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Order O (order + o)

Distribution by Scientific Domains

Mathematics and Statistics	50%
Engineering	33%

Selected Abstracts

A fast multi-level convolution boundary element method for transient diffusion problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
C.-H. Wang
Abstract A new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods (BEM) for transient diffusion. This approach, which is based upon the multi-level multi-integration concepts of Brandt and Lubrecht, provides a fast, accurate and memory efficient time domain method for this entire class of problems. Conventional BEM approaches result in operation counts of order O(N2) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(N3/2) for three two-dimensional model problems using the multi-level convolution BEM. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Simulation of shockwave propagation with a thermal lattice Boltzmann model

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003
ShiDe Feng
Abstract A two-dimensional 19-velocity (D2Q19) lattice Boltzmann model which satisfies the conservation laws governing the macroscopic and microscopic mass, momentum and energy with local equilibrium distribution order O(u4) rather than the usual O(u3) has been developed. This model is applied to simulate the reflection of shockwaves on the surface of a triangular obstacle. Good qualitative agreement between the numerical predictions and experimental measurements is obtained. As the model contains the higher-order terms in the local equilibrium distribution, it performs much better in terms of numerical accuracy and stability than the earlier 13-velocity models with the local equilibrium distribution accurate only up to the second order in the velocity u. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Computation and analysis of multiple structural change models

JOURNAL OF APPLIED ECONOMETRICS, Issue 1 2003
Jushan Bai
In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least-squares operations of order O(T2) for any number of breaks. Our method can be applied to both pure and partial structural change models. Second, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Artificial boundary conditions for viscoelastic flows

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2008
Sergueï A. Nazarov
Abstract The steady three-dimensional exterior flow of a viscoelastic non-Newtonian fluid is approximated by reducing the corresponding nonlinear elliptic,hyperbolic system to a bounded domain. On the truncation surface with a large radius R, nonlinear, local second-order artificial boundary conditions are constructed and a new concept of an artificial transport equation is introduced. Although the asymptotic structure of solutions at infinity is known, certain attributes cannot be found explicitly so that the artificial boundary conditions must be constructed with incomplete information on asymptotics. To show the existence of a solution to the approximation problem and to estimate the asymptotic precision, a general abstract scheme, adapted to the analysis of coupled systems of elliptic,hyperbolic type, is proposed. The error estimates, obtained in weighted Sobolev norms with arbitrarily large smoothness indices, prove an approximation of order O(R,2+,), with any ,>0. Our approach, in contrast to other papers on artificial boundary conditions, does not use the standard assumptions on compactly supported right-hand side f, leads, in particular, to pointwise estimates and provides error bounds with constants independent of both R and f. Copyright © 2007 John Wiley & Sons, Ltd. [source]

On the vibrations of a plate with a concentrated mass and very small thickness

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2003
D. Gómez
Abstract We consider the vibrations of an elastic plate that contains a small region whose size depends on a small parameter ,. The density is of order O(,,m) in the small region, the concentrated mass, and it is of order O(1) outside; m is a positive parameter. The thickness plate h being fixed, we describe the asymptotic behaviour, as ,,O, of the eigenvalues and eigenfunctions of the corresponding spectral problem, depending on the value of m: Low- and high-frequency vibrations are studied for m>2. We also consider the case where the thickness plate h depends on ,; then, different values of m are singled out. Copyright © 2003 John Wiley & Sons, Ltd. [source]

An unconditionally stable and O(,2 + h4) order L, convergent difference scheme for linear parabolic equations with variable coefficients

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2001
Zhi-Zhong Sun
Abstract M. K. Jain, R. K. Jain, and R. K. Mohanty presented a finite difference scheme of O(,2 + ,h2 + h4) for solving the one-dimensional quasilinear parabolic partial differential equation, uxx = f(x, t, u, ut, ux), with Dirichlet boundary conditions. The method, when applied to a linear constant coefficient case, was shown to be unconditionally stable by the Von Neumann method. In this article, we prove that the method, when applied to a linear variable coefficient case, is unconditionally stable and convergent with the convergence order O(,2 + h4) in the L, -norm. In addition, we obtain an asymptotic expansion of the difference solution, with which we obtain an O(,4 + ,2h4 + h6) order accuracy approximation after extrapolation. And last, we point out that the analysis method in this article is efficacious for complex equations. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:619,631, 2001 [source]