Application of Hierarchical Higher-Order Tangential Vector Finite Elements in a Hybrid Fem/Mom Method
Keywords:
Application of Hierarchical Higher-Order Tangential Vector Finite Elements in a Hybrid Fem/Mom MethodAbstract
Hybrid FEM/MoM methods combine the finite
element method (FEM) and the method of moments
(MoM) to model inhomogeneous unbounded
problems. These two methods are coupled by
enforcing field continuity on the boundary that
separates the FEM and MoM regions. Hierarchical
higher-order tangential vector finite elements
(TVFE’s) are of practical interest because they can be
easily combined with low-order elements to improve
the accuracy of numerical solutions. This paper
presents a hybrid FEM/MoM formulation applying a
set of hierarchical TVFE’s developed by Webb and
Forghani. Higher-order FEM elements are coupled to
MoM elements based on Rao-Wilton-Glisson (RWG)
functions. The FEM matrix assembly procedure is
described in sufficient detail to aid other investigators
who wish to develop codes employing this technique.
Three practical electromagnetic problems are
presented that demonstrate the advantages of the
higher-order elements.
Downloads
References
J. C. Nedelec, “Mixed finite elements
in R3,” Num. Math., vol. 35, pp. 315-
, 1980.
J. L. Volakis, A. Chatterjee, and L. C.
Kempel, Finite element method for
electromagnetics. New York: IEEE Press,
, ch. 2.
J. P. Webb and B. Forghani, “Hierarchical
scalar and vector tetrahedra,” Digest of the
Fifth Biennial IEEE Conference on
Electromagnetic Field Computation, Aug.,
J. S. Savage and A. F. Peterson, “Higher-
order vector finite elements for tetrahedral
cells,” IEEE Trans. Microwave Theory
Tech., vol. 44, pp. 874-879, June 1996.
R. Graglia, D. R. Wilton, and A. F. Petersen.
“High order interpolatory vector bases for
computational electromagnetics,” IEEE
Transactions on Antennas and Propagation,
vol. AP-45, pp. 329-342, March 1997.
L. S. Andersen and J. L. Volakis,
“Hierarchical tangential vector finite
elements for tetrahedral,” IEEE Microwave
and Guided Wave Letters, vol. 8, pp. 127-
, no. 3, 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 Antenna and Propagation,
vol. AP-47, pp. 112-120, January 1999.
ACES JOURNAL, VOL. 18, NO. 1, MARCH 20039
J. S. Savage. “Comparing high order vector
basis functions,” Proc. Of the 14th Annual
Review of Progress in Applied
Computational Electromagnetics, Monterey,
CA, USA, pp. 524-529, March 1999.
L. S. Andersen and J. L. Volakis, “Condition
numbers for various FEM matrices,”
Journal of Electromagnetic Waves and
Applications, vol. 13, pp. 1661-1677.
December 1999.
Y. Ji and T. H. Hubing, “EMAP5: A 3D
hybrid FEM/MoM code,” Appl. Computat.
Electromagn. Soc. (ACES) J., vol. 15, pp. 1-
, March 2000.
A. F. Petersen, S. L. Ray, and R. Mittra,
Computational Methods for
Electromagnetics, New York: IEEE Press
and Oxford University Press, 1997.
J. J. H. Wang, Generalized Moment Methods
in Electromagnetics, New York: John Wiley
& Sons, 1990, ch. 6.
S. M. Rao, D. R. Wilton, and A. W. Glisson,
“Electromagnetic scattering by surfaces of
arbitrary shape,” IEEE Trans. Antennas and
Propagation, vol. AP-30, no. 3, pp. 409-
, May 1982.
Y. Ji, H. Wang, and T. H. Hubing, “A novel
preconditioning technique and comparison
of three formulations for the hybrid
FEM/MoM method,” Appl. Computat.
Electromagn. Soc. (ACES) J., vol. 15, pp.
-114, July 2000.
J. J. Bowman, T. B. A. Senior, P. L. E.
Uslenghi, Electromagnetic and acoustic
scattering by simple shapes, Hemisphere
Publishing Corporation, New York: 1987.
H. Wang, C. Guo, T. Hubing, J. Drewniak,
T. Van Doren and R. DuBroff, “Application
of higher-order FEM elements to the
analysis of microstrip structures”,
Proc. of the 2002 IEEE International
Symposium on Electromagnetic
Compatibility, Minneapolis, MN, August
, pp. 1015-1019.
J. –M. Jin, The Finite Element Method in
Electromagnetic, 2nd edition, New York:
John Wiley & Sons, 2002.
D. M. Pozar, Microwave Engineering, 2nd
edition, New York: John Wiley & Sons,
