bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical solution of the equations of compressible flow by a transport method
Authors: Rivlin J. , Kaniel S. 
Published: August 2005

AbstractThis paper implements a numerical solution of the equations of compressible flow, by a transport method. The model is based on a kinetic model, built for the fluid motion. It transforms the equations of motion into integral equations, solved by an analytical‐numerical method. Precomputation of tables for some canonical integrals reduces the amount of work. A boundary value problem (flow into a wedge) is treated and numerical solutions are exhibited. The paper deals with isentropic flow. It is an important special case, among the variety of problems where the assumption of constant entropy causes a negligible error.
A fourth order difference method for the one‐dimensional general quasilinear parabolic partial differential equation
Authors: Jain M. K. , Jain R. K. , Mohanty R. K. 
Published: August 2005

AbstractA two‐level implicit difference scheme using three spatial grid points of Crandall form of O(k2 + kh2 + h4) is obtained 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 convection‐diffusion problem, is shown to be unconditionally stable. The numerical results show that the proposed method produces accurate and oscillation‐free solutions.
A coupled double splitting ADI scheme for the first biharmonic using collocation
Authors: Cooper K. D. , Prenter P. M. 
Published: August 2005

AbstractA new method for solving the first biharmonic equation via a double splitting into coupled systems of ordinary differential equations is presented. The first splitting reduces this fourth order partial differential equation into the coupled system uxx + uyy = v and vxx + vyy = f, where u carries both Dirichlet and Neumann boundary data and v carries no boundary data. The pair is then iteratively solved using coupled alternating direction collocation on the resulting systems of ordinary differential equations. This can also be viewed as an alternating direction method of lines for a system of partial differential equations. Although there is no separation of variables underlying the splitting, the method yields a convergent sequence of iterates for a variety of examples under a restricted range of acceleration parameters, and possesses O(h4) accuracy. Desirable features of the algorithm are discussed together with the reduction of bandwidth of the associated collocation matrices under intersticing of u and v variables. Interesting open questions are also discussed.
The h‐p version of the finite element method for parabolic equations. II. The h‐p version in time
Authors: Babuš Ivo , Janik Tadeusz 
Published: August 2005

AbstractThe paper is the second in the series addressing the h‐p version of the finite element method for parabolic equations. The present paper addresses the case when in both variables, the spatial and time, the h‐p version is used. Error estimation is given and numerical computations are presented.
Approximation of radial functions by piecewise polynomials on arbitrary grids
Authors: Tourigny Y. , Sanz‐Serna J. M. , Morris J. Li. 
Published: August 2005

AbstractWe study the approximation of radial functions in IRN, N ≥ 2, by means of Lagrange finite elements on arbitrary grids. As an application, error estimates are obtained for the finite‐element discretization of the radial Schrödinger equation. (AMS subject classification number: 65M60).
An O(h6) cubic spline interpolating procedure for harmonic functions
Authors: Papamichael N. , Soares Maria Joana 
Published: August 2005

AbstractAn O(h6) method for the interpolation of harmonic functions in rectangular domains is described and analyzed, The method is based on an earlier cubic spline technique [N. Papamichael and J.R. Whiteman, BIT 14, 452–459 (1974)], and makes use of recent results concerning the a posteriori correction of interpolatory cubic splines.
Parallel finite element splitting‐up method for parabolic problems
Authors: Tai Xue‐Cheng , Neittaanmäki Pekka 
Published: August 2005

AbstractAn efficient method for solving parabolic systems is presented. The proposed method is based on the splitting‐up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B‐splines. Several numerical examples are presented.
Construction of a novel finite‐difference scheme for a nonlinear diffusion equation
Authors: Mickens Ronald E. 
Published: August 2005

AbstractA novel finite‐difference scheme is constructed for a particular nonlinear diffusion equation. This scheme does not correspond to any of those that might be expected to follow from application of the standard procedures. A major advantage is that in the appropriate limit the difference equation model reduces to schemes that reproduce exactly the behaviors of the solution to the corresponding differential equation.
Discrete least‐squares global approximations to solutions of partial differential equations
Authors: Pen Ue‐Li 
Published: August 2005

AbstractSolutions of partial differential equations (PDEs) using globally nonvanishing approximating functions are discussed, and the particular case of global polynomial solutions is studied. Convergence and error bounds are examined. Examples are given and compared with analytic solutions. This method seems particularly well suited for elliptic PDEs with continuous boundary conditions and nonhomogeneous terms, even for irregular domains, offering geometric convergence rates. By providing the minimized residues, strong error indicators are obtained. This algorithm's implementation retains simplicity under a variety of applications.
Finite element approach to the Stokes problem
Authors: Chinosi C. , Comodi M. I. 
Published: August 2005

