200
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics

, &
Pages 1211-1223 | Received 23 Jan 2007, Accepted 02 Mar 2007, Published online: 28 Aug 2007

References

  • Lu , C. C. and Chew , W. C. 2000 . A coupled surface-volume integral equation approach for the calculation of electromagnetic scattering from composite metallic and material targets . IEEE Transactions on Antennas and Propagation , 48 ( 12 ) : 1866 – 1868 .
  • Kolundzija , B. M. 1999 . Electromagnetic modeling of composite metallic and dielectric structures . IEEE Transactions on Microwave Theory and Techniques , 47 ( 7 ) : 1021 – 1032 .
  • Vaupel , T. and Hansen , V. 1999 . Electrodynamic analysis of combined microstrip and coplanar/solution structure with 3-D components based on a surface/volume integral equation approach . IEEE Transactions on Microwave Theory and Techniques , 47 ( 9 ) : 1788 – 1800 .
  • Wang , C. F. and Jin , J. M. 1998 . A fast full-wave analysis of scattering and radiation from large finite arrays of microstrip antennas . IEEE Transactions on Antennas and Propagation , 46 ( 10 ) : 1467 – 1474 .
  • Rao , S. M. , Wilton , D. R. and Glisson , A. W. 1982 . Electromagnetic scattering by surface of arbitrary shape . IEEE Transactions on Antennas and Propagation , AP-30 ( 3 ) : 409 – 418 .
  • Vorobyev , Y. V. 1965 . Method of Moments in Applied Mathematics , New York : Gordon & Breach Science .
  • Carpentieri , B. , Duff , I. S. and Giraud , L. 2001 . Experiments with sparse preconditioning of dense problems from electromagnetic applications . Technical Report TR/PA/00/04, CERFACS, Toulouse, France
  • Carpentieri , B. , Duff , I. S. , Giraud , L. and Sylvand , G. An embedded iterative scheme in electromagnetism . Proceedings of the Fifth International Conference on Parallel Processing and Applied Mathematics . Czestochowa, (Poland). Vol. 3019 , pp. 977 – 984 .
  • Carpentieri , B. , Duff , I. S. , Giraud , L. and Magolu monga Made , M. 2004 . Sparse symmetric preconditioners for dense linear systems in electromagnetism . Numerical Linear Algebra with Applications , 11 : 753 – 771 .
  • Carpentieri , B. , Duff , I. S. , Giraud , L. and Sylvand , G. 2005 . Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations . SIAM Journal on Scientific Computing , 27 ( 3 ) : 774 – 792 .
  • Axelsson , O. 1994 . Iterative Solution Methods , Cambridge : Cambridge University Press .
  • Coifman , R. , Rokhlin , V. and Wandzura , S. 1993 . The fast multipole method for the wave equation: a pedestrian prescription . IEEE Antenna and Propagation Magazine , 35 ( 3 ) : 7 – 12 .
  • Rokhlin , V. 1990 . Rapid solution of integral equations of scattering theory in two dimensions . Journal of Computational Physics , 86 ( 2 ) : 414 – 439 .
  • Chew , W. C. , Jin , J. M. , Michielssen , E. and Song , J. M. 2001 . Fast and Efficient Algorithms in Computational Electromagnetics , Boston : Artech House .
  • Lu , C. C. and Chew , W. C. 1994 . A multilevel algorithm for solving a boundary integral equation of wave scattering . IEEE Transactions on Microwave and Optical Technology Letters , 7 ( 10 ) : 466 – 470 .
  • Song , J. M. and Chew , W. C. 1995 . Multilevel fast multipole algorithm for solving combined field integral equation of electromagnetic scattering . IEEE Transactions on Microwave and Optical Technology Letters , 10 ( 1 ) : 14 – 19 .
  • Song , J. M. , Lu , C. C. and Chew , W. C. 1997 . Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects . IEEE Transactions on Antennas and Propagation , AP-45 ( 10 ) : 1488 – 1493 .
