Finite Volume Discretizations for Eigenvalue Problems with Applications to Electronic Structure Calculations
2011
To introduce the finite volume method to electronic structure calculations, we study a symmetric finite volume scheme for a class of linear eigenvalue problems and present a priori error analysis of the finite volume eigenpair approximations. Based on finite volume-finite element coupled discretizations, in particular, we design several higher order approximate schemes. We also demonstrate a series of numerical experiments in electronic structure calculations that illustrate the effectiveness of our finite volume discretization approaches.
Keywords:
- Mathematical analysis
- Finite volume method
- Mixed finite element method
- Mathematical optimization
- Extended finite element method
- Mathematics
- Finite element method
- Discretization
- Finite volume method for one-dimensional steady state diffusion
- Regular grid
- Finite difference coefficient
- Eigenvalues and eigenvectors
- Correction
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