Efficient Implementation for 3-D Laguerre-Based Finite-Difference Time-Domain Method

When the Laguerre-based finite-difference time-domain (FDTD) method is used for electromagnetic problems, a huge sparse matrix equation results, which is very expensive to solve. We previously introduced an efficient algorithm for implementing an unconditionally stable 2-D Laguerre-based FDTD method...

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Bibliographic Details
Published in:IEEE transactions on microwave theory and techniques 2011-01, Vol.59 (1), p.56-64
Main Authors: DUAN, Yan-Tao, BIN CHEN, FANG, Da-Gang, ZHOU, Bi-Hua
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Applied classical electromagnetism
Applied sciences
Boundary conditions
Computational electromagnetics
Electromagnetic wave propagation, radiowave propagation
Electromagnetism
electron and ion optics
Electronics
Exact sciences and technology
Finite difference method
Finite difference methods
Finite difference time domain method
finite-difference time-domain (FDTD) method
Fundamental areas of phenomenology (including applications)
Laguerre polynomials
Magnetic devices
Mathematical analysis
Mathematical model
Mathematical models
Microwaves
perfectly matched layer (PML)
Perfectly matched layers
Physics
Polynomials
Radiocommunications
Radiowave propagation
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
Sparse matrices
Sparsity
Studies
Telecommunications
Telecommunications and information theory
Time domain analysis
unconditionally stable method
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Summary:When the Laguerre-based finite-difference time-domain (FDTD) method is used for electromagnetic problems, a huge sparse matrix equation results, which is very expensive to solve. We previously introduced an efficient algorithm for implementing an unconditionally stable 2-D Laguerre-based FDTD method. We numerically verified that the efficient algorithm can save CPU time and memory storage greatly while maintaining comparable computational accuracy. This paper presents new efficient algorithm for implementing unconditionally stable 3-D Laguerre-based FDTD method. To do so, a factorization-splitting scheme using two sub-steps is adopted to solve the produced huge sparse matrix equation. For a full update cycle, the presented scheme solves six tri-diagonal matrices for the electric field components and computes three explicit equations for the magnetic field components. A perfectly matched layer absorbing boundary condition is also extended to this approach. In order to demonstrate the accuracy and efficiency of the proposed method, numerical examples are given.
ISSN:0018-9480
1557-9670
DOI:10.1109/TMTT.2010.2091206