Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique

Real-time adaptive finite element solution of time-dependent Kohn–Sham equation

“…For a Kohn-Sham system which contains N wavefunctions, φ j , j = 1, 2, · · · , N, each of these wavefunctions obeys (2). In the following description of the spatial discretization, the subscript of the wavefunction will be dropped for the simplification.…”

“…The main parameters for the hardware are Intel(R) Core(TM) i5-3470 CPU @ 3.20 GHz (4 cores, 6 M cache), and 8 Gb memory. The software we used in the simulation is AFEABIC [1,2], which is implemented in C++. AFEABIC supports both all-electron and pseudopotential calculations.…”

“…People may refer to [23] for the finite element methods in the electronic structure calculations. Although the finite element methods have been developed for the groundstate calculations of the electronic system in [29,35,2,1,3,10,17], etc., little is known about the application of finite element methods for the RT-TDKS. In [27], a finite element method solver for time-dependent and stationary Schrödinger equations is proposed.…”

Matrix‐Free Locally Adaptive Finite Element Solution of Density‐Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning

“…This is in contrast to a substantial amount of global communication in the plane waves basis with the fast Fourier transform . We note that the FEM has been used as a spatial discretization technique both in the case of Self Consistent Field solution of the DFT as well as the direct minimization of the energy functional . It can also be applied to infinite systems with periodic boundary conditions …”

Simulation of thin film flows with a moving mesh mixed finite element method

“…The moving mesh strategy used in this work is originally proposed in [18,19] and has been widely extended and applied to many applications. For example, it has been successfully utilized in the 1D and 2D hyperbolic systems of conservation laws [20], the spike dynamics of the singularity perturbed Gierer-Meinhardt model in 2D [21], the dendritic growth in 2D and 3D governed by a phase-field model [22] and the simulations of Kohn-Sham equation [23]. A review of this moving mesh strategy may be found in [24].…”