Efficient Multilevel Compressed Block Decomposition for Large-Scale Electromagnetic Problems using Asymptotic Phasefront Extraction
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Efficient Multilevel Compressed Block Decomposition for Large-Scale Electromagnetic Problems using Asymptotic Phasefront ExtractionAbstract
A large dense complex linear system can be obtained when solving an electromagnetic scattering problem with the surface integral equation approach. To analyze the large dense complex linear system efficiently, the multilevel compressed block decomposition (MLCBD) is used to accelerate the matrix-vector multiplication operations. Although the MLCBD is efficient compared with the direct method of moments, it is still less efficient for the large-scale electromagnetic problems. Therefore, an efficient version of MLCBD is proposed in this paper. It utilizes the asymptotic phasefront extraction (APE) to reduce the exorbitant dependence on computer storage and solution time in the MLCBD for analyzing the large-scale electromagnetic problems. The numerical results demonstrate that the APE combined with MLCBD is much more efficient than conventional MLCBD for analyzing the large-scale electromagnetic scattering problems.
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References
R. F. Harrington, Field Computations by Moment
Methods, MacMillan, New York, 1968.
S. M. Rao, D. R. Wilton, and A. W. Glisson,
‘‘Electromagnetic Scattering by Surfaces of
Arbitrary Shape,’’ IEEE Trans. Antennas
Propagat., vol. AP-30, pp. 409-418, May 1982.
R. Coifman, V.Rokhlin, and S.Wandzura, “The
fast multipole methodfor the wave equation: A
pedestrian prescription,” IEEE Antennas Propag.
Mag., vol. 35, no. 6, pp. 7-12, Jun. 1993.
W. C. Chew, J. M. Jin, E. Michielssen, and J. Song,
Fast efficient algorithms in computational
electromagnetics, Boston, MA: ArtechHouse,
J. M. Rius, J. Parron, A. Heldring, J. M. Tamayo,
and E. Ubeda, “Fast iterative solution of integral
equations with method of moments and matrix
decomposition algorithm - singular value
decomposition,” IEEE Trans. Antennas Propag,
vol. 56, no. 8, pp. 2314-2324, Aug. 2008.
J. M. Rius, A. Heldring, J.M. Tamayo, and J.
Parron, “The MDA-SVD algorithm for fast direct
or iterative solution of discrete integral equations,”
Antennas Propag, EuCAP The Second European
Conference on, pp. 1-8, 2007.
M. Bebendorf and S. Rjasanow, “Adaptive
low-rank approximation of collocation matrices,”
Computing, 70, pp. 1-24, 2003.
J. Shaeffer, “Direct Solve of Electrically Large
Integral Equations for Problem Sizes to 1 M
Unknowns,” IEEE Trans. Antennas Propag, vol.
, no. 8, pp. 2306-2313, Aug. 2008.
A. Heldring, J. M. Rius, J.M. Tamayo, and J.
Parron, “Compressed Block-Decomposition
Algorithm for Fast Capacitance Extraction,”IEEE
Transactions on computer-aided design of
integrated circuits and systems, vol. 27, no. 2, pp.
-271, Feb. 2008.
A. Heldring, J. M. Rius, J.M. Tamayo, and J.
Parron, “Multilevel MDA-CBI for fast direct
solution of large scattering and radiation
problems,” Antennas and Propagation Society
International Symposium, 2007.
A. Heldring, J.M. Tamayo, J. M. Rius, J. Parron,
and E. Ubeda, “Multiscale CBD for Fast Direct
Solution of MoM Linear System,”Antennas and
Propagation Society International Symposium,
E. Michielssen and A. Boag, “A multilevel matrix
decomposition algorithm for analyzing scattering
from large structures,”IEEE Trans. Antennas
Propag, vol. 44, no. 8, pp. 1086–1093, Aug. 1996.
J. Parron, G. Junkin, andJ. M. Rius, “Improving
the performance of the multilevel matrix
decomposition algorithm for 2.5-d structures
application to metamaterials,” in Proc. Antennas
Propag. Soc. Int. Symp, pp. 2941-2944, Jul. 2006.
A. Heldring, “Full wave analysis of electrically
large reflector antenna,”Ph.D. dissertation, Dept.
Elect. Eng., Delft Univ. Technol., Delft,the
Netherlands, April 2002.
D.H. Kwon, R.J. Burkholder, and P.H. Pathak,
“Efficient method of moments formulation for
large PEC scattering problems using asymptophasefront extraction (APE),” IEEE Trans.
Antennas Propag, vol. 49, no. 4, pp. 583-591, Apr.
F. Vico, G. Vecchi,and M. Ferrando, “Asymptotic
phase extraction as a preconditioning technique for
mom,” Antennas and Propagation Society
International Symposium, 2007.
R. M. James, “A contribution to scattering
calculation for small wavelengths-the high
frequency panel method,” IEEE Trans. Antennas
Propag, vol. 38, no. 10, pp. 1625-1630, Oct. 1990.
K. R. Aberegg and A. F. Peterson, “Application of
the integral equation – asymptotic phase method to
two-dimensional scattering,” IEEE Trans.
Antennas Propag, vol. 43, no. 5, pp. 534-537, May.
T. Abboud, J.-C. Nedelec, and B. Zhou,
“Improvement of the integral equation methodfor
high frequency problems,”Third International
Conference on Mathematical Aspects of Wave
Propagation Phenomena, SIAM, 1995.
X. Shen, A. W. Davis, K. R. Aberegg, and A. F.
Peterson, “Highly parallel implementation of the
D integral equation asymptotic phase method for
electromagnetic scattering,” Applied
Computational Electromagnetics Society (ACES)
Journal, vol. 13, pp. 107-115, July 1998.
M. E. Kowalski, B. Singh, L.C. Kempel, K.D.
Trott, and J-M Jin, “Application of the Integral
Equation-Asymptotic Phase (IE-AP) Method to
Three-Dimensional Scattering,” J. Electromagnetic
Waves Appl., 15, pp. 885-900, July 2001.
Z. Altman, R. Mittra, O.Hashimoto, and E.
Michielssen, “Efficient representation of induced
currents on large scatterers using the generalized
pencil of function method,” IEEE Trans. Antennas
Propag, vol. 44, no. 1, pp. 51-57, Jan. 1996.
A. Heldring, J.M. Rius, J.M. Tamayo, J. Parron,
and E. Ubeda, “Fast direct solution of method of
moments linear system,” IEEE Trans. Antennas
Propag, vol. 55, no. 11, pp. 3220-3228, Nov. 2007.
