大学）；Universität Göttingen（哥廷根大学）
Efficient calculation of the integral equation for simulating 2D TE scattering in a homogeneous medium using the Ewald method and a Gabor frame discretization
Transient Propagation and Scattering of Quasi-Rayleigh Waves in Plates: Quantitative comparison between Pulsed TV-Holography Measurements and FC(Gram) elastodynamic simulations
University of Southern California（南加州大学）；California Institute of Technology（加州理工学院）；Universidade de Vigo（维戈大学）
