117 research outputs found
Absorbing boundary conditions for the Westervelt equation
The focus of this work is on the construction of a family of nonlinear
absorbing boundary conditions for the Westervelt equation in one and two space
dimensions. The principal ingredient used in the design of such conditions is
pseudo-differential calculus. This approach enables to develop high order
boundary conditions in a consistent way which are typically more accurate than
their low order analogs. Under the hypothesis of small initial data, we
establish local well-posedness for the Westervelt equation with the absorbing
boundary conditions. The performed numerical experiments illustrate the
efficiency of the proposed boundary conditions for different regimes of wave
propagation
Super-resolution of faces using texture mapping on a generic 3D model
This paper proposes a novel face texture mapping framework to transform faces with different poses into a unique texture map. Under this framework, texture mapping can be realized by utilizing a generic 3D face model, standard Haar-like feature based detector, active appearance model and pose estimation algorithm. By this texture map, correspondence of every pixel at the face across multiple distinct input images can then be established, which enables super-resolution algorithms to be applied directly on registered texture map to render high resolution faces. This paper details the proposed framework, and illustrates how the proposed super-resolution algorithm works with the help of weighted average and median filters. Convincing experimental results are also presented to validate the effectiveness of the proposed framework and superresolution algorithm. © 2009 IEEE.published_or_final_versio
Time reversal methods in acousto-elastodynamics
The aim of the article is to solve an inverse problem in order to determine the presence and some properties of an elastic “inclusion” (an unknown object, characterized by elastic properties discriminant from the surrounding medium) from partial observa- tions of acoustic waves, scattered by the inclusion. The method will require developing techniques based on Time Reversal methods. A finite element method based on varia- tional acousto-elastodynamics formulation will be derived and used to solve to solve the forward, and then, the time reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help use to construct images of the inclusions to be determined. Our approach will be applied to configurations modeling breast cancer detection, using simulated ultrasound waves
A unified approach to split absorbing boundary conditions for nonlinear Schr\"{o}dinger equations
An efficient method is proposed for numerical solutions of nonlinear
Schr\"{o}dinger equations in an unbounded domain. Through approximating the
kinetic energy term by a one-way equation and uniting it with the potential
energy equation, absorbing boundary conditions are designed to truncate the
unbounded domain, which are in nonlinear form and can perfectly absorb the
waves outgoing from the truncated domain. We examine the stability of the
induced initial boundary value problems defined on the computational domain
with the boundary conditions by a normal mode analysis. Numerical examples are
given to illustrate the stable and tractable advantages of the method.Comment: 17 pages, 6 figures, 40 conference
Adaptive Mesh Refinement for Characteristic Grids
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when
numerically solving partial differential equations with wave-like solutions,
using characteristic (double-null) grids. Such AMR algorithms are naturally
recursive, and the best-known past Berger-Oliger characteristic AMR algorithm,
that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on
individual "diamond" characteristic grid cells. This leads to the use of
fine-grained memory management, with individual grid cells kept in
2-dimensional linked lists at each refinement level. This complicates the
implementation and adds overhead in both space and time.
Here I describe a Berger-Oliger characteristic AMR algorithm which instead
recurses on null \emph{slices}. This algorithm is very similar to the usual
Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory
management, allowing entire null slices to be stored in contiguous arrays in
memory. The algorithm is very efficient in both space and time.
I describe discretizations yielding both 2nd and 4th order global accuracy.
My code implementing the algorithm described here is included in the electronic
supplementary materials accompanying this paper, and is freely available to
other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are
viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3
document class, includes C++ source code. Changes from v1: revised in
response to referee comments: many references added, new figure added to
better explain the algorithm, other small changes, C++ code updated to latest
versio
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress is traced from
the early stage of 1D feasibility studies to 2D axisymmetric codes that
accurately simulate the oscillations and gravitational collapse of relativistic
stars and to current 3D codes that provide pieces of a binary black spacetime.
A prime application of characteristic evolution is to compute waveforms via
Cauchy-characteristic matching, which is also reviewed.Comment: Published version http://www.livingreviews.org/lrr-2005-1
A stratified dispersive wave model with high-order nonreflecting boundary conditions
http://dx.doi.org/10/1016/j.camwa.2004.10.013A layered-model in introduced to approximate the effects of stratification on linearized shallow wave equations. This time-dependent dispersive wave model is appropriate for describing geophysical (e.g. atmmospheric or oceanic) dynamics. However, computational models that embrace these very large domains that are global in magnitude can quickly overwhelm computer capabilities. The domain is therefore truncated via artificial boundaries, and nonreflecting boundary conditions (NRBC) devised by Higdon are imposed. A scheme previously proposed by Neta and Givoli that easily discretizes high-order Higdon NRBCs is used. The problem is solved by finite difference (FD) methods. Numerical examples follow the discussion
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