Erdogan Alkan

Dual-Grid Finite-Difference Frequency-Domain Method for Modeling Chiral Medium

A dual-grid finite-difference frequency-domain (DG-FDFD) method is introduced to solve for scattering of electromagnetic waves from bianisotropic objects. The formulations are based on a dual-grid scheme in which a traditional Yee grid and a transverse Yee grid are combined to achieve coupling of electric and magnetic fields that is imposed by the bianisotropy. Thus the underlying grid naturally supports the presented formulations. Introduction of a dual-grid scheme doubles the number of electromagnetic field components to be solved, which in turn implies increased time and memory of the computational resources for solution of the resulting matrix equation. As a remedy to this problem, an efficient iterative solution technique is presented that effectively reduces the solution time and memory. The presented formulations can solve problems including bianisotropic objects. The validity of the formulations is verified by calculating bistatic radar cross-sections of three-dimensional chiral objects. The results are compared with those obtained from analytical and other numerical solutions.

Electromagnetic scattering from chiral objects using double-grid finite-difference frequency-domain (DG-FDFD) method

In this paper, a double-grid finite-difference frequency domain (DG-FDFD) method is introduced to solve for scattering of electromagnetic waves from chiral objects. The formulations are based on a double-grid scheme in which a traditional Yee grid and a transverse Yee grid are combined to achieve coupling of electric and magnetic fields that is imposed by the bianisotropy. While the presented formulations can solve problems including bianisotropic objects, the validity of the formulations is verified by calculating bistatic radar cross-sections of three-dimensional chiral objects and comparing the results to those obtained from analytical and other numerical solutions.

An Algorithm for Efficient Solution of Finite-Difference Frequency-Domain (FDFD) Methods [EM Programmer's Notebook]

Finite-Difference Frequency-Domain methods (FDFD) require solution of large linear systems of equations. These large systems are represented by matrix equations including highly sparse coefficient matrices, and they can often only be solved by using iterative methods. This paper presents an algorithm in which the matrix-equation solution approach in an iterative method is replaced by a multi-step solution process. Instead of using a coefficient matrix, the coefficients in the FDFD formulations are kept as three-dimensional arrays, and they are treated as operators. The algorithm is used together with the Bi-Conjugate Gradients Stabilized (BICGSTAB) method. This is applied to a three-dimensional FDFD method to solve for scattering from dielectric objects. It is also applied to two other FDFD methods (a single-grid and a double-grid FDFD) to solve for scattering from chiral objects. It has been shown that the presented algorithm effectively reduces the solution time and memory requirements.

Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects

Abstract This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid (DG-FDFD) approach for general bianisotropic materials. The validity of the derived formulations for different scattering problems has been shown by comparing the obtained results to exact and other solutions obtained using different numerical methods. Table of Contents: Introduction / Chiral Media / Basics of the Finite-Difference Frequency-Domain (FDFD) Method / The Double-Grid Finite-Difference Frequency-Domain (D...

An efficient solution of Finite-Difference Frequency-Domain (FDFD) equations

Finite-Difference Frequency-Domain methods (FDFD) require solution of large linear systems of equations. These large systems are represented by matrix equations including highly sparse coefficient matrices and they can often only be solved by using iterative methods. This paper presents an algorithm in which the matrix-vector product in an iterative method is replaced by a three-step process. It has been shown that the presented algorithm effectively reduces the solution time and memory requirements.