Automatic generation of subdomain models in 2D FDTD using reduced order modeling

A new method combining a finite difference method and a reduced order model (ROM) algorithm is presented for two-dimensional (2-D) electromagnetic problems. The problem space is subdivided into subdomains of a generic type. By discretizing the spatial derivatives in a way similar to the finite-difference in time-domain technique (FDTD), the state equations are written down in each subdomain. From that, an FDTD-subdomain model is derived. Finally, the different subdomains are reconnected and the original problem is solved by a leapfrog time-stepping algorithm. Some numerical results are presented to illustrate the new approach.