ANDRIULLI, F

Cools, Kristof

MICHIELSSEN, E

Olyslager, Femke

English

Ghent University Academic Bibliography

A Multiplicative Calderòn Preconditioner for the Electric Field Integral Equation  Francesco P. Andriulli(1), Kristof Cools(2), Femke Olyslager(2), and Eric Michielssen(1)  (1) University of Michigan at Ann Arbor, EECS department, Ann Arbor, Michigan (2) Ghent University, INTEC department, Ghent, Belgium   Among all integral equations pertinent to the analysis of scattering from three-dimensional perfect electrically conducting surfaces, the Electric Field Integral Equation (EFIE) remains the most widely used. Unfortunately, the EFIE operator is ill-posed as its eigenvalues accumulate at zero and infinity. For this reason, the linear system matrix that results upon discretization the EFIE using the Method of Moments (MoM) is highly ill-conditioned whenever the surface mesh is dense. The need for dense surface discretizations commonly often arises when analyzing electromagnetic phenomena on structures with sub-wavelength geometric features, e.g. millimeter and microwave integrated circuits, antenna feeds and beam-forming networks, aircraft fuselage details, etc.  The recent literature abounds with techniques to precondition EFIEs by leveraging Calderòn identities (H. Contopanagos et al., IEEE Trans. Antennas Propagat., 50(12), 2002, 1824-1830, R. J. Adams and N. J. Champagne, IEEE Trans. Antennas Propagat., 52(9), 2004, 2262-2266), S. Borel, D. Levadoux, and F. Alouges, IEEE Trans. Antennas Propagat., 83(9), 2005, 2995-3004). These techniques exploit the self-regularizing property of the EFIE, i.e. the fact that the square of the EFIE operator has a bounded spectrum, thus giving rise to MoM matrices that are well-conditioned independent of the surface mesh used. Unfortunately, none of the Calderòn preconditioners introduced to date are easily integrated into existing codes. Invariably, implementation bottlenecks can be traced to the need to properly discretize the spaces in between the two EFIE operators, and the difficulty in constructing well-conditioned Gram matrices linking them.    This paper presents a multiplicative Calderòn EFIE preconditioner that is trivially integrated into existing MoM codes.  The preconditioned EFIE is obtained by multiplying two standard EFIE matrices (produced with a Rao-Wilton-Glisson code) weighted by sparse Gram and projection matrices, containing O(N) nonzero elements that are evaluated using closed-form expressions. The proposed multiplicative preconditioner leverages a recently developed set of basis functions that properly discretizes the range of the EFIE operator on a barycentric mesh (A. Buffa and S. Christiansen, Comptes rendus. Mathématique, 340(6), pp. 461-464). The multiplicative preconditioner is obtained by exploiting a simple relationship between ordinary and barycentric Rao-Wilton-Glisson basis functions to analytically map one basis set into the other.    The effectiveness of the new preconditioner in lowering the condition number of the EFIE operator and the number of iterations required for convergence, will be demonstrated.  B-85: Numerical Techniques: IE and FE Methods Thursday, July 26, 2007   •   BallroomCo-Chairs:  D. Wilton, University of Houston, USA A. Barka, Office National d'Etudes et de Recherches Aérospatiales-Toulouse, France8:30 AM  URSI468:  "Interior Green's Function for a Thick and Finite Dielectric Slab"  A. Parsa, R. Paknys, Concordia University, Canada Presenter: Armin Parsa, Concordia University, Canada8:50 AM  URSI689:  "Efficient Computation of the Ewald Representation for Periodic Green's Functions"  F.T. Celepickay1, F. Capolino2, D.R. Jackson1, D.R. Wilton1,  1University of Houston, USA, 2University of Siena, Italy Presenter: Ferhat Celepickay, University of Houston, USA9:10 AM  URSI685:  "An Investigation of the Ewald Method for Complex Waves"  V.R. Komanduri1, F. Capolino2, D.R. Jackson1, D.R. Wilton1,  1University of Houston, USA, 2University of Siena, Italy Presenter: Varada Komanduri, University of Houston, USA9:30 AM  URSI100:  "MODELING OF RAM COATED INLETS RCS WITH SUB-DOMAIN METHODS  AND HYBRID MODES"  A. Barka, J. Simon, Office National d'Etudes et de Recherches Aérospatiales-Palaiseau, France, P. Soudais, Dassault Aviation, France Presenter: Andre Barka, Office National d'Etudes et de Recherches Aérospatiales-Toulouse, France9:50 AM  URSI591:  "Hybrid Use of AWE with Spatial Matrix Interpolation in the Analysis of Printed Structures"  G. Ogucu, University of Gaziantep, Turkey Presenter: Golge  Ogucu, University of Gaziantep, Turkey10:30 AM URSI202:  "A Comparison of Several Local Error Estimators for Integral Equation Formulations"  U. Saeed, A.F. Peterson, Georgia Institute of Technology, USA Presenter: Usman Saeed, Georgia Institute of Technology, USA10:50 AM URSI357:  "Applications of the Generalized Moment Method to Augmented Integral Operators"  N.V. Nair, B.S. Shanker, Michigan State University, USA Presenter: Naveen Nair, Michigan State University, USA11:10 AM URSI695:  "A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation"  F.P. Andriulli1, K. Cools2, F. Olyslager2, E. Michielssen1,  1University of Michigan at Ann Arbor, USA, 2Ghent University, Belgium Presenter: Francesco Andriulli, University of Michigan at Ann Arbor, USA11:30 AM URSI379:  "A Generalized Moment Method Solution to Vector Electromagnetic Integral Equations"  N.V. Nair, B. Shanker, Michigan State University, USA Presenter: Naveen Nair, Michigan State University, USA11:50 AM URSI418:  "Analysis of complex structures using generalized finite element methods"  C. Lu, B. Shanker, Michigan State University, USA Presenter: Chuan Lu, Michigan State University, USA12:10 PM  URSI267:  "Dispersion Analysis of Vector Generalized Finite Element Method"  O. Tuncer, C. Lu, B. Shanker, L.C. Kempel, Michigan State University, USA Presenter: Ozgur Tuncer, Michigan State University, USANorth American Radio Science MeetingJuly 22 - 26, 2007Ottawa, Ontario, CANADAISBN:  978-0-9738425-2-4All graphics were designed and provided byCommunications Research Centre of Canada,Graphic Design ServicesCopyright © 2007 by Antem Inc.CNC / USNC

A multiplicative Calderón preconditioner for the electric field integral equation

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A multiplicative Calderón preconditioner for the electric field integral equation

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