Application of the Characteristic Basis Function Method for the Electromagnetic Analysis of Electrically Large and Complex Bodies
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Application of the Characteristic Basis Function Method for the Electromagnetic Analysis of Electrically Large and Complex BodiesAbstract
An overview of a parallel implementation of the Characteristic Basis Function Method combined with the Multilevel Fast Multipole Algorithm is presented. This approach allows an accurate analysis of very large electromagnetic problems. The geometry is described by means of Non-Uniform Rational BSplines, and the macro-basis functions are expressed in terms of subsectional functions totally conformed to the original geometry. A number of representative examples are considered in order to show the performance of the proposed approach.
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G. T. Ruck, D. E. Barrick, W. D. Stuart, and
C. K. Krichbaum, Radar Cross Section
Handbook, Vol. 1, Plenum Press, 1970.
D. A. McNamara, C. W. I. Pistorius and J.
A. G. Maherbe, Introduction to the Uniform
Geometric Theory of Diffraction , Norwood,
MA: Artech House, 1990.
U. Jakobus and F.M. Landstorfer:
“Improved PO-MM hybrid formulation
for scattering from three-dimensional
perfectly conducting bodies of arbitrary
shape”, IEEE Trans. Antennas Propagat.,
vol. 43, pp. 162-169, Feb. 1995.
G. A. Thiele and G. A. Newhouse, “A
Hybrid Technique for Combining Moment
Methods with the Geometrical Theory of
Diffraction”, IEEE Trans. Antennas
Propagat., vol. 23, pp. 551-558, July 1975.
W. D. Burnside, C. L. Yu, and R.J.
Marhefka: “A technique to combine the
geometrical theory of diffraction and the
moment method”, IEEE Trans. Antennas
Propagat., AP-23, pp. 551-558, July 1975.
E. P. Ekelman and G. A. Thiele: “A hybrid
technique for combining the moment method
treatment of wire antennas with the GTD for
curved surfaces”, IEEE Trans. Antennas
Propagat., AP-28, pp. 831-839, November
W. Gropp, E. Lusk, and A. Skjellum, Using
MPI, MIT Press, October 1994.
R. F. Harrington, Field Computation by
Moment Methods , New York, McMillan,
N. Engheta, W. D. Murphy, V. Rokhlin, and
M. S. Vassiliou, “The Fast Multipole
Method (FMM) for Electromagnetic
Scattering Problems”, IEEE Trans. Antennas
Propagat., vol. 40, no. 6, pp. 634-641, June
W. C. Chew, J. Jin, E. Michielssen, and J.
Song, Fast and Efficient Algorithms in
Computational Electromagnetics , Artech
House Inc., 2001.
A. Boag and R. Mittra, “Complex multipole
beam approach to electromagnetic scattering
problems,” IEEE Trans. Antennas
Propagat., vol. 42, pp. 366-372, Mar. 1994.
F. X. Canning, “The Impedance Matrix
Localization (IML) Method for Moment-
Method Calculations”, IEEE Anntenas
Propagat. Mag., vol. 32, no. 5, pp. 18-30,
Oct 1990.
E. Bleszynski, M. Bleszynski, and T.
Jaroszewicz, "AIM: Adaptative Integral
Method for Solving Large Scale
Electromagnetic Scattering and Radiation
Problems", Radio sci ., vol. 31, no.5, pp.
-1251, 1996.
Gene H. Golub and Charles van Loan,
Matrix Computations, Johns Hopkins
University Press, 1989.
R.J. Burkholder and J.F. Lee, “Fast Dual-
MGS Block-Factorization Algorithm for
Dense MoM Matrices”, IEEE Trans.
Antennas Propagat., Vol-52, NO. 7, pp.
-1699, July 2004.
M. Bebendorf, “Approximation of boundary
element matrices”, Numer. Math ., vol. 86,
no. 4, pp. 565–589, 2000.
K. Zhao, M. Vouvakis, and J. F. Lee, “The
adaptive cross approximation algorithm for
accelerated method of moment computations
of EMC problems”, IEEE Trans. Electro.
Comp., vol. 47, no. 4, pp. 763–773, Nov.
E. Michielssen and A. Boag, “A multilevel
matrix decomposition algorithm for
analyzing scattering from large structures”,
IEEE Trans. Electro. Comp. , vol. 44, no. 8,
pp. 1086–1093, Aug. 1996.
