Numerical Methods, Algorithms and Results
Olena O. Bulatsyk, B. Z. Kat︠s︡enelenbaum, Yury P. Topolyuk, Nikolai N. Voitovich · 2010
This chapter analyzes some numerical methods that applies to the formulated problems. It describes some theoretical aspects of the iterative methods for direct minimization of the functionals and for the solution of nonlinear integral equations and their systems. The chapter also describes the modification of the Newton method that is applied to the concrete problems. As a rule, this method is most effective when used together with the above iterative ones. A specific numerical technique known as the ‘opposite directions’ method is utilized for the optimization of linearly extended systems. Almost all the methods are demonstrated on two-dimensional problems described by one-dimensional equations. The chapter discusses the method of generalized separation of variables using examples of the optimization problem for two dimensional antenna arrays. The problems concerning eigen functions of certain homogeneous integral equations which describe the eigenwaves and eigenoscillations of physical systems are considered. Controlled Vocabulary Terms antenna arrays; eigenvalues and eigenfunctions; integral equations; Newton method; numerical analysis; optimisation