High-order PML Algorithm Based On FDTD And Its Application In Integrated Circuit Simulation

Among the algorithms for solving the electromagnetic problems,the finite difference time domain(FDTD)is one of the most effective method.However,due to the restriction of computer memory,FDTD computation can only be performed in a limited region.In order to simulate the open problem,the absorbing boundary conditions were proposed.Among them,the perfectly matched layer(PML)is the most widely used and effective absorbing boundary condition.Among the many implementations of the PML,the convolutional perfectly matched layer(CPML)is one of the most effective implementations.It has a wide application prospect.However,the first-order PML is inefficient for absorbing low-frequency waves.In order to solve this problem,the high-order PML was proposed.This thesis mainly studies the algorithms of the high-order CPML based on the FDTD algorithms,which is divided into the following three parts:1.A novel higher-order CPML algorithm based on the traditional FDTD(2nd-CPML)algorithm is proposed,which is applied in truncating free space and the three common microstrip circuit structures in integrated circuit.Under the same conditions,this algorithm is compared with the first-order CPML algorithm(1st-CPML)and the higher-order PML algorithm implemented by the auxiliary differential equation method(ADE-2nd-PML).The results of numerical examples show that the 2nd-CPML algorithm can significantly improve the absorbing performance of the PML compared with the 1st-CPML algorithm.And compared with the ADE-2nd-PML algorithm,the 2nd-CPML algorithm consumes less computational time and memory,and improves the computational efficiency.2.A novel higher-order CPML algorithm based on the Alternating-Direction-Implicit FDTD(2nd-ADI-CPML)algorithm is proposed,which is applied in truncating free space and the three microstrip circuit structures in integrated circuit.The validity of the algorithm is verified by the numerical examples.The results show that the 2nd-ADI-FDTD algorithm can significantly improve the absorbing performance of the PML compared with the first-order CPML algorithm based on the ADI-FDTD algorithm(1st-ADI-CPML).And compared with the traditional first-order CPML algorithm,with the increase of the CFLN,the 2nd-ADI-FDTD algorithm consumes less and less computational time,and the computational efficiency is gradually improved.Besides,compared with the ADE-2nd-PML algorithm based on the ADI-FDTD algorithm,the 2nd-ADI-FDTD algorithm also improves the computational efficiency.3.A novel higher-order CPML algorithm based on the complex envelope FDTD(2nd-CE-CPML)algorithm is proposed,which is applied in truncating free space and the three microstrip circuit structures in integrated circuit.The numerical example results show that the proposed algorithm can greatly improve the absorbing performance of the PML compared with the first-order CPML algorithm based on the CE-FDTD algorithm(1st-CE-CPML).And compared with the traditional 2nd-CPML algorithm,the 2nd-CE-CPML algorithm improves the absorbing performance of the PML.