关键词: 椭圆特征值问题, 径向基函数, 径向基函数差分法, 形状参数

Abstract: This paper is concerned with the application of the local RBF-FD method for the elliptic eigenvalue problem. The main idea of this method is to select the influential region corresponding to each interpolation node artificially and consider only the influence of the interpolation point in the region on the interpolation node, ignoring the influence of the nodes outside the region. This localization method obtains sparse matrices while losing a certain degree of computational accuracy, so that the algorithm can be applied to the computation of large-scale interpolation node scientific calculations. Through numerical experiments, we study the influence of node layouts, interpolation points, and the shape parameter on the calculation result of the eigenvalue problem, and using three radial basis functions to calculate and compare. The results obtained from the experiments are in good agreement with the analytical solutions to the problem.

Key words: elliptic eigenvalue problem, radial basis function, RBF-FD method, shape parameter