Preconditioning Techniques in the Analysis of Finite Metamaterial Slabs

Úbeda, Eduard; Rius, J.M.; Romeu, J.

doi:10.1109/tap.2005.861508

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…Although BDP is successful in reducing the iteration counts for second‐kind integral equations [ Song et al , 1997], such as the combined‐field integral equation (CFIE), it may not accelerate the iterative solutions of first‐kind integral equations [ Gürel and Ergül , 2006], such as the electric field integral equation (EFIE). In fact, EFIE solutions are usually decelerated with BDP [ Gürel and Ergül , 2003], and BDP is rarely useful for EFIE [ Ubeda et al , 2006; Ergül et al , 2007].…”

Section: Block‐diagonal Preconditioning Of Jmcfiesupporting

confidence: 62%

Efficient solution of the electric and magnetic current combined‐field integral equation with the multilevel fast multipole algorithm and block‐diagonal preconditioning

Ergül

Gürel

2009

Radio Science

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[1] We consider the efficient solution of electromagnetics problems involving dielectric and composite dielectric-metallic structures, formulated with the electric and magnetic current combined-field integral equation (JMCFIE). Dense matrix equations obtained from the discretization of JMCFIE with Rao-Wilton-Glisson functions are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm. JMCFIE usually provides well conditioned matrix equations that are easy to solve iteratively. However, iteration counts and the efficiency of solutions depend on the contrast, i.e., the relative variation of electromagnetic parameters across dielectric interfaces. Owing to the numerical imbalance of off-diagonal matrix partitions, solutions of JMCFIE become difficult with increasing contrast. We present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. 4PBDP is useful, especially when the contrast increases, and the standard block-diagonal preconditioner fails to provide a rapid convergence.Citation: Ergül, Ö ., and L. Gürel (2009), Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning, Radio Sci., 44, RS6001,

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Section: Block‐diagonal Preconditioning Of Jmcfiesupporting

confidence: 62%

Efficient solution of the electric and magnetic current combined‐field integral equation with the multilevel fast multipole algorithm and block‐diagonal preconditioning

Ergül

Gürel

2009

Radio Science

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“…Due to its simplicity and favorable computing cost, this preconditioner is commonly used for the MLFMA solutions of second-kind integral equations, such as the magnetic-field integral equation and the combined-field integral equation [17]. Although it usually has an adverse effect on the convergence of EFIE [33,34], the block-diagonal preconditioner may also accelerate the iterative solutions of metamaterial problems formulated with EFIE [35]. Nevertheless, we observe that the block-diagonal preconditioner is insufficient to improve the convergence at the resonance frequencies of the metamaterials.…”

Section: Iterative Solutions and Preconditioningmentioning

confidence: 99%

Fast and Accurate Analysis of Large Metamaterial Structures Using the Multilevel Fast Multipole Algorithm

Gürel¹,

Ergül

Ünal³

et al. 2009

PIER

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Abstract-We report fast and accurate simulations of metamaterial structures constructed with large numbers of unit cells containing split-ring resonators and thin wires. Scattering problems involving various metamaterial walls are formulated rigorously using the electric-field integral equation, discretized with the Rao-WiltonGlisson basis functions. Resulting dense matrix equations are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm. For rapid solutions at resonance frequencies, convergence of the iterations is accelerated by using robust preconditioning techniques, such as the sparse-approximate-inverse preconditioner. Without resorting to homogenization approximations and periodicity assumptions, we are able to obtain accurate solutions of realistic metamaterial problems discretized with millions of unknowns.

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“…The supported propagation constants are extracted and the waveguiding conditions lead to the suppression of a guided-wave regime for both polarizations. Similar analyses are presented in [5][6][7] where surface and guided waves are observed and examined. Moreover in [7] slabs of metamaterials are studied by solving the related electrictype integral equation via the method of moments.…”

Section: Introductionmentioning

confidence: 66%

Effect of Cylindrical Scatterer With Arbitrary Curvature on the Features of a Metamaterial Slab Antenna

Valagiannopoulos

2007

PIER

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Abstract-The metamaterial slab with low refractive index exhibits directive properties which make it suitable to work as antenna.The characteristics of such a device are affected under the presence of a conducting rod of arbitrary shape placed over the slab. A qualitative and quantitative approach is presented which is possible by implementing the method of auxiliary sources. For the evaluation of the far field quantities the method of stationary phase is employed. A validation example considering a circular rod is solved rigorously with use of the method of moments. Several numerical results are shown and discussed.

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Preconditioning Techniques in the Analysis of Finite Metamaterial Slabs

Cited by 5 publications

References 16 publications

Efficient solution of the electric and magnetic current combined‐field integral equation with the multilevel fast multipole algorithm and block‐diagonal preconditioning

Efficient solution of the electric and magnetic current combined‐field integral equation with the multilevel fast multipole algorithm and block‐diagonal preconditioning

Fast and Accurate Analysis of Large Metamaterial Structures Using the Multilevel Fast Multipole Algorithm

Effect of Cylindrical Scatterer With Arbitrary Curvature on the Features of a Metamaterial Slab Antenna

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