自相关小波配置法在电磁场数值计算中的应用

近年来小波插值方法已应用到电磁场的数值计算中,且取得了一系列成果.文章指出了目前这方面主要文献未能解决的问题,将基于紧支撑、具有整数平移正交性的小波构造出的自相关小波作为插值函数应用于电磁场的数值分析和计算,其计算量仅是紧支撑正交小波的一半,并讨论了插值函数的收敛性,导出了适用于多种媒质边值问题的小波-配置方法模型,将配置方法取代Galerkin方法,避免了用小波插值函数代替电流密度函数时所带来的误差,从而提高了解的精度.此外,该方法对相同剖分节点在相邻区域的不同方程中求出的值是唯一的.

SELF-RELATIVE WAVELET COLLOCATION METHOD AND ITS APPLICATION TO ELECTROMAGNETIC NUMERICAL CALCULATION

In recent years, wavelet interpolating methods are applied to the calculation of electromagnetic fields and many results are obtained in many references. Some problems which are not considered in these main references are pointed out and solved. Firstly, correlative wavelet, which is constructed on the basis of the compact support wavelet with integral shift orthogonal feature, is applied to the analysis and calculation of electromagnetic fields. Its expression is succinct and its computational complexity is only half of the original wavelet. Meanwhile, the convergence of interpolating functions is researched. Secondly, instead of Galerkin method, the models of wavelet collocation method fitting to solve some kinds of media boundary problems is derived. So, replacing the current density function by wavelet interpolating function, the error appearing in reference [1] can be avoided, thus the accuracy of the solution is improved. The value of same cutting nodes in adjacent areas which is solved by different equations is unique.