NDLI: Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis

Content Provider	IEEE Xplore Digital Library
Author	Jin Yan Dan Jiao
Copyright Year	1963
Abstract	We develop a new time-domain method that is naturally matrix free, i.e., requiring no matrix solution, regardless of whether the discretization is a structured grid or an unstructured mesh. Its matrix-free property, manifested by a naturally diagonal mass matrix, is independent of the element shape used for discretization and its implementation is straightforward. No dual mesh, interpolation, projection, and mass lumping are required. Furthermore, we show that such a capability can be achieved with conventional vector basis functions without any need for modifying them. Moreover, a time-marching scheme is developed to ensure the stability for simulating an unsymmetrical numerical system whose eigenvalues can be complex-valued and even negative, while preserving the matrix-free merit of the proposed method. Extensive numerical experiments have been carried out on a variety of unstructured triangular, tetrahedral, triangular prism element, and mixed-element meshes. Correlations with analytical solutions and the results obtained from the time-domain finite-element method, at all points in the computational domain and across all time instants, have validated the accuracy, matrix-free property, stability, and generality of the proposed method.
Sponsorship	IEEE Microwave Theory and Techniques Society
Starting Page	4201
Ending Page	4214
Page Count	14
File Size	2470781
File Format	PDF
ISSN	00189480
Volume Number	63
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Time-domain analysis Accuracy Finite difference methods Power system stability Numerical stability Stability analysis Shape unstructured mesh Electromagnetic analysis finite-difference time domain (FDTD) methods matrix-free methods time-domain finite-element methods time-domain methods
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering Radiation

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