L. Matekovits, V. A. Laza, and G. Vecchi,
“Analysis of Large Complex Structures With
the Synthetic-Functions Approach”, IEEE
Trans. Antennas Propagat., vol. 55, no. 9,
pp. 2509-2521, September 2007.
V. V. S. Prakash and R. Mittra,
“Characteristic Basis Function Method: A
New Technique for Efficient Solution of
Method of Moments Matrix Equation”,
Micro. Opt. Tech. Lett., vol. 36, no. 2, pp.
-100, Jan. 2003.
S. M. Rao, D. R. Wilton, and A. W. Glisson,
“Electromagnetic scattering by surfaces of
arbitrary shape”, IEEE Trans. Antennas
Propagat., vol. 30, pp. 409-412, May 1982.
A. W. Glisson and D. R. Wilton, “Simple
and Efficient Numerical Methods for
Problems of Electromagnetic Radiation and
DELGADO, GARCÍA, CÁTEDRA, MITTRA: APPLICATION OF CHARACTERISTIC BASIS FUNCTION METHOD
Scattering from Surfaces”, IEEE Trans.
Antennas Propagat., vol. 28, no. 5, pp. 593-
, Sept. 1980.
E. García , C. Delgado, I. González , and F.
Cátedra, “An iterative solution for
electrically large problems combining the
Characteristic Basis Function Method and
the Multilevel Fast Multipole Algorithm”,
IEEE Trans. Antennas Propagat., accepted
for publication.
G. Farin, Curves and Surfaces for Computer
Aided Geometric Design: A Practical Guide ,
Boston, Academic Press, 1998.
E. Lucente , A. Monorchio, and R. Mittra,
“An Iteration-Free MoM Approach Based on
Excitation Independent Characteristic Basis
Functions for Solving Large Multiscale
Electromagnetic Scattering Problems”, IEEE
Trans. Antennas Propagat., vol. 56, no. 4,
pp. 999-1007, April 2008.
C. Delgado, R. Mittra, and F Cátedra,
“Accurate Representation of the Edge
Behavior of Current when Using PO-
Derived Characteristic Basis Functions”,
IEEE Antennas and Wireless Propagat.
Lett., vol. 7, pp. 43-45, March 2008.
G. Tiberi, M. Degiorgi, A. Monorchio, G.
Manara, and R. Mittra, “A Class of Physical
Optics-SVD Derived Basis Functions for
Solving Electromagnetic Scattering
Problems”, Antennas and Propagation
Society Int. Symposium, Washington D.C,
USA, July 2005.
C. Delgado, F. Cátedra, and R. Mittra:
“Application of the Characteristic Basis
Function Method Utilizing a Class of Basis
and Testing Functions Defined on NURBS
Patches”, IEEE Trans. Antennas Propagat.,
vol. 56, no. 3, pp. 784-791, March 2008.
L. Valle, F. Rivas, and M. F. Cátedra,
“Combining the Moment Method with
Geometrical Modelling by NURBS Surfaces
and Bézier Patches”, IEEE Trans. Antennas
Propagat., vol. 42, no. 3, pp 373-381, March
M. F. Cátedra, F. Rivas, and L. Valle: “A
Moment Method Approach Using Frequency
Independent Parametric Meshes”, IEEE
Trans. Antennas Propagat., vol. 45, no. 10,
pp. 1567-1568, October 1997.
J. Liu and J. Jin, “Scattering Analysis of a
Large Body with Deep Cavities”, IEEE
Trans. Antennas Propagat, Vol. AP-51,
Issue 5, pp 1157-1167, June 2003.
A. K. Dominek, H. Shamanski, R. Wood,
and R. Barger, "A Useful Test Body", in
Proceedings Antenna Measurement
Techniques Association , September 24,
Özgür Ergül and Levent Gürel, “Efficient
Parallelization of Multilevel Fast Multipole
Algorithm”. Proceedings of the European
Conference on Antennas and Propagation:
EuCAP 2006. Nice, France, November 2006.
P. S. Pacheco, Parallel Programing with
MPI, Morgan Kaufmann Publishers Inc.,
W. C. Chew, J. Jin, E. Michielssen, and J.
Song, Fast and Efficient Algorithms in
Computational Electromagnetics , Artech
House Inc., 2001.
E. García, C. Delgado, I. González, and F.
Cátedra “A Parallel CBFM-MLFMA
Implementation for the Analysis of Complex
Problems” ACES 2008 Meeting, April 2008.
