A 3D nonlinear Maxwell's equations solver based on a hybrid numerical method

In this paper, we explore the possibility of solving 3D Maxwell's equations in the presence of a nonlinear and/or inhomogeneous material response. We propose using a hybrid approach, which combines a boundary integral representation with a domain-based method. This hybrid approach has previously been successfully applied to 1D linear and nonlinear transient wave scattering problems. The basic idea of the approach is to propagate Maxwell's equations inside the scattering objects forward in time using a domain-based method, while a boundary integral representation of the electromagnetic field is used to supply the domain-based method with the Required surface values. Thus, no grids outside the scattering objects are needed, and this greatly reduces the computational cost and complexity.