Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method

2016 ◽  
Vol 59 (2) ◽  
pp. 317-334 ◽  
Author(s):  
Jinyou Xiao ◽  
Hang Zhou ◽  
Chuanzeng Zhang ◽  
Chao Xu
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Ritz Method ◽  
Nonlinear Eigenvalue Problems ◽  
Nonlinear Eigenvalue

Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics

2011 ◽  
Vol 3 (4) ◽  
pp. 493-518 ◽  
Author(s):  
Huajie Chen ◽  
Xingao Gong ◽  
Lianhua He ◽  
Aihui Zhou
Keyword(s):  
Finite Element ◽  
Quantum Physics ◽  
Eigenvalue Problems ◽  
Energy Functional ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Nonlinear Eigenvalue Problems ◽  
Finite Element Approximations ◽  
Nonconvex Energy ◽  
Nonlinear Eigenvalue

AbstractIn this paper, we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy functional. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.

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