1,631 research outputs found
Spectral-based Propagation Schemes for Time-Dependent Quantum Systems with Application to Carbon Nanotubes
Effective modeling and numerical spectral-based propagation schemes are
proposed for addressing the challenges in time-dependent quantum simulations of
systems ranging from atoms, molecules, and nanostructures to emerging
nanoelectronic devices. While time-dependent Hamiltonian problems can be
formally solved by propagating the solutions along tiny simulation time steps,
a direct numerical treatment is often considered too computationally demanding.
In this paper, however, we propose to go beyond these limitations by
introducing high-performance numerical propagation schemes to compute the
solution of the time-ordered evolution operator. In addition to the direct
Hamiltonian diagonalizations that can be efficiently performed using the new
eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a
basis transformed propagation scheme (BTPS) which allow to reduce considerably
the simulation times needed by time intervals. It is outlined that BTPS offers
the best computational efficiency allowing new perspectives in time-dependent
simulations. Finally, these numerical schemes are applied to study the AC
response of a (5,5) carbon nanotube within a 3D real-space mesh framework
Parallel eigensolvers in plane-wave Density Functional Theory
We consider the problem of parallelizing electronic structure computations in
plane-wave Density Functional Theory. Because of the limited scalability of
Fourier transforms, parallelism has to be found at the eigensolver level. We
show how a recently proposed algorithm based on Chebyshev polynomials can scale
into the tens of thousands of processors, outperforming block conjugate
gradient algorithms for large computations
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
Progress in multi-dimensional upwind differencing
Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes
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