Summary of the Project Summary of the ProjectNowadays, the use of advanced computer simulation in R&D and industrial projects of microwave engineering becomes more and more popular. However, straightforward application of computational tools for analysis of the problem may not bring many direct recommendations as to how the construction of the system should be changed to improve its performance. In response to this situation, this work suggests a simple but efficient deterministic optimization algorithm applicable to many practically meaningful microwave systems and components. The algorithm is combined with the reliable and accurate 3D conformal FDTD electromagnetic simulator QuickWave-3D (www.qwed.com.pl).
In the algorithm, S-parameters taken from the simulator as from a black box are processed with the use of hyper-surface fitting. The response surface is approximated by a 2nd-order polynomial, which in many cases appears in a reduced form. Least squares method is applied for finding the coefficients in the approximating polynomial. An error analysis assessing normality of the error term distribution evaluates the quality of the applied approximation. The constructed hyper-surface is used as an input data for direct numerical constrained optimization (Sequential Quadratic Programming).
The optimization procedure is illustrated by solution of practical problems of optimal design for a slotted waveguide as a radiating element, a waveguide T-junction with a matching post, and a water load in a waveguide. This algorithm implemented as a MATLAB code looks promising for CAD of many applied microwave systems and, particularly, systems of microwave heating. It is ready to use jointly with QuickWave-3D in practical design as an alternative to a general-purpose optimization module incorporated in the QuickWave-3D package.
Table of Contents1 Introduction
1.1 General Motivation2 Elements of Problem Formulation
1.2 Some Concepts and Terms
1.3 Preliminary Study
2.1 Electromagnetic Issues 2.2 Mathematical Issues3 Model and Optimization3.1 Model Specification4 Implementation of the Algorithm
3.1.1 Representation of the Approximating Function3.2 Procedure of Constrained Optimization
3.1.2 The Least-Squares Concept in Surface Fitting
5 Illustrations of the Method5.1 Slotted Waveguide6 Conclusions
5.2 Waveguide T-Junction with a Post
5.3 Water Load in a Waveguide
5.4 General Comments
Appendix
A. MATLAB ScriptBibliography
B. Input and Output Files
C. QuickWave-3D Parameterized Object
Publications1. V.A. Mechenova, and V.V. Yakovlev, Efficient optimization of S-parameters of systems and components in microwave heating, Abstract Book of the 3rd World Congress on Microwave & Radio Frequency Processing (Sydney, Australia, Sept. 2002), pp. M4A.24-M4A.25.
2. V.A. Mechenova, and V.V. Yakovlev, Method of efficient optimization of microwave systems and elements, Paper in preparation.
The present M.S. Thesis was successfully
presented to the Departmet of Mathematical Sciences on April 30, 2002.