# Cartesian Grid Mapper: Transformation Media for Modeling Arbitrary Curved Boundaries With Cartesian Grids

2014-01-01
ÖZGÜN, ÖZLEM
Kuzuoğlu, Mustafa
A transformation electromagnetics-based approach is presented to facilitate the use of fixed Cartesian grids for modeling arbitrarily shaped (convex or nonconvex) curved boundaries in finite methods. The basic idea is to design transformation media adapted to the Cartesian grid by using the duality between the material parameters of the media and the coordinate transformation that maps the points of the Cartesian grid to the points on the original curved boundary. Such a transformation medium is named Cartesian grid mapper, and its main mission is to create an illusion to make the Cartesian grid behave like a conformal grid over the curved boundary. The techniques are validated via the results of some numerical simulations.
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS

# Suggestions

 Series solution of the wave equation in optic fiber Çıldır, Sema; Çakır, Serhat; Department of Physics (2007) In this study, the mapped Galerkin method was applied to solve the vector wave equation based on H field and to obtain the propagation constant in x y space. The vector wave equation was solved by the transformation of the infinite x y plane onto a unit square. Two-dimensional Fourier series expansions were used in the solutions. Modal fields and propagation constants of dielectric waveguides were calculated. In the first part of the study, all of the calculations were made in step index fibers. Transvers...
 Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01) Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
 Geometric measures of entanglement UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01) The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
 Thermal refocusing method for spaceborne high-resolution optical imagers Selimoglu, Ozgur; Ekinci, Mustafa; Karci, Ozgur (2016-05-20) We describe the design of a thermal refocusing method for spaceborne high-resolution imagers where Korsch optical design is usually implemented. The secondary mirror is made of aluminum, a high thermal expansion coefficient material, instead of conventional zero-expansion glass ceramics. In this way, the radius of the curvature can be controlled by means of temperature change of the mirror. Change in the radius of curvature also changes the effective focal length of the camera which is used for compensation...
 Non-linear optical properties of two dimensional quantum well structures Ağanoğlu, Ruzin; Tomak, Mehmet; Department of Physics (2006) In this work optical properties of two dimensional quantum well structures are studied. Variational calculation of the eigenstates in an isolated quantum well structure with and without the external electrical field is presented. At weak fields a quadratic Stark shift is found whose magnitude depends strongly on the finite well depth. It is observed that under external electrical field, the asymmetries due to lack of inversion symmetry leads to higher order nonlinear optical effects such as second order opt...
Citation Formats
Ö. ÖZGÜN and M. Kuzuoğlu, “Cartesian Grid Mapper: Transformation Media for Modeling Arbitrary Curved Boundaries With Cartesian Grids,” IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, pp. 1771–1774, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37937. 