A Novel Symplectic Multi-Resolution Time-Domain Scheme for Electromagnetic Simulations

A symplectic scheme is applied to the multi-resolution time-domain (MRTD) method, resulting in a highly stable novel symplectic MRTD scheme. First, the time-domain Maxwell's equations are rewritten as a matrix equation. Then, we discretize the Maxwell's equations in the time direction using symplectic propagation integrator (SPI) technique and evaluate the equations in the spatial direction with high order spatial multi-resolution approximation to construct novel symplectic MRTD scheme. The stability and numerical dispersion analysis are also included. Numerical results are given to show the high efficiency and accuracy of the method.