2,916 research outputs found
Accuracy control in ultra-large-scale electronic structure calculation
Numerical aspects are investigated in ultra-large-scale electronic structure
calculation. Accuracy control methods in process (molecular-dynamics)
calculation are focused. Flexible control methods are proposed so as to control
variational freedoms, automatically at each time step, within the framework of
generalized Wannier state theory. The method is demonstrated in silicon
cleavage simulation with 10^2-10^5 atoms. The idea is of general importance
among process calculations and is also used in Krylov subspace theory, another
large-scale-calculation theory.Comment: 8 pages, 3 figures. To appear in J.Phys. Condens. Matter. A preprint
PDF file in better graphics is available at
http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm
Large-scale electronic structure theory for simulating nanostructure process
Fundamental theories and practical methods for large-scale electronic
structure calculations are given, in which the computational cost is
proportional to the system size. Accuracy controlling methods for microscopic
freedoms are focused on two practical solver methods, Krylov-subspace method
and generalized-Wannier-state method. A general theory called the
'multi-solver' scheme is also formulated, as a hybrid between different solver
methods. Practical examples are carried out in several insulating and metallic
systems with 10^3-10^5 atoms. All the theories provide general guiding
principles of constructing an optimal calculation for simulating nanostructure
processes, since a nanostructured system consists of several competitive
regions, such as bulk and surface regions, and the simulation is designed to
reproduce the competition with an optimal computational cost.Comment: 19 pages, 6 figures. To appear in J. Phys. Cond. Matt. A preprint PDF
file in better graphics is available at
http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm
An order-N electronic structure theory with generalized eigenvalue equations and its application to a ten-million-atom system
A linear-algebraic theory called 'multiple Arnoldi method' is presented and
realizes large-scale (order-N) electronic structure calculation with
generalized eigen-value equations. A set of linear equations, in the form of
(zS-H) x = b, are solved simultaneously with multiple Krylov subspaces. The
method is implemented in a simulation package ELSES (http://www.elses.jp) with
tight-binding-form Hamiltonians. A finite-temperature molecular dynamics
simulation is carried out for metallic and insulating materials. A calculation
with atoms was realized by a workstation. The parallel efficiency is
shown upto 1,024 CPU cores.Comment: 9 pages, 3 figures. To appear in J. Phys.: Condens. Matte
Dynamical brittle fractures of nanocrystalline silicon using large-scale electronic structure calculations
A hybrid scheme between large-scale electronic structure calculations is
developed and applied to nanocrystalline silicon with more than 10 atoms.
Dynamical fracture processes are simulated under external loads in the [001]
direction. We shows that the fracture propagates anisotropically on the (001)
plane and reconstructed surfaces appear with asymmetric dimers. Step structures
are formed in larger systems, which is understood as the beginning of a
crossover between nanoscale and macroscale samples.Comment: 10 pages, 4 figure
Krylov Subspace Method for Molecular Dynamics Simulation based on Large-Scale Electronic Structure Theory
For large scale electronic structure calculation, the Krylov subspace method
is introduced to calculate the one-body density matrix instead of the
eigenstates of given Hamiltonian. This method provides an efficient way to
extract the essential character of the Hamiltonian within a limited number of
basis set. Its validation is confirmed by the convergence property of the
density matrix within the subspace. The following quantities are calculated;
energy, force, density of states, and energy spectrum. Molecular dynamics
simulation of Si(001) surface reconstruction is examined as an example, and the
results reproduce the mechanism of asymmetric surface dimer.Comment: 7 pages, 3 figures; corrected typos; to be published in Journal of
the Phys. Soc. of Japa
Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations
We present a simple and efficient technique in ab initio electronic-structure
calculation utilizing real-space double-grid with a high density of grid points
in the vicinity of nuclei. This technique promises to greatly reduce the
overhead for performing the integrals that involves non-local parts of
pseudopotentials, with keeping a high degree of accuracy. Our procedure gives
rise to no Pulay forces, unlike other real-space methods using adaptive
coordinates. Moreover, we demonstrate the potential power of the method by
calculating several properties of atoms and molecules.Comment: 4 pages, 5 figure
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