215 research outputs found
Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations
The iterative diagonalization of a sequence of large ill-conditioned
generalized eigenvalue problems is a computational bottleneck in quantum
mechanical methods employing a nonorthogonal basis for {\em ab initio}
electronic structure calculations. We propose a hybrid preconditioning scheme
to effectively combine global and locally accelerated preconditioners for rapid
iterative diagonalization of such eigenvalue problems. In partition-of-unity
finite-element (PUFE) pseudopotential density-functional calculations,
employing a nonorthogonal basis, we show that the hybrid preconditioned block
steepest descent method is a cost-effective eigensolver, outperforming current
state-of-the-art global preconditioning schemes, and comparably efficient for
the ill-conditioned generalized eigenvalue problems produced by PUFE as the
locally optimal block preconditioned conjugate-gradient method for the
well-conditioned standard eigenvalue problems produced by planewave methods
On (non-)monotonicity and phase diagram of finitary random interlacement
In this paper, we study the evolution of a Finitary Random Interlacement
(FRI) with respect to the expected length of each fiber. In contrast to the
previously proved phase transition between sufficiently large and small fiber
length, we show that for , FRI is NOT stochastically monotone as fiber
length increasing. At the same time, numerical evidences still strongly support
the existence of a unique and sharp phase transition on the existence of a
unique infinite cluster, while the critical value for phase transition is
estimated to be an inversely proportional function with respect to the system
intensity
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