Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method

In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Ma...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on microwave theory and techniques 2007-06, Vol.55 (6), p.1322-1331
Main Authors: Movahhedi, M., Abdipour, A., Nentchev, A., Dehghan, M., Selberherr, S.
Format: Article
Language:English
Subjects:
Alternating-direction implicit (ADI) technique
Amplification
Applied classical electromagnetism
Crank-Nicolson (CN) method
Electromagnetic transients
Electromagnetic wave propagation, radiowave propagation
Electromagnetism
electron and ion optics
Exact sciences and technology
Finite difference methods
Finite element method
Finite element methods
finite-element time-domain (FETD) method
Fundamental areas of phenomenology (including applications)
instability
Mathematical analysis
Mathematical models
Maxwell equation
Maxwell equations
Maxwell's equations
Microwaves
Nodular iron
Nonlinear equations
Partial differential equations
Perfectly matched layers
Physics
Stability analysis
Time domain analysis
Transient analysis
unconditional stability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Maxwell curl equations in order to obtain an unconditionally stable FETD approach, unlike the conventional FETD method, which is conditionally stable. A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived. Investigation of the proposed method formulation shows that it does not generally lead to a tri-diagonal system of equations. Therefore, the Crank-Nicolson FETD method is introduced as another alternative in order to obtain an unconditionally stable method. Numerical results are presented to demonstrate the effectiveness of the proposed methods and are compared to those obtained using the conventional FETD method.
ISSN:0018-9480
1557-9670
DOI:10.1109/TMTT.2007.897777