The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
J.c. West - One of the best experts on this subject based on the ideXlab platform.
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Preconditioned Iterative Solution of scattering from rough surfaces
IEEE Transactions on Antennas and Propagation, 2000Co-Authors: J.c. WestAbstract:Extensions to the functionally identical forward-backward (FB) and method of ordered multiple interactions Iterative techniques have been introduced that improve the convergence characteristics with specific scattering geometries. These extensions are shown to be mathematically equivalent to applying preconditioners to the discretized integral equation that is Iteratively solved. The same preconditioners can be used with any Iterative Solution technique. Numerical examples show that the generalized minimal residual (GMRES) and bi-conjugate gradient-stable (BICGSTAB) algorithms give similarly rapid convergence when applied to a preconditioned discretized integral equation.
Hao Ling - One of the best experts on this subject based on the ideXlab platform.
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An efficient wavelet preconditioner for Iterative Solution of three-dimensional electromagnetic integral equations
IEEE Transactions on Antennas and Propagation, 2003Co-Authors: Hai Deng, Hao LingAbstract:A wavelet-based preconditioning method is proposed to facilitate the Iterative Solution of three-dimensional (3-D) electromagnetic integral equations. The preconditioner is derived from the wavelet transform of the moment matrix. It is based on the observation that both the moment matrix and its inverse exhibit a sparse, multilevel finger structure. A method based on the Forbenius-norm minimization is used to solve the inverse of the matrix under the multilevel finger structure. Numerical results on a 3-D cavity show that the iteration numbers are significantly reduced with the wavelet-preconditioned system. The computational cost of the preconditioner is kept under O(NlogN).
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A wavelet-packet based preconditioner for Iterative Solution of electromagnetic integral equations
IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction, 2000Co-Authors: Hai Deng, Hao LingAbstract:It has been demonstrated that the pre-defined wavelet packet (PWP) basis is very efficient for representing the electromagnetic integral equation. We construct an effective preconditioner for moment equations from the PWP-transformed moment matrix. The preconditioning can be implemented in either the transform domain or the regular space domain. However, the computational complexity and memory requirement are at least on the order of O(N/sup 2/) to transform the moment equation from the space domain to the wavelet packet domain. Therefore, we devise a scheme to compute the PWP preconditioner directly from the PWP basis functions and implement the preconditioning operation in the space domain. Numerical results show that the PWP preconditioner is effective in accelerating the convergence rate of Iterative Solution for deep cavity structures. We also demonstrate that the total computational complexity and memory costs for the preconditioner can be kept to O(NlogN), making it compatible with fast matrix-vector multiplication algorithms such as the multi-level fast multiple method (MLFMM).
Erik Bängtsson - One of the best experts on this subject based on the ideXlab platform.
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Robust preconditioned Iterative Solution methods for large-scale nonsymmetric problems
2020Co-Authors: Erik BängtssonAbstract:We study robust, preconditioned, Iterative Solution methods for large-scale linear systems of equations, arising from different applications in geophysics and geotechnics.The first type of linear s ...
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Numerical simulations of glacial rebound using preconditioned Iterative Solution methods
Applications of Mathematics, 2005Co-Authors: Erik Bängtsson, Maya NeytchevaAbstract:This paper discusses finite element discretization and preconditioning strategies for the Iterative Solution of nonsymmetric indefinite linear algebraic systems of equations arising in modelling of glacial rebound processes. Some numerical experiments for the purely elastic model setting are provided. Comparisons of the performance of the Iterative Solution method with a direct Solution method are included as well.
David J Silvester - One of the best experts on this subject based on the ideXlab platform.
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fast Iterative Solution of stabilised stokes systems part ii using general block preconditioners
SIAM Journal on Numerical Analysis, 1994Co-Authors: David J Silvester, Andrew J WathenAbstract:Mixed finite element approximation of the classical Stokes problem describing slow viscous incompressible flow gives rise to symmetric indefinite systems for the discrete velocity and pressure variables. Iterative Solution of such indefinite systems is feasible and is an attractive approach for large problems. Part I of this work described a conjugate gradient-like method (the method of preconditioned conjugate residuals) which is applicable to symmetric indefinite problems [A. J. Wathen and D. J. Silvester, SIAM J. Numer. Anal., 30 (1993), pp. 630–649]. Using simple arguments, estimates for the eigenvalue distribution of the discrete Stokes operator on which the convergence rate of the iteration depends are easily derived. Part I discussed the important case of diagonal preconditioning (scaling). This paper considers the more general class of block preconditioners, where the partitioning into blocks corresponds to the natural partitioning into the velocity and pressure variables. It is shown that, provid...
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fast Iterative Solution of stabilised stokes systems part i using simple diagonal preconditioners
SIAM Journal on Numerical Analysis, 1993Co-Authors: Andrew J Wathen, David J SilvesterAbstract:Mixed finite element approximation of the classical Stokes problem describing slow viscous incompressible flow gives rise to symmetric indefinite systems for the discrete velocity and pressure variables. Iterative Solution of such indefinite systems is feasible and is an attractive approach for large problems. The use of stabilisation methods for convenient (but unstable) mixed elements introduces stabilisation parameters. We show how these can be chosen to obtain rapid Iterative convergence. We propose a conjugate gradient-like method (the method of preconditioned conjugate residuals) which is applicable to symmetric indefinite problems, describe the effects of stabilisation on the algebraic structure of the discrete Stokes operator and derive estimates of the eigenvalue spectrum of this operator on which the convergence rate of the iteration depends. Here we discuss the simple case of diagonal preconditioning. Our results apply to both locally and globally stabilised mixed elements as well as to elements which are inherently stable. We demonstrate that convergence rates comparable to that achieved using the diagonally scaled conjugate gradient method applied to the discrete Laplacian are approachable for the Stokes problem.
Hai Deng - One of the best experts on this subject based on the ideXlab platform.
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An efficient wavelet preconditioner for Iterative Solution of three-dimensional electromagnetic integral equations
IEEE Transactions on Antennas and Propagation, 2003Co-Authors: Hai Deng, Hao LingAbstract:A wavelet-based preconditioning method is proposed to facilitate the Iterative Solution of three-dimensional (3-D) electromagnetic integral equations. The preconditioner is derived from the wavelet transform of the moment matrix. It is based on the observation that both the moment matrix and its inverse exhibit a sparse, multilevel finger structure. A method based on the Forbenius-norm minimization is used to solve the inverse of the matrix under the multilevel finger structure. Numerical results on a 3-D cavity show that the iteration numbers are significantly reduced with the wavelet-preconditioned system. The computational cost of the preconditioner is kept under O(NlogN).
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A wavelet-packet based preconditioner for Iterative Solution of electromagnetic integral equations
IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction, 2000Co-Authors: Hai Deng, Hao LingAbstract:It has been demonstrated that the pre-defined wavelet packet (PWP) basis is very efficient for representing the electromagnetic integral equation. We construct an effective preconditioner for moment equations from the PWP-transformed moment matrix. The preconditioning can be implemented in either the transform domain or the regular space domain. However, the computational complexity and memory requirement are at least on the order of O(N/sup 2/) to transform the moment equation from the space domain to the wavelet packet domain. Therefore, we devise a scheme to compute the PWP preconditioner directly from the PWP basis functions and implement the preconditioning operation in the space domain. Numerical results show that the PWP preconditioner is effective in accelerating the convergence rate of Iterative Solution for deep cavity structures. We also demonstrate that the total computational complexity and memory costs for the preconditioner can be kept to O(NlogN), making it compatible with fast matrix-vector multiplication algorithms such as the multi-level fast multiple method (MLFMM).
