A combinational efficient algorithm for elliptic eigenvalue problems. Issue 2 (June 2016)

• Record Type: Journal Article
• Authors: Zhang, Huirong; Cao, Jianwen
• Is Part Of: Journal of algorithms & computational technology. Volume 10:Issue 2(2016)
• Page Start: 115
• Page End: 126
• Publication Date: 2016-06
• Subjects: Combinational algorithm -- quasi-optimal -- mass lumping -- eigenproblem; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748301816651942
• Languages: English
• ISSNs: 1748-3018

Abstract

In this paper, we present a combinational efficient algorithm for solving second-order elliptic ordinary differential equation eigenvalue problems on four kinds of meshes. Firstly, a combinational scheme is proposed by leveraging the linear finite element scheme and the second-order finite difference scheme based on mass lumping method. An efficient algorithm is constructed by using the combinational scheme with a constant combined parameter. Then, we improve the efficient algorithm by computing the quasi-optimal combined parameters for different eigenvalues. Finally, numerical experiments tested on both uniform and nonuniform meshes are shown to illustrate the efficiency of our algorithms.