Stanislav Ogurtsov

Multi-Objective Design of Antennas Using Variable-Fidelity Simulations and Surrogate Models

A computationally-efficient procedure for multi-objective design of antenna structures is presented. Our approach exploits the multi-objective evolutionary algorithm (MOEA) working with a fast antenna surrogate model obtained with kriging interpolation of coarse-discretization simulation data. Response correction techniques are subsequently applied to refine the designs obtained by MOEA. Our methodology allows us to obtain-at a low computational cost-a set of designs corresponding to various trade-offs between the antenna size and the refection coefficient. Two illustration examples are considered: (i) an UWB monocone with two objectives being reduction of the antenna size and minimization of the antenna reflection coefficient in the bandwidth of interest, and (ii) a planar Yagi antenna with the objectives being an increase of the end-fire gain and minimization of the reflection coefficient, both in the bandwidth of interest.

Reliable Space-Mapping Optimization Integrated With EM-Based Adjoint Sensitivities

We present a robust space mapping (SM) algorithm exploiting electromagnetic (EM)-based adjoint sensitivities for microwave design optimization. Our approach utilizes low-cost EM-based adjoint sensitivities and trust region methods to improve an SM algorithm at three levels, which are: 1) to build a better overall surrogate while ensuring convergence; 2) to speed up and safeguard the parameter extraction steps; and 3) to speed up and safeguard the surrogate optimization process. We describe the implementation at each level in detail. We review relevant adjoint sensitivity analysis methods. We also review prior SM methods that exploit both sensitivity and adjoint sensitivity. We summarize these methods in four categories. We compare our proposed approach with them. Efficiency, robustness, and versatility of our method are demonstrated by three design examples: an antenna, a planar filter, and a 3-D resonator filter. We compare the results with those obtained by SM without using adjoint sensitivity information and by direct optimization of the high-fidelity EM models.

Robust multi-fidelity simulation-driven design optimization of microwave structures

Simple and robust optimization methodology for the simulation-driven design of microwave structures is presented. Our technique exploits a set of EM-based models of increasing discretization density that are sequentially optimized with the optimal design of the “coarser” model being the initial design for the “finer” one. The final design is refined using a polynomial-based approximation model constructed from the coarse-discretization EM-simulation data and corrected using single high-fidelity EM-simulation. The presented technique is easy to implement. It is particularly suitable for structures for which simulation-driven design is a must (e.g., because of the lack of good theoretical models). Operation of our algorithm is demonstrated using two examples of planar ultrawideband antennas and a microstrip filter. In all cases, an optimal design is obtained at a low computational cost corresponding to a few high-fidelity EM simulations of the structure being optimized.

Variable-Fidelity Electromagnetic Simulations and Co-Kriging for Accurate Modeling of Antennas

Accurate and fast models are indispensable in contemporary antenna design. In this paper, we describe the low-cost antenna modeling methodology involving variable-fidelity electromagnetic (EM) simulations and co-Kriging. Our approach exploits sparsely sampled accurate (high-fidelity) EM data as well as densely sampled coarse-discretization (low-fidelity) EM simulations that are accommodated into one model using the co-Kriging technique. By using coarse-discretization simulations, the computational cost of creating the antenna model is greatly reduced compared to conventional approaches, where high-fidelity simulations are directly used to set up the model. At the same time, the modeling accuracy is not compromised. The proposed technique is demonstrated using three examples of antenna structures. Comparisons with conventional modeling based on high-fidelity data approximation, as well as applications for antenna design, are also discussed.

Design of a Planar UWB Dipole Antenna With an Integrated Balun Using Surrogate-Based Optimization

A design of an ultrawideband (UWB) antenna with an integrated balun is presented. A fully planar balun configuration interfacing the microstrip input of the structure to the coplanar stripline (CPS) input of the dipole antenna is introduced. The electromagnetic (EM) model of the structure of interest includes the dipole, the balun, and the microstrip input to account for coupling and radiation effects over the UWB band. The EM model is then adjusted for low reflection over the UWB band by means of fast simulation-driven surrogate-based optimization. This approach allows us to obtain the final design at low computational costs and at a high-fidelity level of structure description. Measurements of the manufactured optimal design validate the use of the balun as well as the design approach.

