  To enhance the scalability and performance of the traditional
finite-difference time-domain (FDTD) methods, a three-dimensional
summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is
developed to solve complex electromagnetic problems. It is theoretically stable
and can be further used for multiple mesh blocks with different mesh sizes.
This paper mainly focuses on the fundamental theoretical aspects upon its
three-dimensional implementation, the SAT for various boundary conditions, and
the numerical dispersion properties and the comparison with the FDTD method.
The proposed SBP-SAT FDTD method inherits all the merits of the FDTD method,
which is matrix-free, easy to implement, and has the same level of accuracy
with a negligible overhead of runtime (0.13\%) and memory usage (1.2\%). Four
numerical examples are carried out to validate the effectiveness of the
proposed method.
