1,559 research outputs found
Left-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)
In this work we study the formulation of convection/diffusion equations on
the 3D motion group SE(3) in terms of the irreducible representations of SO(3).
Therefore, the left-invariant vector-fields on SE(3) are expressed as linear
operators, that are differential forms in the translation coordinate and
algebraic in the rotation. In the context of 3D image processing this approach
avoids the explicit discretization of SO(3) or , respectively. This is
particular important for SO(3), where a direct discretization is infeasible due
to the enormous memory consumption. We show two applications of the framework:
one in the context of diffusion-weighted magnetic resonance imaging and one in
the context of object detection
Spectral Characteristic Evolution: A New Algorithm for Gravitational Wave Propagation
We present a spectral algorithm for solving the full nonlinear vacuum
Einstein field equations in the Bondi framework. Developed within the Spectral
Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a
technical precursor to Cauchy Characteristic Extraction (CCE), a rigorous
method for obtaining gauge-invariant gravitational waveforms from existing and
future astrophysical simulations. We demonstrate the new algorithm's stability,
convergence, and agreement with existing evolution methods. We explain how an
innovative spectral approach enables a two orders of magnitude improvement in
computational efficiency.Comment: 28 pages, 9 figure
Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis
The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.
Schnelle Löser für Partielle Differentialgleichungen
This workshop was well attended by 52 participants with broad geographic representation from 11 countries and 3 continents. It was a nice blend of researchers with various backgrounds
Numerical Relativity: A review
Computer simulations are enabling researchers to investigate systems which
are extremely difficult to handle analytically. In the particular case of
General Relativity, numerical models have proved extremely valuable for
investigations of strong field scenarios and been crucial to reveal unexpected
phenomena. Considerable efforts are being spent to simulate astrophysically
relevant simulations, understand different aspects of the theory and even
provide insights in the search for a quantum theory of gravity. In the present
article I review the present status of the field of Numerical Relativity,
describe the techniques most commonly used and discuss open problems and (some)
future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and
Quantum Gravity. (uses iopart.cls
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