  • Varga , R. S. 1960 . “ Factorization and normalized iterative methods ” . In Boundary Problems in Differential Equations , Edited by: Langer , R. E. 121 – 124 . Madison : University of Wisconsin Press .
  • Wachspress , E. 1966 . Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics , Englewood Cliffs : Prentice-Hall .
  • Saad , Y. 1996 . Iterative Methods for Sparse Linear Systems , New York : PWS Publishing .
  • Benzi , M. 2002 . Preconditioning techniques for large linear systems: A survey . Journal of Computational Physics , 182 : 418 – 477 .
  • Chan , T. F. and Chen , K. 2002 . On two variants of an algebraic wavelet preconditioner . SIAM Journal on Scientific Computing , 24 : 260 – 283 .
  • Chen , K. 1998 . On a class of preconditioning methods for dense linear systems from boundary elements . SIAM Journal on Scientific Computing , 20 : 684 – 698 .
  • Lee , J. , Zhang , J. and Lu , C. C. 2004 . Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics . IEEE Transactions on Antennas and Propagation , 52 ( 9 ) : 2277 – 2287 .
  • Lee , J. , Zhang , J. and Lu , C. C. 2003 . Performance of preconditioned Krylov iterative methods for solving hybrid integral equations in electromagnetics . Journal of Applied Computational Electromagnetics Society , 18 ( 4 ) : 54 – 61 .
  • Bunse-Gerstner , A. and Gutiérrez-Cańas , I. 2006 . A preconditioned GMRES for complex dense linear systems from electromagnetic wave scattering problems . Linear Algebra and its Applications , 416 : 135 – 147 .
  • Deng , H. and Ling , H. 2002 . An efficient preconditioner for electromagnetic integral equations using predefined wavelet packet basis . IEEE Transactions on Antennas and Propagation , 50 ( 11 ) : 1633 – 1640 .
  • Deng , H. and Ling , H. 2003 . An efficient wavelet preconditioner for iterative solution of three-dimensional electromagnetic integral equations . IEEE Transactions on Antennas and Propagation , 51 ( 3 ) : 654 – 660 .
  • Antoine , X. and Boubendir , Y. 2008 . An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations. To appear in . International Journal of Computer Mathematics ,
  • Leem , K. H. and Pelekanos , G. 2006 . Algebraic multigrid preconditioner for homogeneous scatterers in electromagnetics . IEEE Transactions on Antennas and Propagation , 54 ( 7 ) : 2081 – 2087 .
  • Carpentieri , B. 2006 . A matrix-free two-grid preconditioner for solving boundary integral equations in electromagnetism . Computing , 77 ( 3 ) : 275 – 296 .
  • Antoine , X. , Bendali , A. and Darbas , M. 2005 . Analytic preconditioners for the boundary integral solution of the scattering of acoustic waves by open surfaces . Journal of Computational Acoustics , 13 ( 3 ) : 477 – 498 .
  • Ford , J. M. , Chen , K. and Evans , D. 2003 . On a recursive Schur preconditioner for iterative solution of a class of dense matrix problems . International Journal of Computer Mathematics , 80 ( 1 ) : 105 – 122 .
  • Guo , C. and Hubing , T. H. 2005 . Effective preconditioners for the solution of hybrid FEM/MoM matrix equations using combined formulations . Journal of Applied Computational Electromagnetics Society , 20 ( 2 ) : 96 – 106 .
  • Duff , I. S. , Giraud , L. and Langou , J. 2005 . Using spectral low rank preconditioners for large electromagnetic calculations . International Journal for Numerical Methods in Engineering , 62 ( 3 ) : 416 – 434 .
  • Liu , J. and Jin , J. M. 2002 . A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering . IEEE Transactions Antennas and Propagation , 50 ( 9 ) : 1212 – 1221 .
  • von Hagen , J. and Wiesbeck , W. 2002 . Physics-based preconditioner for iterative algorithms in MoM-problems . IEEE Transactions Antennas and Propagation , 50 ( 9 ) : 1315 – 1316 .
  • Ashby , S. F. , Manteuffel , T. A. and Saylor , P. E. 1989 . Adaptive polynomial preconditioning for hermitian indefinite linear system . BIT , 29 : 583 – 609 .
