This article presents a Taylor collocation method for the approximate solution of high-order linear Volterra-Fredholm integrodifferential equations with linear functional arguments. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Some numerical examples, which consist of initial and boundary conditions, are given to show the properties of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
viernes, 6 de noviembre de 2009
A collocation approach for the numerical solution of certain linear retarded and advanced integrodifferential equations with linear functional arguments
This article presents a Taylor collocation method for the approximate solution of high-order linear Volterra-Fredholm integrodifferential equations with linear functional arguments. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Some numerical examples, which consist of initial and boundary conditions, are given to show the properties of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Difference methods for computing the Ginzburg-Landau equation in two dimensions
In this article, three difference schemes of the Ginzburg-Landau Equation in two dimensions are presented. In the three schemes, the nonlinear term is discretized such that nonlinear iteration is not needed in computation. The plane wave solution of the equation is studied and the truncation errors of the three schemes are obtained. The three schemes are unconditionally stable. The stability of the two difference schemes is proved by induction method and the time-splitting method is analysized by linearized analysis. The algebraic multigrid method is used to solve the three large linear systems of the schemes. At last, we compute the plane wave solution and some dynamics of the equation. The numerical results demonstrate that our schemes are reliable and efficient. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
B-spline collocation algorithms for numerical solution of the RLW equation
Both sextic and septic B-spline collocation algorithms are presented for the numerical solutions of the RLW equation. Numerical results resolve the fine structure of the single solitary wave propagation, two and three solitary waves interaction, and evolution of solitary waves. Comparison of the numerical results is done by the results of some earlier schemes mentioned in the article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Vertex singularities associated with conical points for the 3D Laplace equation
The solution u to the Laplace equation in the neighborhood of a vertex in a three-dimensional domain may be described by an asymptotic series in terms of spherical coordinates u = [sum] iAi[rho][nu]ifi([thetas],[phiv]). For conical vertices, we derive explicit analytical expressions for the eigenpairs [nu]i and fi([thetas],[phiv]), which are required as benchmark solutions for the verification of numerical methods. Thereafter, we extend the modified Steklov eigen-formulation for the computation of vertex eigenpairs using p/spectral finite element methods and demonstrate its accuracy and high efficiency by comparing the numerically computed eigenpairs to the analytical ones. Vertices at the intersection of a crack front and a free surface are also considered and numerical eigenpairs are provided. The numerical examples demonstrate the efficiency, robustness, and high accuracy of the proposed method, hence its potential extension to elasticity problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
A block monotone iterative method for numerical solutions of nonlinear elliptic boundary value problems
The aim of this article is to develop a new block monotone iterative method for the numerical solutions of a nonlinear elliptic boundary value problem. The boundary value problem is discretized into a system of nonlinear algebraic equations, and a block monotone iterative method is established for the system using an upper solution or a lower solution as the initial iteration. The sequence of iterations can be computed in a parallel fashion and converge monotonically to a maximal solution or a minimal solution of the system. Three theoretical comparison results are given for the sequences from the proposed method and the block Jacobi monotone iterative method. The comparison results show that the sequence from the proposed method converges faster than the corresponding sequence given by the block Jacobi monotone iterative method. A simple and easily verified condition is obtained to guarantee a geometric convergence of the block monotone iterations. The numerical results demonstrate advantages of this new approach. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem
In this article we analyze the well-posedness (unique solvability, stability, and Céa's estimate) of a family of Galerkin schemes for the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. We consider the usual primal formulation in the Stokes domain and the dual-mixed one in the Darcy region, which yields a compact perturbation of an invertible mapping as the resulting operator equation. We then apply a classical result on projection methods for Fredholm operators of index zero to show that use of any pair of stable Stokes and Darcy elements implies the well-posedness of the corresponding Stokes-Darcy Galerkin scheme. This extends previous results showing well-posedness only for Bernardi-Raugel and Raviart-Thomas elements. In addition, we show that under somewhat more demanding hypotheses, an alternative approach that makes no use of compactness arguments can also be applied. Finally, we provide several numerical results illustrating the good performance of the Galerkin method for different geometries of the problem using the MINI element and the Raviart-Thomas subspace of lowest order. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
The journal Communications in Numerical Methods in Engineering with Biomedical Applications becomes the International Journal for Numerical Methods in Biomedical Engineering (IJNMBE) from 1st January 2010
Communications in Numerical Methods in Engineering, founded by Roland W. Lewis in 1985, will change its title to the 'International Journal for Numerical Methods in Biomedical Engineering' and has a revised Aims and Scope. Copyright © 2009 John Wiley & Sons, Ltd.
Predicting User-Cell Association in Cellular Networks from Tracked Data
We consider the problem of predicting user location in the form of user-cell association in a cellular wireless network. This is motivated by resource optimization, for example switching base transceiver stations on or off to save on network energy consumption. We use GSM traces obtained from an operator, and compare several prediction methods. First, we find that, on our trace data, user cell sector association can be correctly predicted in ca. 80% of the cases. Second, we propose a new method, called “MARPL”, which uses Market Basket Analysis to separate patterns where prediction by partial match (PPM) works well from those where repetition of the last known location (LAST) is best. Third, we propose that for network resource optimization, predicting the aggregate location of a user ensemble may be of more interest than separate predictions for all users; this motivates us to develop soft prediction methods, where the prediction is a spatial probability distribution rather than the most likely location. Last, we compare soft predictions methods to a classical time and space analysis (ISTAR). In terms of relative mean square error, MARPL with soft prediction and ISTAR perform better than all other methods, with a slight advantage to MARPL (but the numerical complexity of MARPL is much less than ISTAR).
