27 research outputs found
Multifractality of wavefunctions at the quantum Hall transition revisited
We investigate numerically the statistics of wavefunction amplitudes
at the integer quantum Hall transition. It is demonstrated that
in the limit of a large system size the distribution function of is
log-normal, so that the multifractal spectrum is exactly parabolic.
Our findings lend strong support to a recent conjecture for a critical theory
of the quantum Hall transition.Comment: 4 pages Late
Non-Equilibrium Electron Transport in Two-Dimensional Nano-Structures Modeled by Green's Functions and the Finite-Element Method
We use the effective-mass approximation and the density-functional theory
with the local-density approximation for modeling two-dimensional
nano-structures connected phase-coherently to two infinite leads. Using the
non-equilibrium Green's function method the electron density and the current
are calculated under a bias voltage. The problem of solving for the Green's
functions numerically is formulated using the finite-element method (FEM). The
Green's functions have non-reflecting open boundary conditions to take care of
the infinite size of the system. We show how these boundary conditions are
formulated in the FEM. The scheme is tested by calculating transmission
probabilities for simple model potentials. The potential of the scheme is
demonstrated by determining non-linear current-voltage behaviors of resonant
tunneling structures.Comment: 13 pages,15 figure
A fast multifrontal solver for non-linear multi-physics problems
The paper presents a highly optimized implementation of a multifrontal solver for linear systems arising in the FEM simulation of multi-physics problems related to the behaviour of porous media. The solver features a careful preprocessing
phase that is crucial to considerably speed up both system assembly and Gaussian elimination. When run on a number of relevant test cases, the proposed solver compares very favourably with both its previous unifrontal counterpart and two general multifrontal solvers well known in the literature
Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry
In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork bifurcation occurs when the underlying physical system possesses rotational and reflectional or O(2) symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual Weighted Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented. Here, particular attention is devoted to the problem of flow through a cylindrical pipe with a sudden expansion, which represents a notoriously difficult computational problem
Analysis and comparison of two general sparse solvers for distributed memory computers
This paper provides a comprehensive study and comparison of two state-of-the-art direct solvers for large sparse sets of linear equations on large-scale distributed-memory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. We describe the main algorithmic features of the two solvers and compare their performance characteristics with respect to uniprocessor speed, interprocessor communication, and memory requirements. For both solvers, preorderings for numerical stability and sparsity play an important role in achieving high parallel efficiency. We analyse the results with various ordering algorithms. Our performance analysis is based on data obtained from runs on a 512-processor Cray T3E using a set of matrices from real applications. We also use regular 3D grid problems to study the scalability of the two solvers