Progress in differentiation of approximate data

Author

Omeragic, Dzevat ; Silvester, Peter P.

Author_Institution

Dept. of Electr. Eng., McGill Univ., Montreal, Que., Canada

Volume

38

Issue

1

fYear

1996

fDate

2/1/1996 12:00:00 AM

Firstpage

25

Lastpage

30

Abstract

Accurate derivative calculation is a key process in computational electromagnetics. Differentiation is required for graphic display, a posteriori error estimation, automatic mesh refinement, and result post-processing. The choice of method depends on the accuracy required, and on the order of derivatives to be computed. This paper reviews recent progress, and compares several recent derivative-extraction methods: local smoothing, superconvergent-patch recovery (SPR), and methods based on Green´s second identity. The SPR approach of Zhu and Zienkiewicz (see Finite Elements in Analysis and Design, vol.19, p.1123, 1995) has been extended in several ways to yield good accuracy at low cost, but it can only produce first derivatives. The Green´s identity methods of Silvester and Omeragic (see International Journal of Applied Electomagnetics in Materials, vol.4, p.123-136, 1993) are computationally expensive, but extremely accurate, even for third and fourth derivatives. Representative numerical results illustrate the methods discussed

Keywords

Green´s function methods; approximation theory; computer aided analysis; differentiation; electrical engineering; electrical engineering computing; electromagnetism; error analysis; Green´s identity methods; Green´s second identity; accuracy; approximate data differentiation; automatic mesh refinement; computational electromagnetics; derivative extraction methods; error estimation; first derivatives; fourth derivatives; graphic display; local smoothing; numerical results; result postprocessing; superconvergent patch recovery; third derivatives; Costs; Displays; Electromagnetics; Error analysis; Finite difference methods; Finite element methods; Graphics; Magnetics; Physics computing; Smoothing methods;

fLanguage

English

Journal_Title

Antennas and Propagation Magazine, IEEE

Publisher

ieee

ISSN

1045-9243

Type

jour

DOI

10.1109/74.491288

Filename

491288