A note on an approximate lagrange multiplier rule
Abstract In this note we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the
approximate multiplier rule.
approximate multiplier rule.
- Content Type Journal Article
- Category Full Length Paper
- DOI 10.1007/s10107-009-0320-7
- Authors
- Joydeep Dutta, Indian Institute of Technology Department of Mathematics and Statistics Kanpur India
- Suvendu Ranjan Pattanaik, Indian Institute of Technology Department of Mathematics and Statistics Kanpur India
- Michel Théra, XLIM (UMR-CNRS 6172) and Université de Limoges 123 Avenue A. Thomas 87060 Limoges Cedex France
- Journal Mathematical Programming
- Online ISSN 1436-4646
- Print ISSN 0025-5610
On totally Fenchel unstable functions in finite dimensional spaces
Abstract We give an answer to the Problem 11.6 posed by Stephen Simons in his book “From Hahn-Banach to Monotonicity”: Do there exist
a nonzero finite dimensional Banach space and a pair of extended real-valued, proper and convex functions which is totally
Fenchel unstable? The answer is negative.
a nonzero finite dimensional Banach space and a pair of extended real-valued, proper and convex functions which is totally
Fenchel unstable? The answer is negative.
- Content Type Journal Article
- Category Full Length Paper
- DOI 10.1007/s10107-009-0311-8
- Authors
- Radu Ioan Boţ, Chemnitz University of Technology Faculty of Mathematics 09107 Chemnitz Germany
- Andreas Löhne, Martin Luther University Halle–Wittenberg Institute of Mathematics 06099 Halle Germany
- Journal Mathematical Programming
- Online ISSN 1436-4646
- Print ISSN 0025-5610
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Abstract Variational models for image segmentation have many applications, but can be slow to compute. Recently, globally convex segmentation
models have been introduced which are very reliable, but contain TV-regularizers, making them difficult to compute. The previously
introduced Split Bregman method is a technique for fast minimization of L1 regularized functionals, and has been applied to
denoising and compressed sensing problems. By applying the Split Bregman concept to image segmentation problems, we build
fast solvers which can out-perform more conventional schemes, such as duality based methods and graph-cuts. The convex segmentation
schemes also substantially outperform conventional level set methods, such as the Chan-Vese level set-based segmentation algorithm.
We also consider the related problem of surface reconstruction from unorganized data points, which is used for constructing
level set representations in 3 dimensions. The primary purpose of this paper is to examine the effectiveness of “Split Bregman”
techniques for solving these problems, and to compare this scheme with more conventional methods.
models have been introduced which are very reliable, but contain TV-regularizers, making them difficult to compute. The previously
introduced Split Bregman method is a technique for fast minimization of L1 regularized functionals, and has been applied to
denoising and compressed sensing problems. By applying the Split Bregman concept to image segmentation problems, we build
fast solvers which can out-perform more conventional schemes, such as duality based methods and graph-cuts. The convex segmentation
schemes also substantially outperform conventional level set methods, such as the Chan-Vese level set-based segmentation algorithm.
We also consider the related problem of surface reconstruction from unorganized data points, which is used for constructing
level set representations in 3 dimensions. The primary purpose of this paper is to examine the effectiveness of “Split Bregman”
techniques for solving these problems, and to compare this scheme with more conventional methods.
- Content Type Journal Article
- DOI 10.1007/s10915-009-9331-z
- Authors
- Tom Goldstein, UCLA Department of Mathematics Box 951555 Los Angeles CA 90095-1555 USA
- Xavier Bresson, UCLA Department of Mathematics Box 951555 Los Angeles CA 90095-1555 USA
- Stanley Osher, UCLA Department of Mathematics Box 951555 Los Angeles CA 90095-1555 USA
- Journal Journal of Scientific Computing
- Online ISSN 1573-7691
- Print ISSN 0885-7474
XFT: Extending the Digital Application of the Fourier Transform. (arXiv:0911.0952v1 [math.NA])
In recent years there has been a growing interest in the fractional Fourier
transform driven by its great number of applications. The literature in this
field follows two main routes. On the one hand the applications fields where
the ordinary Fourier transform can be applied are being revisited to use this
intermediate time-frequency representation of signals; and on the other hand
fast algorithms for numerical computation of the fractional Fourier transform
are devised. In this paper we derive a Gaussian-like quadrature of the
continuous fractional Fourier transform. This quadrature is given in terms of
the Hermite polynomials and their zeros. By using some asymptotic formulae we
are able to solve the quadrature by a diagonal congruence transformation
equivalent to a chirp-FFT-chirp transformation, yielding a fast discretization
of the fractional Fourier transform and its inverse in closed form. We extend
the range of the fractional Fourier transform by considering arbitrary complex
values inside the unitary circle and not only at the boundary. Interestingly
enough, the congruence transformation evaluated at $z=i$, which gives the
Fourier transform, improves the standard discrete Fourier transform, yielding a
new method to compute a more accurate FFT.
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