期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 35, 期 5, 页码 S277-S298出版社
SIAM PUBLICATIONS
DOI: 10.1137/120880604
关键词
Kohn-Sham density functional theory; self-consistent field iteration; fixed point iteration; elliptic preconditioner
资金
- Lawrence Berkeley National Laboratory under the U.S. Department of Energy [DE-AC02-05CH11231]
- Scientific Discovery through Advanced Computing (SciDAC) program
- U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences
We discuss techniques for accelerating the self-consistent field iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied by the total potential. They can be viewed as preconditioners for a fixed point iteration. We point out different requirements for constructing preconditioners for insulating and metallic systems, respectively, and discuss how to construct preconditioners to keep the convergence rate of the fixed point iteration independent of the size of the atomistic system. We propose a new preconditioner that can treat insulating and metallic systems in a unified way. The new preconditioner, which we call an elliptic preconditioner, is constructed by solving an elliptic partial differential equation. The elliptic preconditioner is shown to be more effective in accelerating the convergence of a fixed point iteration than the existing approaches for large inhomogeneous systems at low temperature.
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