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A singular coordinate transformation leads to extreme materials in a transformation-based cloak. If a non-singular transformation is used, the perfect invisibility is lost. The invisibility is also influenced by the homogenization process. In this paper, we investigate these two influences in 2-D circular cylindrical cloaks, obtained from different non-singular mappings. Considering a further deterministic optimization, we also conclude that it is better to use a non-singular cloak based on a mapping scale up to 20%, since it has lower scattering and simpler materials when compared with cloaks based on other mappings. [ABSTRACT FROM AUTHOR]

The generalized finite-element method (GFEM) enriched by plane waves has been proved suitable to solve the 2-D Helmholtz equation. However, when the number of unknowns increases, some difficulties arise, such as bad condition number. Therefore, developing a pre-processing methodology to identify an appropriate number of degrees of freedom for each problem could be useful. This paper presents a systematic approach to determine the optimal number of plane waves for each problem to be used in GFEM solution. It is based on the analysis of the traditional FEM solution with a poor mesh resolution using the fast discrete curvelet transform. The results indicate that the adopted strategy can guarantee accurate and converging responses for GFEM in complex problems, along with remarkable reductions of the computational cost. [ABSTRACT FROM AUTHOR]

A possible strategy for avoiding singular material parameters in a transformation-based invisibility cloak involves an out-of-plane stretching, calculated to compensate the in-plane singular transformation. In this paper, we used numerical simulations to analyze the relation among the out-of-plane transformation, the resulting material anisotropy, and the total scattering cross width. Moreover, we show how this information can be used to optimize a cloak with homogeneous anisotropic layers. [ABSTRACT FROM AUTHOR]

In this paper, we solve the \mathcal E and \mathcal B mixed finite element time domain formulation using the alternating-direction implicit (ADI) scheme in time. To save computational cost, the algorithm is improved using a recursive sparsification procedure that approximates the inverse matrix needed to calculate the electric field. Although the method is unconditionally stable, we show that the numerical performance of the algorithm is strongly related to the time step. Numerical results demonstrated that for the same accuracy our approach is much faster than the ADI with Cholesky factorization. [ABSTRACT FROM PUBLISHER]

This paper addresses the generalized finite-element method enriched by plane waves for the 2-D Helmholtz equation. The enrichment function is modified to reduce the effect of numerical dispersion from coarse meshes and to make it possible to treat essential boundary conditions in a straightforward way. Two numerical examples, the free space propagation problem and the plane wave scattering by a cylinder, demonstrate the effectiveness of the new enrichment function. [ABSTRACT FROM PUBLISHER]