双正交样条小波Petrov-Galerkin法在静电场的应用

Application of Biorthogonal Spline Wavelet Petrov-Galerkin Method to the Electrostatic Field

以张量积形式构造高维双正交样条小波,结合Petrov-Galerkin方法应用于静电场的计算问题.使用小波函数特有的细分关系准确地计算小波积分,双正交样条小波的正交性和紧支性加快了计算速度.并采用添加外小波法降低了边界截断引起的误差.数值算例表明此方法具有求解精度高、计算速度快和单元数量少等优点.

High dimensional biorthogonal spline wavelet is constructed by the tensor product method.With a wavelet Petrov-Galerkin approach,biorthogonal spline wavelets were adapted to the computing of electrostatic field problems.Using the refinement equations for evaluating integrals of wavelets exactly,the orthogonal and compactly supported of biorthogonal spline wavelets could speed up calculating.In order to reduce the error caused by truncation on the boundary,wavelets on the domain boundary were added.The numerical results of this method showed desirable calculation precision,faster computing speed and fewer elements.