Executive Summary : | This project aims to reduce simulation time for Finite-Difference Time-Domain (FDTD) methods incorporating nonlinear circuit elements (NCEs), such as diodes and transistors. The proposed algorithms will be designed to be unconditionally stable for implicit FDTD methods and provide better stability criteria for HIE-FDTD methods. They will allow for larger time-step sizes, particularly for simulations with smaller mesh-sizes, resulting in a significant reduction in simulation time. The updating equations in HIE-FDTD methods can be implicit in one or two directions and explicit in other directions, reducing simulation time significantly compared to explicit FDTD methods. The stability of the proposed algorithms will be analyzed to ensure effectiveness for simulations with small mesh-sizes in one or more directions. The accuracy of the algorithms will be validated by comparing simulation results to analytical results, SPICE models, and existing algorithms. The developed algorithms will be applied to simulate various microwave devices incorporating NCEs, such as microwave amplifier and oscillator, to validate their performance. The results will have practical applications in fields like telecommunications, medical imaging, and radar systems, where accurate and efficient simulations of microwave devices are required. |