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Meta 2010 & FEM 2010 – Rome, 13-15 December 2010 Some comments on the solution of the linear algebraic systems defined by the finite element method when applied to electromagnetic problems involving bianisotropic media Paolo Fernandes (1) , Marina Ottonello (2) and Mirco Raffetto (2) (1) Istituto di Matematica Applicata e Tecnologie Informatiche del Consiglio Nazionale Delle Ricerche, Via De Marini 6, I 16149 Genoa, Italy – E-mail: fernandes@ge.imati.cnr.it (2) Department of Biophysical and Electronic Engineering, University of Genoa, Via Opera Pia 11a, I 16145, Genoa, Italy – E-mail: ottonello@dibe.unige.it, raffetto@dibe.unige.it It is well known that the finite element (FE) method, when applied to the solution of time-harmonic electromagnetic boundary value problems involving linear media, requires the solution of linear algebraic systems of equations characterized by very sparse matrices [1]. For this task different techniques of solution can be considered: direct solvers and iterative solvers [1]. Usually iterative solvers [2] work very well and are used worldwide in FE simulations of electromagnetic boundary value problems. Many types of iterative solvers have been developed [2] and, among these, some solvers like the conjugate gradient [1], [2], the biconjugate gradient [1], [2] and the Conjugate Orthogonal Conjugate Gradient [3], which have received a particular attention in the research community working on the FE method, assume some kind of symmetry of the FE matrices. When the time-harmonic electromagnetic boundary value problem of interest involves innovative and linear media, like the so-called bianisotropic materials [4], [5], the usual symmetry of the FE matrices can be lost and for the most widely used algebraic iterative algorithms convergence is not guaranteed anymore. This is the reason why in [6] the authors considered the medium analyzed in [5] setting a parameter to zero, so reducing the bianisotropic medium to a biisotropic one. In this contribution we analyze what can be done to overcome this difficulty. References [1] J. Jin, The finite element method in electromagnetics, John Wiley & Sons, 1993. [2] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, SIAM, 1994. [3] H. A. van der Vorst and J. B. M. Melissen, “A Petrov-Galerkin type method for solving Ax=b, where A is symmetric complex,” IEEE Trans. Magnetics, vol. 26, pp. 706-708, 1990. [4] J. A. Kong, Theory of Electromagnetic Waves, Wiley, 1975. [5] S. Maruyama and M. Koshiba, “A vector finite element formulation for general bianisotropic waveguides,” IEEE Transactions on Magnetics, vol. 33, pp. 1528- 1531, 1997. [6] P. Fernandes and M. Raffetto, “Well posedness and finite element approximability of time-harmonic electromagnetic boundary value problems involving bianisotropic materials and metamaterials, Mathematical Models and Methods in Applied Sciences, vol. 19, pp. 2299-2335, December 2009. 62
Meta 2010 & FEM 2010 – Rome, 13-15 December 2010 Double negative metamaterials based on ferromagnetic microwire: a numerical study G. Conte (1) , G. Finocchio (1) , A. Faba (2)(3) , A. Prattella (1) , B. Azzerboni (1) , E. Cardelli (2)(3) (1) University of Messina, Department of Matter Physics and Electronic Engineering - Messina, Italy (2) University of Perugia, Polo Scientifico e Didattico di Terni, Terni, Italy (3) University of Perugia, Department of Industrial Engineering Perugia, Italy The double negative (DNG) properties of metamaterials based on array of ferromagnetic thin wires in the RF spectrum have recently been highlighted [1,2]. This fact is interesting due the possibility to control the DNG with a magnetic field applied to the wires (control of the ferromagnetic resonance frequency). This work consists of a systematic study of the electric properties of a periodic array of this kind of media in order to determine how it is influenced the DNG effect. The negative electric permittivity can be tuned by acting on the geometric parameters a and r as suggested by Pendry et al [3]. The FTDT method was employed to analyze 1D and 2D array with size of 3x1 and 3x2 in waveguide environment (8÷12 GHz - WR-90 waveguide). The wires composed by CoSiB have a radius of 2 μm. The performance of the samples are expressed in terms of scattering parameters S11 and S21 and normal absorbed power (Pabs=1-|S11| 2 -|S21| 2 ) and calculated for three values of dc magnetic field (parallel to the wires). For both arrays, the performances are enhanced when the a (distance between the wires) is increased up to a critical value (about 5 mm). For larger value the scattering phenomenon is not negligible. Our computations show the DNG effect is visible only when the radius of the wire is comparable with the skin length. We also see that the transmission of the signal in the DNG region roughly decrease in the double layer case, in the case with a third layer the DNG effects became almost negligible. References [1] J. Carbonell, et al, “Double negative metamaterials based on ferromagnetic microwires,” Phys. Rev. B 81, 024401, 2010. [2] H. García-Miquel, J. Carbonell, V. E. Boria and J. Sánchez-Dehesa, “Experimental evidence of left handed transmission through arrays of ferromagnetic microwires,” Appl- Phys. Lett. 94, 054103, 2009 [3] J. B. Pendry, J. A. Holden, J. D. Robbins, and J. W. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condensed Matter, vol. 10, pp. 4785–4809, 1998 [4] N. Engheta and R. W. Ziolkowski, “Metamaterials. Physics and Engineering Explorations,” Wiley Inter-Science, IEEE Press, Piscataway, NJ, 2006 63
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Meta 2010 - Committees Chairmen Met
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FEM 2010 Foreword Ladies and Gentle
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Abstracts - Dipartimento di Elettronica Applicata

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