基于三角小波的Galerkin边界元法

A Galerkin Boundary Element Method Based on Interpolatory Hermite Trigonometric Wavelets

采用三角小波函数作为基函数和检验函数提出了一种Galerkin边界元法.当问题区域是单位圆时,推导了系数矩阵元素的计算公式,其显示了大多数元素是零,从而系数矩阵是稀疏的,且可由一些循环的对称或反对称子矩阵构成,因此存储空间和计算复杂度大大减少.数值算例验证了方法的有效性.

A Galerkin boundary element method based on trigonometric wavelets is proposed in this paper.In this approach,the Hermite trigonometric wavelets are employed as the trial and test functions of variational formulation.The simple computational formulae of the entries in coefficient matrix are obtained when the domain is a unit disk.Most of the matrix entries are naturally zero without any truncating technology.It shows that the coefficient matrix consists of some symmetric and antisymmetric circular submatrices.Hence the memory spaces and computational complexity can be reduced greatly.Finally,some test examples are presented.