Can Onol

Efficient and Accurate Electromagnetic Optimizations Based on Approximate Forms of the Multilevel Fast Multipole Algorithm

We present electromagnetic optimizations by heuristic algorithms supported by approximate forms of the multilevel fast multipole algorithm (MLFMA). Optimizations of complex structures, such as antennas, are performed by considering each trial as an electromagnetic problem that can be analyzed via MLFMA and its approximate forms. A dynamic accuracy control is utilized in order to increase the efficiency of optimizations. Specifically, in the proposed scheme, the accuracy is used as a parameter of the optimization. We show that the developed mechanism with dynamic accuracy control provides faster optimizations without deteriorating the quality of the final results in comparison to optimizations with full MLFMA.

Efficient three-layer iterative solutions of electromagnetic problems using the multilevel fast multipole algorithm

We present a three-layer iterative algorithm for fast and efficient solutions of electromagnetic problems formulated with surface integral equations. The strategy is based on nested iterative solutions employing the multilevel fast multipole algorithm and its approximate forms. We show that the three-layer mechanism significantly reduces solution times, while it requires no additional memory as opposed to algebraic preconditioners. Numerical examples involving three-dimensional scattering problems are presented to demonstrate the effectiveness of the proposed algorithm.

Full-wave electromagnetic optimizations using surface integral equations and the multilevel fast multipole algorithm

We present an electromagnetic optimization environment based on full-wave solutions via surface integral equations and the multilevel fast multipole algorithm (MLFMA). Optimizations are performed by using genetic algorithms, while the required trials are performed accurately via MLFMA. The developed mechanism can handle many different operations, such as portion moving/removing, rotation, and gap opening, that have different effects in the constructed matrix equations but that can efficiently be executed in numerical simulations. The effectiveness of the optimization environment is demonstrated on alternative problems, such as the design of pixel antennas and corrugated sheets for optimal electromagnetic responses.

Modified superformula contours optimized via genetic algorithms for fastly converging 2D solutions of EFIE

It is known that solutions of the integral equations converge at the smoothness rate of the parametrical function representing the boundary contour. Thus using an infinitely smooth parametrical representation with derivatives of all orders results into exponentially converging solutions. A version of superformula tailored for this purpose is exposed to optimization of its parameters via genetic algorithms to obtain smooth parameterization for desired boundaries in two dimensional problems. The convergence of the resulting solutions of the electric-field integral equation will be presented.

Antenna switch optimizations using genetic algorithms accelerated with the multilevel fast multipole algorithm

We present antenna switch optimizations using an efficient mechanism based on genetic algorithms and the multilevel fast multipole algorithm (MLFMA). Genetic algorithms are used to determine switch states for desired radiation and input characteristics, while cost-function evaluations are performed efficiently via an MLFMA implementation with dynamic error control. MLFMA is integrated into the genetic algorithm by extracting common computations to be performed once per optimization. Iterative convergence rates are further accelerated by using earlier solutions as initial-guess vectors. The efficiency of the developed mechanism is demonstrated on antennas with relatively large numbers of switches.

Optimizations of EFIE and MFIE combinations in hybrid formulations of conducting bodies

We present generalized hybrid surface-integral-equation formulations for three-dimensional conductors with arbitrary shapes. The proposed formulations are based on flexible applications of the electric-field integral equation and the magnetic-field integral equation with varying combinations on different regions of the given objects. As a proof of concept, we demonstrate hybrid formulations using two-region maps and their parametric analysis. We show that hybrid formulations may enable optimal solutions in terms of accuracy and efficiency, in comparison to the conventional CFIE implementations with fixed combination parameters.

Fastly converging 2D solutions of TE-EFIE on modified superformula contours optimized via genetic algorithms

An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of hyper-singular electric field integral equation (EFIE) in 2D. A version of superformula tailored for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the hyper-singular kernel and convergence of the solution for EFIE assuming TE polarization will be presented.

Multilayer iterative solutions of large-scale electromagnetic problems using MLFMA

We present multilayer solutions of large-scale electromagnetic problems using the multilevel fast multipole algorithm (MLFMA). With the conventional algebraic preconditioners based on the available near-field interactions, the cost of iterative solutions may exceed the linearithmic complexity, particularly for ill-conditioned systems, despite the efficient matrix-vector multiplications by MLFMA. We show that, using a multilayer approach employing approximate and full versions of MLFMA, the complexity can be reduced to the desired levels without deteriorating the accuracy. The proposed approach significantly accelerates iterative solutions also for well-conditioned system, while it does not require any extra memory as opposed to memory-hungry algebraic preconditioners. Numerical results of scattering problems involving both canonical and complicated structures are presented to demonstrate the efficiency of the multilayer strategy.

Dual-band antenna array optimizations using heuristic algorithms and the multilevel fast multipole algorithm

We consider design and simulations of dual-band antenna arrays and their optimizations via heuristic algorithms, particularly, genetic algorithms (GAs) and particle swarm optimization (PSO) methods. As shown below, these arrays consist of patch antennas of different sizes, depending on the target frequencies. The resulting radiation problems are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm (MLFMA). MLFMA allows for realistic simulations of antenna arrays of finite extent, without any periodicity and similarity assumptions, while including all mutual couplings between the antennas. This way, we obtain effective and realistic optimizations.