### Abstract

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

Original language | English (US) |
---|---|

Pages (from-to) | 743-758 |

Number of pages | 16 |

Journal | Journal of Computational Physics |

Volume | 281 |

DOIs | |

State | Published - Jan 5 2015 |

### Profile

### Keywords

- Crank-Nicolson
- Finite element methods
- Mesh adaptive methods
- Multigrid for complex system
- Time-dependent Kohn-Sham

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Computational Physics*,

*281*, 743-758. DOI: 10.1016/j.jcp.2014.10.052

**Real-time adaptive finite element solution of time-dependent Kohn-Sham equation.** / Bao, Gang; Hu, Guanghui; Liu, Di.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol 281, pp. 743-758. DOI: 10.1016/j.jcp.2014.10.052

}

TY - JOUR

T1 - Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

AU - Bao,Gang

AU - Hu,Guanghui

AU - Liu,Di

PY - 2015/1/5

Y1 - 2015/1/5

N2 - In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

AB - In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

KW - Crank-Nicolson

KW - Finite element methods

KW - Mesh adaptive methods

KW - Multigrid for complex system

KW - Time-dependent Kohn-Sham

UR - http://www.scopus.com/inward/record.url?scp=84909619184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84909619184&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2014.10.052

DO - 10.1016/j.jcp.2014.10.052

M3 - Article

VL - 281

SP - 743

EP - 758

JO - Journal of Computational Physics

T2 - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -