62 research outputs found
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment
Impurity effects in quasiparticle spectrum of high-Tc superconductors
The revision is made of Green function methods that describe the dynamics of electronic quasiparticles in disordered superconducting systems with d-wave symmetry of order parameter. Various types of impurity perturbations are analyzed within the simplest T-matrix approximation. The extension of the common selfconsistent T-matrix approximation (SCTMA) to the so-called group expansions in clusters of interacting impurity centers is discussed and hence the validity criteria for SCTMA are established. A special attention is payed to the formation of impurity resonance states and localized states near the characteristic points of energy spectrum, corresponding to nodal points on the Fermi surface
Snapshot-Based Methods and Algorithms
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science
Fast iterative solvers for Cahn-Hilliard problems
Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016von M. Sc. Jessica BoschLiteraturverzeichnis: Seite [247]-25
Model Order Reduction
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science
Splitting methods based on algebraic factorization for fluid-structure interaction
We discuss in this paper the numerical approximation of fluid-structure interaction (FSI) problems dealing with strong added-mass effect. We propose new semi-implicit algorithms based on inexact block- factorization of the linear system obtained after the space-time discretization and linearization of the FSI problem. As a result, the fluid velocity is computed separately from the coupled pressure-structure velocity system at each iteration, reducing the computational cost. We investigate explicit-implicit decomposition through algebraic splitting techniques originally designed for the FSI problem. This approach leads to two different families of methods which extend to FSI the algebraic pressure correction method and the Yosida method, two schemes that were previously adopted for pure fluid problems. Furthermore, we have considered the inexact factorization of the fluid-structure system as a preconditioner. The numerical properties of these methods have been tested on a model problem representing a blood-vessel system. 
Numerical modelling in a multiscale ocean
Systematic improvement in ocean modelling and prediction systems over the past several decades has resulted from several concurrent factors. The first of these has been a sustained increase in computational power, as summarized in Moore\u27s Law, without which much of this recent progress would not have been possible. Despite the limits imposed by existing computer hardware, however, significant accruals in system performance over the years have been achieved through novel innovations in system software, specifically the equations used to represent the temporal evolution of the oceanic state as well as the numerical solution procedures employed to solve them. Here, we review several recent approaches to system design that extend our capability to deal accurately with the multiple time and space scales characteristic of oceanic motion. The first two are methods designed to allow flexible and affordable enhancement in spatial resolution within targeted regions, relying on either a set of nested structured grids or, alternatively, a single unstructured grid. Finally, spatial discretization of the continuous equations necessarily omits finer, subgrid-scale processes whose effects on the resolved scales of motion cannot be neglected. We conclude with a discussion of the possibility of introducing subgrid-scale parameterizations to reflect the influences of unresolved processes
Recommended from our members
High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs
Partial differential equations constrained by involutions provide the highest fidelity mathematical models for a large number of complex physical systems of fundamental interest in critical scientific and technological disciplines. The applications described by these models include electromagnetics, continuum dynamics of solid media, and general relativity. This workshop brought together pure and applied mathematicians to discuss current research that cuts across these various disciplines’ boundaries. The presented material illuminated fundamental issues as well as evolving theoretical and algorithmic approaches for PDEs with involutions. The scope of the material covered was broad, and the discussions conducted during the workshop were lively and far-reaching
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