42,502 research outputs found
Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
This paper introduces a new sweeping preconditioner for the iterative
solution of the variable coefficient Helmholtz equation in two and three
dimensions. The algorithms follow the general structure of constructing an
approximate factorization by eliminating the unknowns layer by layer
starting from an absorbing layer or boundary condition. The central idea of
this paper is to approximate the Schur complement matrices of the factorization
using moving perfectly matched layers (PMLs) introduced in the interior of the
domain. Applying each Schur complement matrix is equivalent to solving a
quasi-1D problem with a banded LU factorization in the 2D case and to solving a
quasi-2D problem with a multifrontal method in the 3D case. The resulting
preconditioner has linear application cost and the preconditioned iterative
solver converges in a number of iterations that is essentially indefinite of
the number of unknowns or the frequency. Numerical results are presented in
both two and three dimensions to demonstrate the efficiency of this new
preconditioner.Comment: 25 page
Adaptive mesh refinement techniques for high-order finite-volume WENO schemes
This paper demonstrates the capabilities of Adaptive Mesh Refinement Techniques (AMR) on 2D hybrid unstructured meshes, for high order finite volume WENO methods. The AMR technique developed is a conformal adapting unstructured hybrid quadrilaterals and triangles (quads & tris) technique for resolving sharp flow features in accurate manner for steady-state and time dependent flow problems. In this method, the mesh can be refined or coarsened which depends on an error estimator, making decision at the parent level whilst maintaining a conformal mesh, the unstructured hybrid mesh refinement is done hierarchically.When a numerical method can work on a fixed conformal mesh this can be applied to do dynamic mesh adaptation. Two Refinement strategies have been devised both following a H-P refinement technique, which can be applied for providing better resolution to strong gradient dominated problems. The AMR algorithm has been tested on cylindrical explosion test and forward facing step problems
Validity of the one-dimensional limp model for porous materials
A straightforward criterion to determine the limp model validity for porous
materials is addressed here. The limp model is an "equivalent fluid" model
which gives a better description of the porous behavior than the well known
"rigid frame" model. It is derived from the poroelastic Biot model assuming
that the frame has no bulk stiffness. A criterion is proposed to identify the
porous materials for which the limp model can be used. It relies on a new
parameter, the Frame Stiffness Influence FSI based on porous material
properties. The critical values of FSI under which the limp model can be used,
are determined using a 1D analytical modeling for a specific boundary set:
radiation of a vibrating plate covered by a porous layer.Comment: 12th International Student Conference on Electrical Engineering,
Prague : Tch\`eque, R\'epublique (2008
Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
The principle part of Einstein equations in the harmonic gauge consists of a
constrained system of 10 curved space wave equations for the components of the
space-time metric. A new formulation of constraint-preserving boundary
conditions of the Sommerfeld type for such systems has recently been proposed.
We implement these boundary conditions in a nonlinear 3D evolution code and
test their accuracy.Comment: 16 pages, 17 figures, submitted to Phys. Rev.
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
STV-based Video Feature Processing for Action Recognition
In comparison to still image-based processes, video features can provide rich and intuitive information about dynamic events occurred over a period of time, such as human actions, crowd behaviours, and other subject pattern changes. Although substantial progresses have been made in the last decade on image processing and seen its successful applications in face matching and object recognition, video-based event detection still remains one of the most difficult challenges in computer vision research due to its complex continuous or discrete input signals, arbitrary dynamic feature definitions, and the often ambiguous analytical methods. In this paper, a Spatio-Temporal Volume (STV) and region intersection (RI) based 3D shape-matching method has been proposed to facilitate the definition and recognition of human actions recorded in videos. The distinctive characteristics and the performance gain of the devised approach stemmed from a coefficient factor-boosted 3D region intersection and matching mechanism developed in this research. This paper also reported the investigation into techniques for efficient STV data filtering to reduce the amount of voxels (volumetric-pixels) that need to be processed in each operational cycle in the implemented system. The encouraging features and improvements on the operational performance registered in the experiments have been discussed at the end
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