Low-Memory Implementation of PITD Method Using a Thresholding Scheme

被引：9
作者：
Zhu, Xiaojie [1 ]
Ma, Xikui [1 ]
Shao, Jinghui [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Elect Engn, State Key Lab Elect Insulat & Power Equipment, Xian 710049, Peoples R China
来源：
IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS | 2021年 / 31卷 / 06期
基金：
中国博士后科学基金;
关键词：
Sparse matrices; Time-domain analysis; Finite difference methods; Eigenvalues and eigenfunctions; Memory management; Wireless communication; Stability criteria; Electromagnetic (EM) wave; matrix exponential; precise-integration time-domain (PITD) method; thresholding scheme; PRECISE INTEGRATION METHOD; TIME-DOMAIN METHOD; REALIZATION; STABILITY; MATRIX;
D O I：
10.1109/LMWC.2021.3069643
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
A precise-integration time-domain (PITD) method with a thresholding scheme is proposed to reduce the computation cost of the matrix exponential for solving electromagnetic (EM) problems. The finiteness of EM wave speed is used to analyze the structure of the matrix exponential, revealing that the dense matrix exponential can become sparse. A thresholding scheme for eliminating tiny and thus unimportant elements is established to obtain the sparse matrix exponential, where the threshold value is selected by Von Neumann stability criterion and induced spurious solutions are avoided. Theoretical analyses and numerical results confirm that the proposed method can save a large amount of memory and the accuracy of the original method is inherited.
引用
收藏
页码：537 / 540
页数：4
相关论文
共 18 条
[1]   DISPERSION ANALYSIS OF ANISOTROPIC INHOMOGENEOUS WAVE-GUIDES USING COMPACT 2D-FDTD [J].
ASI, A ;
SHAFAI, L .
ELECTRONICS LETTERS, 1992, 28 (15) :1451-1452
[2]   A Low-Dispersion Realization of Precise Integration Time-Domain Method Using a Fourth-Order Accurate Finite Difference Scheme [J].
Bai, Zhong-Ming ;
Ma, Xi-Kui ;
Sun, Gang .
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2011, 59 (04) :1311-1320
[3]  
Gao Q, 2012, STRUCT ENG MECH, V43, P1
[4]   SPARSE MATRICES IN MATLAB - DESIGN AND IMPLEMENTATION [J].
GILBERT, JR ;
MOLER, C ;
SCHREIBER, R .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1992, 13 (01) :333-356
[5]   The Scaling and Squaring Method for the Matrix Exponential Revisited [J].
Higham, Nicholas J. .
SIAM REVIEW, 2009, 51 (04) :747-764
[6]   On the numerical stability of the precise integration time-domain (PITD) method [J].
Jiang, Lele ;
Chen, Zhizhang ;
Mao, Junfa .
IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, 2007, 17 (07) :471-473
[7]   An Efficient 2-D Compact Precise-Integration Time-Domain Method for Longitudinally Invariant Waveguiding Structures [J].
Kang, Zhen ;
Ma, Xikui ;
Xu Zhuansun .
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2013, 61 (07) :2535-2544
[8]   A 3-D precise integration time-domain method without the restraints of the Courant-Friedrich-Levy stability condition for the numerical solution of Maxwell's equations [J].
Ma, Xikui ;
Zhao, Xintai ;
Zhao, Yanzhen .
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2006, 54 (07) :3026-3037
[9]   Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later [J].
Moler, C ;
Van Loan, C .
SIAM REVIEW, 2003, 45 (01) :3-49
[10]  
Radke R.J., 1996, A MATLAB Implementation of the Implicitly Restarted Arnoldi Method for Solving Large-scale Eigenvalue Problems
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