A boundary integral approach to linear and nonlinear transient wave scattering

In this work, 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 in which 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 non-linearities, is easily considered using the domain-based method, and the boundary conditions supplied by the boundary integral method makes it possible to confine the domain-method to the inside of each scattering object. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.