Superconvergence of high order FEMs for eigenvalue problems with periodic boundary conditions

Huang, Hung‐Tsai; Chang, S.-L.; Chien, C.-S.; Zou, Xiaoyong

doi:10.1016/j.cma.2009.02.038

Cited by 8 publications

(1 citation statement)

References 31 publications

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“…Typically, the FE method has been used to solve engineering problems [19], but recently it has also been applied to solve the Kohn-Sham equations as well [20][21][22][23][24][25][26][27], as described in some review papers [28,29]. The key aspects of the FE method are: (i) strict mathematical variational formulation; (ii) welldefined procedure for generation of basis functions.…”

Section: Introductionmentioning

confidence: 99%

B-spline solver for one-electron Schrödinger equation

Romanowski¹

2011

Molecular Physics

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A numerical algorithm for solving the one-electron Schro¨dinger equation is presented. The algorithm is based on the Finite Element method, and the basis functions are tensor products of univariate B-splines. The application of cubic or higher order B-splines guarantees that the searched solution belongs to a continuous and one time differentiable function space, which is a desirable property in the Kohn-Sham equation context from the Density Functional Theory with pseudopotential approximation. The theoretical background of the numerical algorithm is presented, and additionally, the implementation on parallel computers with distributed memory is described. The current implementation of the algorithm uses the MPI, HYPRE and ParMETIS libraries to distribute matrices on processing units. Additionally, the LOBPCG algorithm from HYPRE library is used to solve the algebraic generalized eigenvalue problem. The proposed algorithm works for any smooth interaction potential, where the domain of the problem is a finite subspace of the R 3 space. The accuracy of the algorithm is demonstrated for a selected interaction potential. In the current stage, the algorithm can be applied to solve the linearized Kohn-Sham equation for molecular systems.

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