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Title: Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory

We discuss techniques for accelerating the self consistent field (SCF) 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 system 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.
 [1] ;  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1064-8275
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 35; Journal Issue: 5
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING Kohn-Sham density functional theory; self consistent field iteration; fixed point iteration; elliptic preconditioner