The High-Order Symplectic Finite-Difference Time-Domain Scheme

The book chapter will aim at introducing the background knowledge, basic theories, supporting techniques, numerical results, and future research for the high-order symplectic finite-difference time-domain scheme. The theories of symplectic geometry and Hamiltonian are reviewed in Section 2 followed by the symplectiness of Maxwell’s equations presented in Section 3. Next, the numerical stability and dispersion analyses are given in Section 4. Then, in Section 5, we will make a tour of the supporting techniques but do not discuss them in detail. These techniques involve source excitation, perfectly matched layer, near-to-farfield transformation, inhomogeneous boundary treatments, and parameter extractions. The numerical results on propagation, scattering, and guided-wave problems are shown in Section 6. The high-order symplectic finite-difference time-domain scheme demonstrates the powerful advantages and potentials for the time-domain solution of Maxwell’s equations, especially for electrically-large objects and for long-term simulation. Finally, the conclusion and future research are summarized in Section 7.