一类高阶奇异积分方程的快速小波解法

利用一类三角小波作为基函数Galerkin方法,将一类高阶奇异积分方程离散化,得到的刚度矩阵是一个对称循环矩阵,并由此获得了一个基于FFT和IFFT的快速算法。该算法不但不需要计算刚度矩阵的值,而且还避免了求广义逆矩阵所带来的麻烦。数值算例表明:当积分方程的真实解几乎具有奇性时,该数值方法仍然十分有效。

A Fast Wavelet Method for a Kind of Hypersingular Integral Equation

Using trigonometric wavelets as trial functions and Galerkin method, the obtained stiffness matrix from discretization the hypersingular integral equation is symmetrical and circulant, which leads us to a fast numerical method based on fast Fourier transform. Furthermore, this method dont need to compute the entries of the stiffness matrix and overcome the drawback to solve generalized inverse matrix. The example states that it still has good accuracy when the accurate solution is almost singular.