一种消除stokes积分卷积化近似误差影响的有效方法

在应用快速Hartly变换(FHT)或快速Fourier变换(FFT)计算Stokes积分公式时,总是先将Stokes 公式化成卷积形式,然后用 FHT或 FFT完成卷积运算,从而避免了复杂费时的积分计算。但由于 Stokes公式不严格满足卷积定义,欲将其化成卷积形式必须作一些近似。这种近似虽能在一定精度范围满足要求,但对于高精度要求仍有不能允许的计算误差。本文建议采用球面坐标转换方法,能有效地消除无论是用 FHT或 FFT 计算Stokes 积分卷积化所带来的误差影响。

An Effective Method of Eliminating the Approximation Errors in Stokes Integration Convolution Formula

When stokes integration is performed using the fast Hartley transform (FHT)techniques or fast Fourier transform (FFT) techniques,it must be modified as the explicitconvolution form, then the convolution can be evaluated by FHT (or PFT) techniques. Inthis way,numerital quadature procedures which are usually time consuming can be avoided.However,Stokes formula itself does not strictly satisfy convolution definition so that its con-volution form includes an approximate term. Although such an approximation could meetsome accuracy in most practical application, for higher accuracy application there still existthe inadmissible errors in the calculated results. This paper presents a method of spherical co-ordinate transformation which can effectively eliminate the errors due to the approximateterm in the convolution form of stokes integration farmula.