  • Johnson , O. G. , Micchelli , C. A. and Paul , G. 1983 . Polynomial preconditioning for conjugate gradient calculations . SIAM Journal on Numerical Analysis , 20 : 362 – 376 .
  • Meijerink , J. A. and van der Vorst , H. A. 1977 . An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix . Mathematics of Computation , 31 : 148 – 162 .
  • Benson , M. W. 1973 . Iterative Solution of Large Linear Systems Ontario MSc Thesis, Lakehead University, Thunder Bay
  • Benson , M. W. and Frederickson , P. O. 1982 . Iterative solution of large sparse linear system arising in certain multidimensional approximation problem . Utilitas Mathematica , 22 : 127 – 140 .
  • Alléon , G. , Benzi , M. and Giraud , L. 1997 . Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics . Numerical Algorithms , 16 : 1 – 15 .
  • Carpentieri , B. , Duff , I. S. and Giraud , L. 2000 . Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism . Numerical Linear Algebra with Applications , 7 ( 7–8 ) : 667 – 685 .
  • Manteuffel , T. A. 1980 . An incomplete factorization technique for positive definite linear systems . Mathematics of Computation , 34 ( 150 ) : 473 – 497 .
  • Robert , Y. 1982 . Regular incomplete factorizations of real positive definite matrices . Linear Algebra and its Applications , 48 : 105 – 117 .
  • Varga , R. S. , Saff , E. B. and Mehrmann , V. 1980 . Incomplete factorizations of matrices and connections with H-matrices . SIAM Journal on Numerical Analysis , 17 ( 6 ) : 787 – 793 .
  • Chow , E. and Saad , Y. 1997 . Experimental study of ILU preconditioners for indefinite matrices . Journal of Computational and Applied Mathematics , 86 : 387 – 414 .
  • Magolu monga Made , M. 2001 . Incomplete factorization based preconditionings for solving the Helmholtz equation . International Journal for Numerical Methods in Engineering , 50 : 1077 – 1101 .
  • Magolu monga Made , M. , Beauwens , R. and Warzee , G. 2000 . Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix . Communications in Numerical Methods in Engineering , 16 : 801 – 817 .
  • Carpentieri , B. , Duff , I. S. and Giraud , L. 2003 . A class of spectral two-level preconditioners . SIAM Journal on Scientific Computing , 25 ( 2 ) : 749 – 765 .
  • Heldring , A. , Rius , J. M. and Ligthart , L. 2002 . New block ILU preconditioner scheme for numerical analysis of very large electromagnetic problems . IEEE Transactions on Magnetics , 38 ( 2 ) : 337 – 340 .
  • Sertel , K. and Volakis , J. L. 2000 . Incomplete LU preconditioner for FMM implementation . IEEE Transactions on Microwave and Optical Technology Letters , 26 ( 7 ) : 265 – 267 .
  • Lee , J. , Zhang , J. and Lu , C. C. 2003 . Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems . Journal of Computational Physics , 185 : 158 – 175 .
  • D'Azevedo , E. F. , Forsyth , F. A. and Tang , W. P. 1990 . Towards a cost effective ILU preconditioner with high level fill . BIT , 32 ( 3 ) : 442 – 463 .
  • Saad , Y. 1994 . ILUT: a dual threshold incomplete LU factorization . Numerical Linear Algebra with Applications , 1 ( 4 ) : 387 – 402 .
  • Watts , J. W. III . 1981 . A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation . Society of Petroleum Engineers Journal , 21 : 345 – 353 .
  • Frederickson , P. O. 1975 . Fast approximate inversion of large sparse linear systems, Math. Report 7, Lakehead University, Thunder Bay, Ontario .
  • Chow , E. 2000 . A priori sparsity patterns for parallel sparse approximate inverse preconditioners . SIAM Journal on Scientific Computing , 21 ( 5 ) : 1804 – 1822 .
  • Grote , M. and Huckle , T. 1997 . Parallel preconditioning with sparse approximate inverse . SIAM Journal on Scientific Computing , 18 : 838 – 853 .
