The discrete origin of FETD-Newmark late time instability, and a correction scheme
type: Item
instance of: scholarly article
title: The discrete origin of FETD-Newmark late time instability, and a correction scheme
zbMATH Open document ID: 1123.78013
author: N. E. Zubov
published in: Journal of Computational Physics
publication date: 2007-06-14T00:00:00Z
review text: The finite element time domain (FETD) method is commonly used for transient simulation of electromagnetic wave phenomena. Most practitioners consider FETD, when time integrated using the Newmark-Beta method, to be unconditionally stable when \(\beta \geq 0.25\). Unlike the finite difference time domain (FDTD) ``courant criterion'', FETD-Newmark has no limiting timestep above which the method exhibits exponential growth. However, herein the stability properties of FETD-Newmark will be rigorously investigated by reducing the Jordan canonical form of the FETD-Newmark amplification matrix, and it will be demonstrated that the method does exhibit linear growth for certain field configurations. These modes are none other than the pure-gradient fields associated with ``late time instability''. Though many practical simulations are of short duration and will never observe a linearly growing gradient solution, it can be problematic for simulations which require long time periods to be integrated. A correction scheme for eliminating this late time instability shall be suggested, and numerical results will verify its performance.
reviewed by: X. Antoine
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 78A40
zbMATH DE Number: 5164972
zbMATH Keywords: computational electromagnetics
zbMATH Keywords: finite elements
zbMATH Keywords: transient simulation
zbMATH Keywords: numerical stability
zbMATH Keywords: von-Neumann analysis
zbMATH Keywords: Jordan form
describes a project that uses: DistMesh
MaRDI profile type: Publication
full work available at URL: j.jcp.2006.11.021
OpenAlex ID: W2042540390
cites work: Time-domain finite-element methods
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DOI: 10.1016/J.JCP.2006.11.021
description: scientific article; zbMATH DE number 5164972