Geometry Based Preconditioner for Radiation Problems Involving Wire and Surface Basis Functions

Araújo, M. G.; Bertolo, J. M.; Obelleiro, F.; Rodríguez, J.L.; Taboada, J. M.; Landesa, L.

doi:10.2528/pier09042104

Cited by 6 publications

(5 citation statements)

References 20 publications

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“…Occasionally, some eigenvalues suddenly changes their sign (see later). Although the MoM code is based on the Galerkin testing procedure, the Z-matrix is not purely symmetrical [17]. As a result, some eigenvalues have unphysical imaginary parts which should be cut off.…”

Section: Eigenvaluesmentioning

confidence: 99%

A Method for Tracking Characteristic Numbers and Vectors

Čapek¹,

Hazdra²,

Hamouz³

et al. 2011

PIER B

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Abstract-A new method for tracking characteristic numbers and vectors appearing in the Characteristic Mode Theory is presented in this paper. The challenge here is that the spectral decomposition of the moment impedance-matrix doesn't always produce well ordered eigenmodes. This issue is addressed particularly to finite numerical accuracy and slight nonsymmetry of the frequencydependent matrix. At specific frequencies, the decomposition problem might be ill-posed and non-uniquely defined as well. Hence an advanced tracking procedure has been developed to deal with noisy modes, non-continuous behavior of eigenvalues, mode swapping etc. Proposed method has been successfully implemented into our in-house Characteristic Mode software tool for the design of microstrip patch antennas and tested for some interesting examples.

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Section: Eigenvaluesmentioning

confidence: 99%

A Method for Tracking Characteristic Numbers and Vectors

Čapek¹,

Hazdra²,

Hamouz³

et al. 2011

PIER B

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“…Geometric preconditioners exploit additional information specific to the geometry of the underlying problem and can be more special-purpose. For example, it is reported that scaling with the edge lengths of RWG bases [23] is effective in the case of three-dimensional (3D) Maxwell equations [24].…”

Section: Introductionmentioning

confidence: 99%

Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method

Takahashi

Coulier

Darve

2017

Journal of Computational Physics

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We investigate an efficient preconditioning of iterative methods (such as GMRES) for solving dense linear systems Ax = b that follow from a boundary element method (BEM) for the 3D Helmholtz equation, focusing on the low-frequency regime. While matrix-vector products in GMRES can be accelerated through the low-frequency fast multipole method (LFFMM), the BEM often remains computationally expensive due to the large number of GMRES iterations. We propose the application of the inverse fast multipole method (IFMM) as a preconditioner to accelerate the convergence of GMRES. The IFMM is in essence an approximate direct solver that uses a multilevel hierarchical decomposition and low-rank approximations. The proposed IFMM-based preconditioning has a tunable parameter ε that balances the cost to construct a preconditioner M, which is an approximation of A −1 , and the cost to perform the iterative process by means of M. Namely, using a small (respectively, large) value of ε takes a long (respectively, short) time to construct M, while the number of iterations can be small (respectively, large). A comprehensive set of numerical examples involving various boundary value problems with complicated geometries and mixed boundary conditions is presented to validate the efficiency of the proposed method. We show that the IFMM preconditioner (with a nearly optimal ε of 10 −2) clearly outperforms some common preconditioners for the BEM, achieving 1.2-10.8 times speed-up of the computations, in particular when the scale of the underlying scatterer is about five wavelengths or more. In addition, the IFMM preconditioner is capable of solving complicated problems (in a reasonable amount of time) that BD preconditioner can not.

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“…Solving (1) by using MoM, the whole structure is discretized into small segments/triangles. J W and J S are then expanded by using the RWG basic functions defined on each pair of segments/triangles [13][14][15]. In this way, by using Galerkin testing method, we can obtain the following linear equations…”

Section: Modeling Of the Transceiversmentioning

confidence: 99%

An Efficient Hybrid Technique for Analysis of the Electromagnetic Field Distribution Inside a Closed Environment

Bui¹,

Wei²,

Li³

et al. 2011

PIER

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Abstract-This paper presents an efficient hybrid simulation technique for analysis of the electromagnetic field interactions between multi-transmitters and receivers located within a closed environment. The Method of Moments/circuit method is first used for modeling of the transceivers and their nearby surrounding to obtain the equivalent sources/receivers. Then, an approach that combines the asymptotic method and the ray tracing technique is deployed to calculate the long-distance coupling between a pair of transmitter and receiver. The acceleration algorithms for ray tracing have been developed to deal with more complex scenarios. The seamless combination between the circuit, numerical, and asymptotic approaches is the key to get accurate simulation results. Several numerical examples and experimental results are presented to demonstrate the efficiency of the proposed technique.

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Geometry Based Preconditioner for Radiation Problems Involving Wire and Surface Basis Functions

Cited by 6 publications

References 20 publications

A Method for Tracking Characteristic Numbers and Vectors

A Method for Tracking Characteristic Numbers and Vectors

Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method

An Efficient Hybrid Technique for Analysis of the Electromagnetic Field Distribution Inside a Closed Environment

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