| This dissertation presents an accurate and efficient algorithm, the multidomain Pseudospectral Time-Domain (PSTD) method, to solve Maxwell's equations and to model transient electromagnetic phenomena. This novel algorithm is considered as an improvement over the traditional Finite-Difference Time-Domain (FDTD) method in its capacity of achieving higher order accuracy with a lower sampling density requirement.; Unlike the original global single-domain PSTD algorithm, this work is based on a multidomain framework to better characterize the curved geometry and localized inhomogeneities, which for the first time, brings the PSTD algorithm to a variety of real-world applications. It also features a well-posed PML to efficiently truncate the computational domain.; In the implementation phase, I have developed the 2.5-D multidomain PSTD algorithm to model waveguide problems and periodic structures, and the 3-D multidomain PSTD algorithm for scattering problems such as RCS applications. An unconditionally stable scheme has also been developed to extend the capacity of the PSTD method to electrically small structures. The recent highlight of this work is the development of the discontinuous Galerkin PSTD algorithm, in which the discontinuous Galerkin method with a Riemann solver is incorporated to accurately resolve the boundary conditions, leading to a more robust PSTD scheme. The 3-D multidomain PSTD algorithm has been applied to model EMI/EMC, signal integrity and microwave circuit problems. |