AbstractWe approximate the Stokes problem by using a finite element method. This method utilizes the approach of Kleiser–Schumann, in which a boundary condition for the pressure is implicitly defined by a condition on the velocity. We consider a suitable splitting of the unknowns that allows one to reduce the Stokes problem to a cascade of classical Dirichlet problems and to a boundary integral equation.
Numerical simulation of the turbulent boundary layer equations via a Runge‐Kutta algorithm
Authors: Campo Antonio , Schuler Carlos 
Published: August 2005

AbstractThis paper addresses a hybrid computational procedure for the step‐by‐step calculation of momentum transfer in turbulent boundary layer flows along flat plates. The proposed procedure relies on a modified method of lines wherein transversal discretizations are carried out by a “control volume” being infinitesimal in the streamwise direction and finite in the transversal direction of the fluid flow. Using mixing length theory and coarse intervals in the transversal direction, the resulting system of ordinary differential equations of first order may be readily integrated on a personal computer utilizing a fourth‐order Runge‐Kutta algorithm. In general, a maximum number of sixteen lines is necessary at the trailing edge of the flat plate for a typical calculation. As a consequence, computing time and storage for each run were very small when compared to other finite‐difference methods. Furthermore, to validate the hybrid procedure involving the method of lines and control volumes (MOLCV), comparisons with experimental data have been done in terms of both velocity distributions and local skin friction coefficients. For all cases tested, the proposed methodology predicts the growth of the boundary layer of gases correctly.
Projection methods for the numerical solution of non‐self‐adjoint elliptic partial differential equations
Authors: Kamath C. , Weeratunga S. 
Published: August 2005

AbstractWe compare the relative performances of two iterative schemes based on projection techniques for the solution of large sparse nonsymmetric systems of linear equations, encountered in the numerical solution of partial differential equations. The Block–Symmetric Successive Over‐Relaxation (Block‐SSOR) method and the Symmetric–Kaczmarz method are derived from the simplest of projection methods, that is, the Kaczmarz method. These methods are then accelerated using the conjugate gradient method, in order to improve their convergence. We study their behavior on various test problems and comment on the conditions under which one method would be better than the other. We show that while the conjugate‐gradient‐accelerated Block‐SSOR method is more amenable to implementation on vector and parallel computers, the conjugate‐gradient accelerated Symmetric–Kaczmarz method provides a viable alternative for use on a scalar machine.
Comparison of S and V cycles in multigrid method for linear elliptic equations with variable coefficients
Authors: Lyengar Satteluri R. K. , Goyal Anu 
Published: August 2005

AbstractWe implement and compare the Sawtooth (S) and V cycles in multigrid method (mgd) for the Poisson equation and for the fourth‐order 13‐point methods derived by Krishnaiah et al. Defect correction in the mgd context is also studied. Computations reveal that the S cycle is much cheaper compared to the V cycle in most of the situations. Defect correction is much cheaper than the direct application of the 13‐point formula, giving almost the fourth‐order accurate results.
Computation of viscous or nonviscous conservation law by domain decomposition based on asymptotic analysis
Authors: Bourgeat A. , Garbey M. 
Published: August 2005

AbstractAn accurate and efficient numerical method has been developed for a nonlinear diffusion convection‐dominated problem. The scheme combines asymptotic methods with usual solution techniques for hyperbolic problems. After having localized shock or corner layers and rescaling, first terms of the inner expansion are computed. Using the same concepts gives a method to compute a very accurate solution of the nonlinear conservation law. Because our numerical scheme is based on a uniform approximation throughout the domain, the shock is localized very accurately and there is practically no smearing out. Numerical computations are presented. Another novel feature is the ability to break down the problem according to subdomains of different local behavior, based on asymptotic analysis, which may make it feasible to do computations with different processors.
Elliptic partial differential equation and optimal control
Authors: Wan‐xie Zhong , Xiang‐Xiang Zhong 
Published: August 2005

