Further comments on the performances of finite element simulators for the solution of electromagnetic problems involving metamaterials

Abstract

In this paper, we analyze the performances of three‐dimensional finite element (FE) simulators in handling electromagnetic scattering problems involving metamaterials. It has already been proved that the performances of the FE method are worse than usual, when metamaterials are considered. In this work, we extend our previous analysis by providing some additional results on the precision of the FE solution and on the performances of the iterative and direct solvers typically used with FE simulators. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48:2524–2529, 2006; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.22008

Improving the Reliability of Frequency Domain Simulators in the Presence of Homogeneous Metamaterials - A Preliminary Numerical Assessment

“…Indeed, it has been recently demonstrated that waveguide discontinuity problems can become ill-posed even in the presence of lossy media and absorbing boundary conditions [23]. Consequently, several anomalies of the numerical reliability of existing numerical methods, such as the FE 3, have been pointed out in canonical direct scattering problems involving effective MTM s [22,25,31].…”

“…In particular, the presence of complementary or almost complementary MTM s has shown to deeply affect the accuracy of the FE solutions and the convergence rate of some popular iterative solver used for the solution of the associated linear systems [22,25,31]. Accordingly, such preliminary conclusions [22,25,31] have suggested that FE method could have some intrinsic characteristics which make it particularly sensitive to the anomalies of MTM models.…”

“…In the following, the degree of freedom in the choice of χ and ξ will be used to insert the maximum amount of losses in the perturbation layer (i.e., χ = ξ = − π 2 ). Such choice is motivated by the already performed numerical analyses on the stability of numerical solvers in the presence of MTM s [22,31,25].…”

“…In this framework, surprisingly poor performances have been recently obtained by some widely used techniques [e.g., the finite element (FE ) method [21]] when simulating canonical waveguide and scattering problems involving MTM s [22,23]. Moreover, some theoretical analyses of problems involving metamaterials have shown that simple frequency-domain waveguide discontinuity problems can be ill-posed [24] even in the presence of lossy media and of absorbing boundary conditions [23].…”

“…Moreover, some theoretical analyses of problems involving metamaterials have shown that simple frequency-domain waveguide discontinuity problems can be ill-posed [24] even in the presence of lossy media and of absorbing boundary conditions [23]. From a numerical viewpoint, such anomalies have shown to cause a strong numerical instability for the FE method, especially in configurations involving interfaces with "complementary" or nearly complementary media [22,23]. Such results have been demonstrated even using a commercial simulator with problems which are believed to be well-posed [25].…”