Investigation of an Explicit, Residual-Based, a Posteriori Error Indicator for the Adaptive Finite Element Analysis of Waveguide Structures
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Investigation of an Explicit, Residual-Based, a Posteriori Error Indicator for the Adaptive Finite Element Analysis of Waveguide Structures摘要
The performance of an explicit, residual-based, a posteriori error indicator for directing a single level p-refinement of the finite element method, electromagnetic analysis of multiport waveguide structures is evaluated experimentally by considering three different structures. The error indicator consists of a linear combination of element volume and element face residuals. It is found that the indicator is generally very effective in identifying elements that need to be refined. It is also found that the relative weighting of the volume and face residual contributions to the error indicator plays an important role in its performance.
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参考
J.-M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. New
York: John Wiley and Sons, 2002.
C. J. Reddy, M. D. Deshpande, C. R. Cockrell, and F. B. Beck,
“Analysis of three-dimensional-cavity-backed aperture antennas using a
combined finite element method/method of moments/geometrical theory
of diffraction technique,” NASA, Langley Research Center, Tech. Rep.
, November 1995.
D. B. Davidson, “Higher-order (LT/QN) vector finite elements for
waveguide analysis,” Applied Computational Electromagnetics Society
Journal, vol. 17, no. 1, pp. 1–10, March 2002, special Issue on
Approaches to Better Accuracy/Resolution in Computational Electromagnetics.
J. P. Webb, “Finite element methods for junctions of microwave and
optical waveguides,” IEEE Trans. Magn., vol. 26, no. 5, pp. 1754–1758,
September 1990.
J.-F. Lee, D.-K. Sun, and Z. J. Cendes, “Full-wave analysis of dielectric waveguides using tangential vector finite elements,” IEEE Trans.
Microwave Theory Tech., vol. 39, no. 8, pp. 1262–1271, August 1991.
M. Salazar-Palma, T. K. Sarkar, L.-E. Garc´ıa-Castillo, T. Roy, and
A. Djordjevi´c, Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling. Boston: Artech House, 1998.
J. P. Webb, “Edge elements and what they can do for you,” IEEE Trans.
Magn., vol. 29, no. 2, pp. 1460–1465, March 1993.
G. Mur, “Edge elements, their advantages and their disadvantages,” IEEE
Trans. Magn., vol. 30, no. 5, pp. 3552–3557, March 1994.
A. F. Peterson and D. R. Wilton, “Curl-conforming mixed-order edge
elements for discretizing the 2D and 3D vector Helmholtz equation,” in
Finite Element Software for Microwave Engineering, T. Itoh, G. Pelosi,
and P. P. Silvester, Eds. New York: John Wiley and Sons, 1996, pp.
–125.
M. M. Botha and D. B. Davidson, “An explicit a posteriori error indicator
for electromagnetic, finite element-boundary integral analysis,” IEEE
Trans. Antennas Propagat., vol. 53, no. 11, pp. 3717–3725, November
ACES JOURNAL, VOL. 21, NO. 1, MARCH 2006
M. M. Botha, “Efficient finite element electromagnetic analysis of
antennas and microwave devices: the FE-BI-FMM formulation and a
posteriori error estimation for p adaptive analysis,” Ph.D. dissertation,
University of Stellenbosch, Stellenbosch, South Africa, December 2002.
M. Ainsworth and J. T. Oden, “A posteriori error estimation in finite
element analysis,” Computer Meth. in Appl. Mech. and Eng, vol. 142,
pp. 1–88, 1997.
S. Polstyanko and J.-F. Lee, “Adaptive finite element electrostatic
solver,” IEEE Trans. Magn., vol. 37, no. 5, pp. 3120–3124, September
J. R. Stewart and T. J. R. Hughes, “A tutorial in elementary finite element
error analysis: A systematic presentation of a priori and a posteriori error
estimates,” Computer Meth. in Appl. Mech. and Eng, vol. 158, pp. 1–22,
P. Monk, “A posteriori error indicators for Maxwell’s equations,” Jnl of
Comp. and Appl. Math., vol. 100, pp. 173–190, 1998.
K. K. Mei, “Unimoment Method for Electromagnetic Wave Scattering,”
Journal of Electromagnetic Waves and Applications, vol. 1, no. 3, pp.
–222, 1987.
S. Ramo, J. R. Whinnery, and T. van Duzer, Fields and Waves in
Communication Electronics, 3rd ed. John Wiley and Sons, 1994.
J. C. N´ed´elec, “Mixed finite elements in ℜ3
,” Numerische Mathematik,
vol. 35, pp. 315–341, 1980.
J. S. Savage, “Comparing high order vector basis functions,” in Proceedings of the 14th Annual Review of Progress in Applied Computational
Electromagnetics, March 1998, pp. 742–749, monterey, CA.
P. G. Ciarlet, The finite element method for elliptic problems, ser. Studies
in mathematics and its applications 4. Amsterdam: North-Holland,
E. Kreyszig, Introductory Functional Analysis with Applications. New
York: John Wiley and Sons, 1978.
N. Marcuvitz, Waveguide Handbook. Peter Peregrinus, on behalf of
IEE, 1986, originally published 1951.
H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy.
Englewood Cliffs, New Jersey: Prentice-Hall, 1989.
D. B. Davidson, “An evaluation of mixed-order versus full-order vector
finite elements,” IEEE Trans. Antennas Propagat., vol. 51, no. 9, pp.
–2441, Sept. 2003.
M. M. Botha and D. B. Davidson, “A quasi-static condition for enhancing p-adaptive, mixed-order element, FE analysis,” Electromagnetics,
vol. 24, no. 1–2, pp. 13–24, January–March 2004.
M. M. Botha and J.-M. Jin, “Adaptive finite element-boundary integral
analysis for electromagnetic fields in 3-D,” IEEE Trans. Antennas
Propagat., vol. 53, no. 5, pp. 1710–1720, May 2005.
