Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems

Lee, Jeong-Hwa; Zhang, Jun; Lu, Cai‐Cheng

doi:10.1016/s0021-9991(02)00052-9

Cited by 136 publications

(104 citation statements)

References 23 publications

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“…This threshold is defined by the parameter drop-tolerance (drop-tol). ILU-based preconditioning techniques [6], [7] are widely used and become normally more efficient than the approximate inverse preconditioners (AIPC) [3], which are based on the more time-consuming minimization of the Frobenius-norm of the residual matrix I 0 ZP . Recently, Eibert [8] has proposed a preconditioning scheme that implicitly accounts for inv(M ) through an approximate iterative search of P nested in the GMRES-search of the solution.…”

Section: Theorymentioning

confidence: 99%

Preconditioning Techniques in the Analysis of Finite Metamaterial Slabs

Úbeda

Rius

Romeu

2006

IEEE Trans. Antennas Propagat.

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Abstract-In the method of moments (MoM) electric field integral equation (EFIE) analysis of slabs of metamaterials, we show that a left-preconditioning scheme by blocks gathering interactions between basis functions belonging to each basic cell of the metamaterial reaches convergence in less iterations and with less computational time than a left-preconditioner based on discarding interactions between basis functions beyond a given distance.Index Terms-Electromagnetic scattering, method of moments (MoM), numerical analysis, preconditioning.

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Section: Theorymentioning

confidence: 99%

Preconditioning Techniques in the Analysis of Finite Metamaterial Slabs

Úbeda

Rius

Romeu

2006

IEEE Trans. Antennas Propagat.

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“…Despite the simplicity of this approach there are enhancements that offer improved performance [36]. The Incomplete LU preconditioner, in turn, is another popular approach based on the approximate LU factorization of Z n and the use of those factors to perform the operation indicated in (3) [37]. A simple implementation of this preconditioner is denoted as ILU (0), in which the same sparsity pattern as [Z n ] is enforced.…”

Section: Solution Of the Mom Equationmentioning

confidence: 99%

“…This expression allows good parallelization properties of the SAI preconditioners, since given a number of computing nodes the parallelization process will consist on assigning small and independent LLS problems to each node and gather the results to assemble the preconditioning matrix [M ]. The ILU preconditioners are typically more difficult to parallelize due to the more sequential nature of the algorithm involved, although parallel implementation details can also be found in the literature [37]. For a given amount of memory (determined by the sparsity pattern) the ILU-based preconditioning approaches typically present faster convergence [40].…”

Section: Solution Of the Mom Equationmentioning

confidence: 99%

AN OVERVIEW OF THE EVOLUTION OF METHOD OF MOMENTS TECHNIQUES IN MODERN EM SIMULATORS (Invited Paper)

Delgado¹,

García²,

Moreno³

et al. 2015

PIER

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Abstract-This paper presents an evolution of the challenges and solutions found in the application of techniques based on the Method of Moments until the present day. The original MoM presented very high computational restrictions that have motivated the development of more efficient approaches. The main features of these newer improvements are presented, as well as other technical details regarding preconditioning and parallelization techniques. Some representative examples are shown in order to assert the suitability of these approaches for the analysis of complex and realistic scenarios.

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“…For ill-conditioned EFIE matrices, however, ILUT (i.e., threshold-based ILU) with pivoting [19] is required to prevent the potential instability. Other successful adoptions of the ILU preconditioners are presented by Lee et al [20]. Despite the remarkable success of the ILU preconditioners, they are limited to sequential implementations due to difficulties in parallelizing their factorization algorithms and forward-backward solutions.…”

Section: Preconditioners Built From Near-field Matricesmentioning

confidence: 99%

Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

Ergül¹,

Malas²,

Gürel³

2010

PIER

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Abstract-We present an iterative inner-outer scheme for the efficient solution of large-scale electromagnetics problems involving perfectlyconducting objects formulated with surface integral equations. Problems are solved by employing the multilevel fast multipole algorithm (MLFMA) on parallel computer systems.In order to construct a robust preconditioner, we develop an approximate MLFMA (AMLFMA) by systematically increasing the efficiency of the ordinary MLFMA. Using a flexible outer solver, iterative MLFMA solutions are accelerated via an inner iterative solver, employing AMLFMA and serving as a preconditioner to the outer solver. The resulting implementation is tested on various electromagnetics problems involving both open and closed conductors. We show that the processing time decreases significantly using the proposed method, compared to the solutions obtained with conventional preconditioners in the literature.

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Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems

Cited by 136 publications

References 23 publications

Preconditioning Techniques in the Analysis of Finite Metamaterial Slabs

Preconditioning Techniques in the Analysis of Finite Metamaterial Slabs

AN OVERVIEW OF THE EVOLUTION OF METHOD OF MOMENTS TECHNIQUES IN MODERN EM SIMULATORS (Invited Paper)

Solutions of Large-Scale Electromagnetics Problems Using an Iterative Inner-Outer Scheme With Ordinary and Approximate Multilevel Fast Multipole Algorithms

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