Steklov特征值问题的一种有效的Legendre-Galerkin谱逼近

本文给出Steklov特征值问题基于Legendre-Galerkin逼近的一种有效的谱方法.首先利用Legendre多项式构造了一组适当的基函数使得离散变分形式中的矩阵是稀疏的,然后推导了2维及3维情形下离散变分形式基于张量积的矩阵形式,由此可以快速地计算出离散的特征值和特征向量.文章还给出了误差分析和数值试验,数值结果表明本文提出的方法是稳定和有效的.

An efficient Legendre-Galerkin spectral approximation for the Steklov eigenvalue problem

In this paper, we give an effective spectral method based on the Legendre-Galerkin approximation for the Steklov eigenvalue problem. We first construct an appropriate set of basis functions such that the matrices in the discrete variational form are sparse. Then we deduce the matrix formulations based on the tensor-product for the discrete variational form in two- and three-dimensional cases, respectively. By using these tensor-product forms we can compute the discrete eigenvalues and eigenvectors rapidly. We also provide an error analysis and some numerical experiments. The numerical results indicate that our method is very stable and effective.