Toward the Development of a 3-D SBP-SAT FDTD Method: Subgridding Implementation

A 3-D finite-difference time-domain (FDTD) subgridding method with the summation-by-parts simultaneous approximation term (SBP-SAT) technique is proposed to solve challenging multiscale problems. Its long-time stability is proved through the energy method by carefully enforcing the properties of the SBP operators and selecting free parameters in SATs. It is found that the norm compatibility condition should be satisfied to guarantee the stability when multiple mesh blocks with different mesh sizes are used. In addition, interpolation matrices are also detailed derived. Four numerical examples from simple structures to challenging engineering problems are carried out to validate its accuracy, efficiency, and scalability of the proposed subgridding method. Results show that it is accurate and efficient.