A Semianalytical Spectral Element Method for the Analysis of 3-D Layered Structures

作者：Chen, Jiefu^*; Zhu, Bao; Zhong, Wanxie; Liu, Qing Huo

来源：IEEE Transactions on Microwave Theory and Techniques, 2011, 59(1): 1-8.

DOI：10.1109/TMTT.2010.2090408

• Block Thomas algorithm
• block tri-diagonal matrix
• finite-element method (FEM)
• Gauss-Lobatto-Legendre (GLL) polynomials
• Hamiltonian system
• high precision integration (HPI) method
• Lagrangian system
• layered structure
• Riccati equation
• semianalytical spectral element method (SEM)

A semianalytical spectral element method (SEM) is proposed for electromagnetic simulations of 3-D layered structures. 2-D spectral elements are employed to discretize the cross section of a layered structure, and the Legendre transformation is then used to cast the semidiscretized problem from the Lagrangian system into the Hamiltonian system. A Riccati equation-based high precision integration method is utilized to perform integration along the longitudinal direction, which is the undiscretized direction, to generate the stiffness matrix of the whole layered structure. The final system of equations by the semianalytical SEM will take the form of a set of linear equations with a block tri-diagonal matrix, which can be solved efficiently by the block Thomas algorithm. Numerical examples demonstrate the high efficiency and accuracy of the proposed method.

• 出版日期2011-1
• 单位大连理工大学