Linear antenna array synthesis using gradient-based optimization with analytical derivatives

Synthesis of linear antenna arrays using gradient-based optimization is described. Our approach utilizes standard sequential-quadratic programming algorithm exploiting analytical derivatives of the antenna pattern with respect to the designable parameters, as well as optional initialization through smart random search. This allows us to greatly reduce the computational cost of the synthesis process as compared to population-based techniques such as particle swarm optimization or genetic algorithms. Two linear antenna array design cases are demonstrated.

Simulation-Driven Design in Microwave Engineering: Methods

Today, electromagnetic (EM) simulation is inherent in analysis and design of microwave components. Available simulation packages allow engineers to obtain accurate responses of microwave structures. In the same time the task of microwave component design can be formulated and solved as an optimization problem where the objective function is supplied by an EM solver. Unfortunately, accurate simulations may be computationally expensive; therefore, optimization approaches with the EM solver directly employed in the optimization loop may be very time consuming or even impractical. On the other hand, computationally efficient microwave designs can be realized using surrogate-based optimization. In this chapter, simulation-driven design methods for microwave engineering are described where optimization of the original model is replaced by iterative re-optimization of its surrogate, a computationally cheap low-fidelity model which, in the same time, should have reliable prediction capabilities. These optimization methods include space mapping, simulation-based tuning, variable-fidelity optimization, and various response correction techniques.

Examination, Clarification, and Simplification of Stability and Dispersion Analysis for ADI-FDTD and CNSS-FDTD Schemes

We describe a rigorous analysis of unconditional stability for the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) and Crank-Nicholson split step (CNSS-FDTD) schemes avoiding use of the von Neumann spectral criterion. The proof is performed in the spectral domain, and uses skew-Hermitivity of matrix terms in the ADI and CNSS total amplification matrices. A bound for the total ADI amplification matrix is provided. While the CN and CNSS-FDTD amplification matrices are unitary, the bound on the ADI-FDTD depends on the Courant number. Importantly, we have found that the ADI-FDTD amplification matrix is not normal, i.e., the unit spectral radius alone cannot be used to prove the ADI-FDTD unconditional stability. The paper also shows that the ADI-FDTD and CNSS-FDTD schemes share the same dispersion equation by a similarity of their total amplification matrices, and the two schemes have identical numerical dispersion in the frame of plane waves.

ON SAMPLING-BIORTHOGONAL TIME-DOMAIN SCHEME BASED ON DAUBECHIES COMPACTLY SUPPORTED WAVELETS

The multi-resolution time domain (MRTD) technique for electromagnetic field equations was proposed by Krumpholz, Katehi et al., using Battle-Lemarie wavelets. The basis principle behind the MRTD is the wavelet-Galerkin time domain (WGTD) approach. Despite its effectiveness in space discretization, the complexity ofthe MRTD makes it unpopular. Recently, the WGTD was significantly simplified by Cheong et al. based on the approximate sampling property ofthe shifted versions ofthe Daubechies compactly supported wavelets. In this paper, we provide a rigorous analysis ofthe MRTD, employing positive sampling functions and their biorthogonal dual. We call our approach as the sampling biorthogonal time-domain (SBTD) technique. The introduced sampling and dual functions are both originated from Daubechies scaling functions of order 2 (referred as to D2), and form a biorthonormal system. This biorthonormal system has exact interpolation properties and demonstrates superiority over the FDTD in terms ofmemory and speed. Numerical examples and comparisons with the traditional FDTD results are provided.

CPU-budget-driven automated microwave design optimization using variable-fidelity electromagnetic simulations

A robust technique for microwave design optimization is presented. It is based on variable-fidelity electromagnetic (EM) simulations. The algorithm automatically switches between models of different fidelity taking into account the computational budget assumed for the design process. Additional mechanisms enhancing the algorithm include: frequency scaling to reduce the misalignment between the models of different fidelity; and the local response surface approximation to reduce the number of simulations. Our method is demonstrated using two filters and one antenna example.