AbstractThe theory of optimal control and the semianalytical method of elliptic partial differential equation (PDE) in a prismatic domain are mutually simulated issues. The simulation of discrete‐time linear quadratic (LQ) control with the substructural chain problem in static structural analysis is given first. From the minimum potential energy variational principle of substructural chain, the generalized variational principle with two kinds of variables and the dual equations are derived. The simulation relation is then recognized by comparing the variational principle and dual equations of the LQ control theory. The simulation between elliptic PDE in the prismatic domain and continuous‐time LQ control is established in the same way, and the interval energy is naturally introduced, as in the case of substructural chain. The assembling and condensation equations can help one to derive the differential equations of the submatrices of potential energy and mixed energy. The well known Riccati equation is one of them. The interval assembling and condensation algorithm can be used to solve the Riccati equation. Some numerical examples are given to illustrate the method.
A fully Sinc‐Galerkin method for Euler–Bernoulli beam models
Authors: Smith Ralph C. , Bowers Kenneth L. , Lund John 
Published: August 2005

AbstractA fully Sinc‐Galerkin method in both space and time is presented for fourth‐order time‐dependent partial differential equations with fixed and cantilever boundary conditions. The sine discretizations for the second‐order temporal problem and the fourth‐order spatial problems are presented. Alternate formulations for variable parameter fourth‐order problems are given, which prove to be especially useful when applying the forward techniques of this article to parameter recovery problems. The discrete system that corresponds to the time‐dependent partial differential equations of interest are then formulated. Computational issues are discussed and an accurate and efficient algorithm for solving the resulting matrix system is outlined. Numerical results that highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.
Projection functions for particle‐grid methods
Authors: Bagtzoglou Amvrossios C. , Tompson Andrew F. B. , Dougherty David E. 
Published: August 2005

AbstractRandom walk particle methods (RWPM) can be used in operator splitting schemes to simulate reactive solute transport in porous media. Projection functions are used to transfer particle location and mass information to concentrations at selected spatial points. Because of the stochastic nature of RWPM, concentration estimates made from particle distributions include a “noisy” error component. In some cases of reactive or density‐dependent flows, this type of error may be propagated forward in time. It can be reduced by using larger numbers of particles or by using different projection functions. The effects of using different projection functions or numbers of particles in different flow regimes or dimensions are explored using concentration solutions for a set of one‐, two‐, and three‐dimensional nonreactive test problems. Resulting solutions are compared with analytic results and classical random walk error estimates. A piecewise linear projection function provides a reasonable improvement in accuracy over the more convenient box methods at a modest increase in cost. The support of the projection functions should be O(Δx) to avoid excessive smearing. Multidimensional projection functions may be advantageously formed by products of different one‐dimensional projection functions.
Nodal adjoint method for multigroup diffusion in heterogeneous slab reactors
Authors: Haidar Nassar H. S. 
Published: August 2005

AbstractA variational adjoint nodal method is proposed to yield an approximation theory for the eigenvalues of the multigroup neutron diffusion boundary value problem of a heterogeneous quasicritical one‐dimensional slab reactor. Semianalytical eigensolutions are constructed for the associated whole‐reactor group nodal fluxes. The method appears to be mathematically more consistent, computationally more straightforward, and practically more convenient than alternative nodal or finite element schemes. © 1992 John Wiley & Sons, Inc.
Positive solutions and dynamics of a finite difference reaction–diffusion system
Authors: Pao C. V. 
Published: August 2005

AbstractWe investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time‐dependent and a steady‐state reaction–diffusion problem. The formulation of the discrete equations for the time‐dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time‐dependent and the steady‐state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time‐dependent problem in relation to the corresponding steady‐state problem. This bifurcation point also determines whether the steady‐state problem has one or two non‐negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time‐dependent and the steady‐state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time‐dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction–diffusion problem. © 1993 John Wiley & Sons, Inc.
Numerical grid generator based on Moser's deformation method
Authors: Liao Guojun , Pan Tsorng‐Whay , Su Jianzhong 
Published: August 2005

AbstractA deformation method of grid generation has been recently proposed. The method is based on Moser's deformation scheme in his study of the volume elements of a Riemannian manifold. In this paper, this deformation method is improved so that the grid adaption takes place according to the physical coordinates. Some numerical results are included to demonstrate the method. © 1994 John Wiley & Sons, Inc.
Eulerian‐Lagrangian method of cells based on localized adjoint method
Authors: Herrera G. , Herrera I. 
Published: August 2005

AbstractThe localized adjoint method, when applied using an Eulerian‐Lagrangian frame, has been quite successful in treating advection‐dominated transport. The resulting methodology is known as ELLAM. In previous work, bilinear functions were used as test functions. In this paper, local constant functions are used instead, leading to procedures which are appealing because, in addition to other advantages of ELLAM methods, they ensure local mass conservation, are easy to apply and can be combined without difficulty with existing solute‐transport codes which are based on finite volumes. In addition, the procedures for deriving the algorithms presented here are used as an illustration of a general methodology for treating numerically partial differential equations, which is advocated by the authors. Such methodology consists in identifying the information about the sought solution which is contained in the approximate one and then using this insight to choose the interpolation procedure to be applied. © 1994 John Wiley & Sons, Inc.
A note on the least squares solution of the groundwater flow equation
Authors: Bentley L. R. 
Published: August 2005

