Journal
MULTISCALE MODELING & SIMULATION
Volume 20, Issue 1, Pages 524-550Publisher
SIAM PUBLICATIONS
DOI: 10.1137/21M1396241
Keywords
electronic structure calculation; planewave method; energy cut-off; a posteriori error estimate; adaptive algorithm; projector augmented wave method
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In this paper, we propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates, effectively updating the energy cut-off for planewave discretizations. It is error controllable for linear eigenvalue problems and shows promising potential for reducing the cost of iterations in self-consistent algorithms for nonlinear eigenvalue problems.
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy cut-off for planewave discretizations, for both linear and nonlinear eigenvalue problems. The method is error controllable for linear eigenvalue problems in the sense that for a given required accuracy, an energy cut-off for which the solution matches the target accuracy can be reached efficiently. Further, the method is particularly promising for nonlinear eigenvalue problems in electronic structure calculations as it shall reduce the cost of early iterations in self-consistent algorithms. We present some numerical experiments for both linear and nonlinear eigenvalue problems. In particular, we provide electronic structure calculations for some insulator and metallic systems simulated with the Kohn--Sham density functional theory and the projector augmented wave method, illustrating the efficiency and potential of the algorithm.
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