Title :
Modal theory for recursive time-stepping numerical methods
Author :
Zhizhang Chen ; Silvester, P.P.
Author_Institution :
Dept. of Electr. Eng., Tech. Univ. Nova Scotia, Halifax, NS, Canada
Abstract :
Numerical time-domain methods have been applied extensively to solve various electromagnetic problems including scattering and radiating problems. The most widely used approaches are the finite-difference time-domain (FD-TD) method and the transmission-line-matrix (TLM) method due to the simplicity of their algorithms. The solutions of these two techniques have been shown to be the superposition of discrete eigenmodes, that is, the numerical solutions can be eigenmodally decomposed. In th the present paper, general eigenmodal formulations of numerical methods are discussed and compositions of numerical solutions are analyzed. It is concluded that solutions of any time-stepping recursive scheme are essentially solutions of an eigenvalue system. As a result, properties of a time-stepping recursive scheme, for example, numerical stability, can be studied.<>
Keywords :
eigenvalues and eigenfunctions; electromagnetic wave scattering; finite difference time-domain analysis; matrix decomposition; numerical stability; recursive functions; transmission line matrix methods; FDTD; TLM method; discrete eigenmodes; eigenmodal formulations; eigenvalue system; electromagnetic problems; finite-difference time-domain method; numerical stability; radiating problems; recursive time-stepping numerical methods; scattering; time-domain method; transmission-line-matrix method; Eigenvalues and eigenfunctions; Electromagnetic radiation; Electromagnetic scattering; Equations; Finite difference methods; Matrix decomposition; Numerical stability; Time domain analysis; Transmission line matrix methods; Visualization;
Conference_Titel :
Antennas and Propagation Society International Symposium, 1994. AP-S. Digest
Conference_Location :
Seattle, WA, USA
Print_ISBN :
0-7803-2009-3
DOI :
10.1109/APS.1994.407892
