28 research outputs found
Analysis of reduced finite element schemes in parameter dependent elliptic problems
This thesis presents an analysis of modified finite element schemes applied to parameter dependent elliptic problems prone to locking. Two different problems of similar type are considered: the problem of anisotropic heat conduction and the thin shell problem.reviewe
Large-scale surface reconstruction energetics of Pt(100) and Au(100) by all-electron DFT
The low-index surfaces of Au and Pt all tend to reconstruct, a fact that is
of key importance in many nanostructure, catalytic, and electrochemical
applications. Remarkably, some significant questions regarding their structural
energies remain even today, in particular for the large-scale quasihexagonal
reconstructed (100) surfaces: Rather dissimilar reconstruction energies for Au
and Pt in available experiments, and experiment and theory do not match for Pt.
We here show by all-electron density-functional theory that only large enough
"(5 x N)" approximant supercells capture the qualitative reconstruction energy
trend between Au(100) and Pt(100), in contrast to what is often done in the
theoretical literature. Their magnitudes are then in fact similar, and closer
to the measured value for Pt(100); our calculations achieve excellent agreement
with known geometric characteristics and provide direct evidence for the
electronic reconstruction driving force.Comment: updated version - also includes EPAPS information as auxiliary file;
related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm
Nonadiabatic Ehrenfest molecular dynamics within the projector augmented-wave method
We have derived equations for nonadiabatic Ehrenfest molecular dynamics which
conserve the total energy in the case of time-dependent discretization for
electrons. A discretization is time-dependent in all cases where it or part of
it depends on the positions of the nuclei, for example, in atomic orbital basis
sets, and in the projector augmented-wave (PAW) method, where the augmentation
functions depend on the nuclear positions. We have derived, implemented, and
analyzed the energy conserving equations and their most common approximations
for a 1D test system where we can achieve numerical results converged to a high
accuracy. Based on the observations in 1D, we implement and analyze the
Ehrenfest molecular dynamics in 3D using the PAW method and the time-dependent
density functional formalism. We demonstrate the applicability of our method by
carrying out calculations for small and medium sized molecules in both the
adiabatic and the nonadiabatic regime.Comment: 12 pages, 10 figure
All-electron density functional theory and time-dependent density functional theory with high-order finite elements
We present for static density functional theory and time-dependent density
functional theory calculations an all-electron method which employs high-order
hierarchical finite element bases. Our mesh generation scheme, in which
structured atomic meshes are merged to an unstructured molecular mesh, allows a
highly nonuniform discretization of the space. Thus it is possible to represent
the core and valence states using the same discretization scheme, i.e., no
pseudopotentials or similar treatments are required. The nonuniform
discretization also allows the use of large simulation cells, and therefore
avoids any boundary effects.Comment: 11 pages, 9 figures; final (=published) versio
All-electron time-dependent density functional theory with finite elements: Time-propagation approach
We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers.Peer reviewe
Student behaviour and engagement with adaptive exercises on a thermodynamics course
A teaching experiment was carried out in a university-level thermodynamics
course using adaptive and interactive e-learning material, created in the new
Moodle question type Stateful extending the original e-learning platform STACK.
The system collects data about the students that is used to algorithmically
classify them according to their behaviour in solving problems. It is observed
that the classification of this data predicts students' success in the other
parts of the course for a majority of students. Also, the classification is
statistically consistent with Thermodynamic Concept Survey and Maryland Physics
Expectation Survey