AbstractThe least squares finite element method is a member of the weighted residuals class of numerical methods for solving partial differential equations. The least squares finite element method is applied to the groundwater flow equation. Space is discretized with a C1 continuous trial function and parameters are approximated with a C0 bilinear basis. Solutions for problems containing parameters with large localized spatial gradients are characterized by errors that are propagated throughout the entire domain. Second‐order spatial convergence is observed, and extreme mesh refinement is required to match Galerkin and mixed least squares finite element results. Temporal discretization should be kept separate from the least squares spatial discretization. © 1994 John Wiley & Sons, Inc.
A best finite‐difference scheme for the fisher equation
Authors: Mickens Ronald E. 
Published: August 2005

AbstractA new class of finite‐difference schemes is constructed for the Fisher partial differential equation. These schemes are constructed according to the nonstandard modeling rules formulated by Mickens. They have the property that, in the appropriate limits, the discrete models obtained are either “exact” or “best” finite‐difference schemes for corresponding differential equation. Consequently, the elementary numerical instabilities will not occur. © 1994 John Wiley & Sons, Inc.
On the numerical solution of axisymmetric domain optimization problems by dual finite element method
Authors: Hlaváček Ivan , Mäkinen Raino 
Published: August 2005

AbstractShape optimization of an axisymmetric three‐dimensional domain with an elliptic boundary value state problem is solved. Since the cost functional is given in terms of the cogradient of the solution, a dual finite element method based on the minimum of complementary energy principle is used. © 1994 John Wiley & Sons, Inc.
Pointwise superconvergence of the gradient for the linear tetrahedral element
Authors: Goodsell George 
Published: August 2005

AbstractWe consider the finite element approximation to the solution of a self‐adjoint, second‐order elliptic boundary value problem in three dimensions over a fully uniform mesh of piecewise linear tetrahedral elements. Although the resulting approximation to the gradient is optimal for functions from the approximating space, it is, however, only O(h). We show how this can be improved by the recovery, from the finite element solution, of an approximation to the gradient, which is pointwise of a higher order of accuracy than that of the gradient of the finite element approximation. This approximation, termed a recovered gradient function, is, thus, superconvergent. The major task of our analysis is the establishing of an (almost) constant bound on the W seminorm of the finite element approximation to a smoothed derivative Green's function. © 1994 John Wiley & Sons, Inc.
A mixed problem for electrostatic potential in semiconductors
Authors: Sacco Riccardo 
Published: August 2005

AbstractIn this article we deal with the solution in Ω ⊂ R2 of the quasi linear equation −Δu = f(x, y, u(x, y)) subject to mixed boundary data and representing Gauss' law in a semiconductor device, where u and f are, respectively, the electrostatic potential and the space charge density after a suitable scaling. In the following we consider the associated variational problem of finding in a suitable subspace of H1(Ω) the minimum of the functional \documentclass{article}\pagestyle{empty}\begin{document}$ J(u)\, = \,\int {_\Omega } (\frac{1}{2}\left| {\nabla u\left| {^2 \, - \,{\cal F}(x,y,u)\,d\Omega,} \right.} \right. $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ {\cal F}(x,y,u)\, = \,\int f (x,y,\xi)\,d\xi, $\end{document} and we prove existence and uniqueness of a weak solution according to the technique of Convex Analysis. The numerical study is then carried on by a piecewise linear finite element approximation, which is proved to converge in the H1‐norm to the exact solution of the variational problem; some numerical examples are also included. © 1994 John Wiley & Sons, Inc.
Difference approximations for wave equations via finite elements. I. Construction and performance
Authors: Card Curtis L. , Allen Myron B. 
Published: August 2005

AbstractMany practical applications of wave equations involve media in which there are interfaces, or discontinuities in material properties. The accurate numerical representation of these interfaces is important in mathematical models. One can develop generalizations of standard finite‐difference methods that accommodate sharp interfaces by modifying a straightforward finite‐element approach. In two space dimensions, these methods yield explicit, 5‐point or 9‐point difference schemes that accurately capture reflection, transmission, and refraction at interfaces. The approach also extends readily to the simulation of waves in elastic media. A companion article presents an error analysis for the approach. © 1995 John Wiley & Sons, Inc.