  • Wang , K. , Kim , S. and Zhang , J. 2003 . A comparative study on dynamic and static sparsity patterns in parallel sparse approximate inverse preconditioning . Journal of Mathematical Modelling and Algorithms , 3 ( 2 ) : 203 – 215 .
  • Kolotilina , L. Y. 1988 . Explicit preconditioning of systems of linear algebraic equations with dense matrices . Journal of Mathematical Sciences , 43 ( 4 ) : 2566 – 2573 .
  • Vavasis , S. A. 1992 . Preconditioning for boundary integral equations . SIAM Journal on Matrix Analysis and Applications , 13 ( 3 ) : 905 – 925 .
  • Helsing , J. 2006 . Approximate inverse preconditioners for some large dense random electrostatic interaction matrices . BIT , 46 ( 2 ) : 307 – 323 .
  • Benzi , M. and Tuma , M. 1998 . A sparse approximate inverse preconditioner for nonsymmetric linear systems . SIAM Journal on Scientific Computing , 19 : 968 – 994 .
  • Luo , J.-G. 1993 . An incomplete inverse as a preconditioner for the conjugate gradient method . Computers & Mathematics with Applications , 25 ( 2 ) : 73 – 79 .
  • Zhang , J. 2002 . A sparse approximate inverse technique for parallel preconditioning of general sparse matrices . Applied Mathematics and Computation , 130 ( 1 ) : 63 – 85 .
  • Kolotilina , L. Y. and Yeremin , A. Y. 1993 . Factorized sparse approximate inverse preconditioning I: theory . SIAM Journal on Matrix Analysis and Applications , 14 : 45 – 58 .
  • Kolotilina , L. Y. and Yeremin , A. Y. 1995 . Factorized sparse approximate inverse preconditioning II: solution of 3D FE systems on massively parallel computers . International Journal of High Speed Computing , 7 : 191 – 215 .
  • Wang , Y. , Lee , J. , Zhang , J. and Lu , C. C. SVD stabilized block preconditioning for large dense linear systems from electromagnetic application . Abstracts of the 8th IMACS International Symposium on Iterative Methods in Scientific Computing . College Station, TX.
  • De Backer , B. , Knockaert , L. and de Zutter , D. 1998 . A singular value-based preconditioner for large scattering problems . IEEE Antennas and Propagation Society Int. Symposium , 3 : 1534 – 1537 .
  • Golub , G. H. and van Loan , C. F. 1996 . Matrix Computations, , 3rd , Baltimore : Johns Hopkins .
  • Zhang , J. 2000 . Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications . Computer Methods in Applied Mechanics and Engineering , 189 ( 3 ) : 825 – 840 .
  • Brand , C. W. 1992 . An incomplete factorization preconditioning using repeated red/black ordering . Numerische Mathematik , 61 : 433 – 454 .
  • Saad , Y. and Zhang , J. 1999 . BILUTM: A domain-based multilevel block ILUT preconditioner for general sparse matrices . SIAM Journal on Matrix Analysis and Applications , 21 : 279 – 299 .
  • Zhang , J. 2000 . Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices . Applied Numerical Mathematics , 35 : 67 – 86 .
  • Lee , J. , Zhang , J. and Lu , C. C. Two-level preconditioning for electromagnetic scattering from composite conducting and dielectric objects . Abstracts of the 8th Copper Mountain Conference on Iterative Methods . Copper Mountain, CO.
  • Ford , J. and Chen , K. 2001 . Wavelet-based preconditioners for dense matrices with non-smooth local features . BIT , 41 ( 2 ) : 282 – 307 .
  • Ford , J. M. 2003 . An improved discrete wavelet transform preconditioner for dense matrix problems . SIAM Journal on Matrix Analysis and Applications , 25 ( 3 ) : 642 – 661 .
  • Hawkins , S. C. and Chen , K. 2004 . New wavelet preconditioner for solving boundary integral equations over nonsmooth boundaries . International Journal of Computer Mathematics , 81 ( 2 ) : 353 – 360 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.