Computational Mathematics

2006, No. 2

A.S. Pimenov

APPLICATION OF SPLINE WAVELET-FUNCTIONS TO NUMERICAL MODELLING OF THIN-WIRE ANTENNAS

Finding function of distribution of the current and the directional diagram for the system of the slender conductors is reduced to the solution of an integral Fredholm equation of the first type. The Galerkin method on the base of spline wavelets is applied to solve it. The algorithms of the technology of the sparse matrices are researched and the results of the numerical experiments are stated.
The computational difficulties of integral equations solving in the tasks of electrodynamics are caused in many respects by the fullness of the matrices that appear during their discretization. It results in an enormous size of computations (especially in 3-dimensional problems). However, as it is shown in [1], in the basis of wavelet functions [2] the most elements of the SLAE matrix turn out to be very small in absolute value, i.e. it will be pseudosparce [3]. That allows to reduce significally the amount of computations and the memory requirements and opens the way to the creation of the effective solution algorithms of essential 3-d problems.
In this work the application of the wavelet-Galerkin method to the system of electrically thin conductors is considered.