8,379 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
Institute for Computational Mechanics in Propulsion (ICOMP)
The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described
An open and parallel multiresolution framework using block-based adaptive grids
A numerical approach for solving evolutionary partial differential equations
in two and three space dimensions on block-based adaptive grids is presented.
The numerical discretization is based on high-order, central finite-differences
and explicit time integration. Grid refinement and coarsening are triggered by
multiresolution analysis, i.e. thresholding of wavelet coefficients, which
allow controlling the precision of the adaptive approximation of the solution
with respect to uniform grid computations. The implementation of the scheme is
fully parallel using MPI with a hybrid data structure. Load balancing relies on
space filling curves techniques. Validation tests for 2D advection equations
allow to assess the precision and performance of the developed code.
Computations of the compressible Navier-Stokes equations for a temporally
developing 2D mixing layer illustrate the properties of the code for nonlinear
multi-scale problems. The code is open source
An Iterative Shrinkage Approach to Total-Variation Image Restoration
The problem of restoration of digital images from their degraded measurements
plays a central role in a multitude of practically important applications. A
particularly challenging instance of this problem occurs in the case when the
degradation phenomenon is modeled by an ill-conditioned operator. In such a
case, the presence of noise makes it impossible to recover a valuable
approximation of the image of interest without using some a priori information
about its properties. Such a priori information is essential for image
restoration, rendering it stable and robust to noise. Particularly, if the
original image is known to be a piecewise smooth function, one of the standard
priors used in this case is defined by the Rudin-Osher-Fatemi model, which
results in total variation (TV) based image restoration. The current arsenal of
algorithms for TV-based image restoration is vast. In the present paper, a
different approach to the solution of the problem is proposed based on the
method of iterative shrinkage (aka iterated thresholding). In the proposed
method, the TV-based image restoration is performed through a recursive
application of two simple procedures, viz. linear filtering and soft
thresholding. Therefore, the method can be identified as belonging to the group
of first-order algorithms which are efficient in dealing with images of
relatively large sizes. Another valuable feature of the proposed method
consists in its working directly with the TV functional, rather then with its
smoothed versions. Moreover, the method provides a single solution for both
isotropic and anisotropic definitions of the TV functional, thereby
establishing a useful connection between the two formulae.Comment: The paper was submitted to the IEEE Transactions on Image Processing
on October 22nd, 200
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