Finite element method for solving Kohn–Sham equations based on self-adaptive tetrahedral mesh

A finite element (FE) method with self-adaptive mesh-refinement technique is developed for solving the density functional Kohn–Sham equations. The FE method adopts local piecewise polynomials basis functions, which produces sparsely structured matrices of Hamiltonian. The method is well suitable for parallel implementation without using Fourier transform. In addition, the self-adaptive mesh-refinement technique can control the computational accuracy and efficiency with optimal mesh density in different regions.