A Rationale for p-refinement with the Vector Helmholtz Equation and Two Dimensional Vector Finite Elements
Keywords:
A Rationale for p-refinement with the Vector Helmholtz Equation and Two Dimensional Vector Finite ElementsAbstract
A preliminary study of p-refinement
with vector finite elements is reported. Results
suggest that improved accuracy can be obtained
from representations employing a mixture of
polynomial orders instead of a uniform
polynomial order. Results also suggest that it
might be possible to jump directly from the local
error in a p=0 expansion to a final representation
employing 5 or more polynomial orders. In
addition, a new set of hierarchical curl-
conforming vector basis functions is proposed.
Downloads
References
J. E. Akin, Finite Elements for Analysis and
Design, Academic Press, San Diego, 1994.
O. C. Zienkiewicz and R. L. Taylor, The
Finite Element Method. McGraw-Hill,
New York, 1989.
M. Salazar-Palma et al., Iterative and Self-
Adaptive Finite Elements in
Electromagnetic Modeling. Boston: Artech
House, 1998.
Ansoft HFSS Users Manual, October 1999.
J. C. Nedelec, “Mixed finite elements in
R3,” Num. Math., vol. 35, pp. 315-341,
A. F. Peterson, S. L. Ray and R. Mittra,
Computational Methods For
Electromagnetics, IEEE Press, New York,
R. D. Graglia, D. R. Wilton and A. F.
Peterson, “Higher Order Interpolatory
Vector Bases for Computational
Electromagnetics,” IEEE Transactions on
Antennas and Propagation, vol. 45, no. 3,
pp. 329-342, March 1997.
J. P. Webb and B. Forghani, “Hierarchal
Scalar and Vector Tetrahedra,” IEEE Trans.
Magnetics, vol. 29, pp. 1495-1498, March
J. S. Wang, “Hierarchic ‘Edge’ Elements
for High-Frequency Problems,” IEEE
Transactions on Magnetics, vol. 33, no. 2,
pp. 1536-1539, March 1997.
C. Carrie and J. P. Webb, “Hierarchal
Triangular Edge Elements Using
Orthogonal Polynomials,” Digest of the
ACES JOURNAL, VOL. 19, NO. 2, JULY 2004
IEEE Antennas and Propagation
International Symposium, vol. 2, pp. 1310-
, July 1997.
J. S. Savage, “Comparing high order vector
basis functions,” Proceedings of the 14th
Annual Review of Progress in Applied
Computational Electromagnetics,
Monterey, CA, pp. 742-749, 1998.
L. S. Andersen and J. L. Volakis,
“Hierarchical Tangential Vector Finite
Elements for Tetrahedra,” IEEE Microwave
and Guided Wave Letters, vol. 8, pp.127-
, March 1998.
L. S. Andersen and J. L. Volakis,
“Development and application of a novel
class of hierarchical tangential vector finite
elements for electromagnetics,” IEEE
Transactions on Antennas and
Propagation, vol. 47, pp. 112-120, January
J. P. Webb, “Hierarchical vector basis
functions of arbitrary order for triangular
and tetrahedral finite elements,” IEEE
Transactions on Antennas and
Propagation, vol. 47, pp. 1244-1253,
August 1999.
R. S. Preissig, Local P Refinement in Two
Dimensional Vector Finite Elements,
Master's Thesis, Georgia Institute of
Technology, Atlanta, GA, 1998
