Reconstruction of shapes and impedance functions using few far-field measurements

Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions

“…In the second configuration a circular dielectric material with permittivity 2.5ε 0 and conductivity 0.01 (S.m −1 ) is coated over an equilateral hexagon PMC object whose vertices are 1 cm away from the outer boundary. This coated object with radius 0.5 m is illuminated at 300 MHz and the data are collected on the circle Γ S with radius 1.0 m. By choosing the truncation parameters as 11,10,11,12,13,11, which are determined by Morozov's discrepancy principle, the presented approach is applied and the relative errors are calculated as 0.25, 0.43 and 0.17 for orders 1, 2 and 3. Although the GIBCs contain higher order derivatives of the width δ(s), the proposed approach yields good reconstructions (especially for order 3) for the coatings having corner singularities as shown Figure 9.…”

“…These studies mostly consist of deriving or dealing with GIBC expressions and using them in a direct scattering problem [9-12, 14, 20-22, 25-27, 30-32]. One can find also some applications of them to the inverse scattering problems for various geometries [3,13,19].…”

Topology optimization for negative permeability metamaterials using level-set algorithm

“…In the SIMP method, the sensitivity of the objective function with respect to the design variables were derived by a two-step adjoint variable method [15] and was applied to a gradient-based optimizer (namely, method of moving asymptotes -MMA [16]) such that the objective function can be minimized. Based upon an increasing popularity of the level-set technique [17] and its special features in a range of fields [18][19][20][21][22][23][24][25][26][27][28][29], we attempted to develop a levelset-based topology optimization algorithm for the electromagnetic metamaterial design in our previous study, where some benchmark topologies were regenerated in a systematic way. The level-set algorithm demonstrated several noticeable advantages, e.g.…”

“…In such an evolution process, the topological variation of the structure can take place in a more natural fashion whilst the objective function is minimized. Due to these features, the level-set technique has been widely used in a range of engineering problems [18][19][20][21][22][23][24][25][26]. In the electromagnetic fields, one of the most prevalent applications of the level-set method is perhaps in the nonlinear inverse problem [31], where the shape of an unknown object can be reconstructed by minimizing the difference between the electromagnetic fields scattered from the real and the in-design objects.…”

Level-set based topology optimization for electromagnetic dipole antenna design

“…The level-set technique established by Osher and Sethian [18] is one such powerful approach. Since this method can unambiguously represent the geometrical shape and is capable of effectively tracking the dynamically-moving interfaces, its breadth of applications has been extensively evidenced in the literature [19][20][21], including various structural optimization [22][23][24], metamaterial design [25] and inverse scattering problems (shape reconstruction from scattered waves) [26,27]. However, limited studies are currently available in the level-set based topology optimization for electromagnetic antenna design.…”