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Two-dimensional Problems (two-dimensional + problem)
Selected AbstractsComplex variable moving least-squares method: a meshless approximation techniqueINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007K. M. Liew Abstract Based on the moving least-squares (MLS) approximation, we propose a new approximation method,the complex variable moving least-squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The meshless method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new meshless method for two-dimensional elasticity problems,the complex variable meshless method (CVMM),and the formulae of the CVMM for two-dimensional elasticity problems are obtained. Compared with the conventional meshless method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM. Copyright © 2006 John Wiley & Sons, Ltd. [source] On optimal income taxation with heterogeneous work preferencesINTERNATIONAL JOURNAL OF ECONOMIC THEORY, Issue 1 2007Ritva Tarkiainen C63; H21; H24 This paper considers the problem of optimal income taxation when individuals are assumed to differ with respect to their earnings potential and work preferences. A numerical method for solving this two-dimensional problem has been developed. We assume an additive utility function, and utilitarian social objectives. Rather than solve the first order conditions associated with the problem, we directly compute the best tax function, which can be written in terms of a second order B-spline function. Our findings show that marginal tax rates are higher than might be anticipated, and that very little bunching occurs at the optimum. Our simulation results show that the correlation between taste for work and productivity has a crucial role in determining the extent of redistribution in our model. [source] Exponential attractor for a planar shear-thinning flowMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2007Dalibor Pra Abstract We study the dynamics of an incompressible, homogeneous fluid of a power-law type, with the stress tensor T = ,(1 + µ|Dv|)p,2Dv, where Dv is a symmetric velocity gradient. We consider the two-dimensional problem with periodic boundary conditions and p , (1, 2). Under these assumptions, we estimate the fractal dimension of the exponential attractor, using the so-called method of ,,-trajectories. Copyright © 2007 John Wiley & Sons, Ltd. [source] Existence of solution in elastic wave scattering by unbounded rough surfacesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2002T. Arens We consider the two-dimensional problem of the scattering of a time-harmonic wave, propagating in an homogeneous, isotropic elastic medium, by a rough surface on which the displacement is assumed to vanish. This surface is assumed to be given as the graph of a function ,,C1,1(,). Following up on earlier work establishing uniqueness of solution to this problem, existence of solution is studied via the boundary integral equation method. This requires a novel approach to the study of solvability of integral equations on the real line. The paper establishes the existence of a unique solution to the boundary integral equation formulation in the space of bounded and continuous functions as well as in all Lp spaces, p,[1, ,] and hence existence of solution to the elastic wave scattering problem. Copyright © 2002 John Wiley & Sons, Ltd. [source] Convergence analysis of a balancing domain decomposition method for solving a class of indefinite linear systemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2009Jing Li Abstract A variant of balancing domain decomposition method by constraints (BDDC) is proposed for solving a class of indefinite systems of linear equations of the form (K,,2M)u=f, which arise from solving eigenvalue problems when an inverse shifted method is used and also from the finite element discretization of Helmholtz equations. Here, both K and M are symmetric positive definite. The proposed BDDC method is closely related to the previous dual,primal finite element tearing and interconnecting method (FETI-DP) for solving this type of problems (Appl. Numer. Math. 2005; 54:150,166), where a coarse level problem containing certain free-space solutions of the inherent homogeneous partial differential equation is used in the algorithm to accelerate the convergence. Under the condition that the diameters of the subdomains are small enough, the convergence rate of the proposed algorithm is established, which depends polylogarithmically on the dimension of the individual subdomain problems and which improves with a decrease of the subdomain diameters. These results are supported by numerical experiments of solving a two-dimensional problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] A versatile software tool for the numerical simulation of fluid flow and heat transfer in simple geometriesCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2010A. M. G. Lopes Abstract The present work describes a software tool aimed at the simulation of fluid flow and heat transfer for two-dimensional problems in a structured Cartesian grid. The software deals with laminar and turbulent situations in steady-state or transient regime. An overview is given on the theoretical principles and on the utilization of the program. Results for some test cases are presented and compared with benchmarking solutions. Although EasyCFD is mainly oriented for educational purposes, it may be a valuable tool for a first analysis of practical situations. EasyCFD is available at www.easycfd.net. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 14,27, 2010; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20230 [source] Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2003Rie Sugimoto Abstract The theory for coupling of mapped wave infinite elements and special wave finite elements for the solution of the Helmholtz equation in unbounded domains is presented. Mapped wave infinite elements can be applied to boundaries of arbitrary shape for exterior wave problems without truncation of the domain. Special wave finite elements allow an element to contain many wavelengths rather than having many finite elements per wavelength like conventional finite elements. Both types of elements include trigonometric functions to describe wave behaviour in their shape functions. However the wave directions between nodes on the finite element/infinite element interface can be incompatible. This is because the directions are normally globally constant within a special finite element but are usually radial from the ,pole' within a mapped wave infinite element. Therefore forcing the waves associated with nodes on the interface to be strictly radial is necessary to eliminate this internode incompatibility. The coupling of these elements was tested for a Hankel source problem and plane wave scattering by a cylinder and good accuracy was achieved. This paper deals with unconjugated infinite elements and is restricted to two-dimensional problems. Copyright © 2003 John Wiley & Sons, Ltd. [source] An accurate integral-based scheme for advection,diffusion equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001Tung-Lin Tsai Abstract This paper proposes an accurate integral-based scheme for solving the advection,diffusion equation. In the proposed scheme the advection,diffusion equation is integrated over a computational element using the quadratic polynomial interpolation function. Then elements are connected by the continuity of first derivative at boundary points of adjacent elements. The proposed scheme is unconditionally stable and results in a tridiagonal system of equations which can be solved efficiently by the Thomas algorithm. Using the method of fractional steps, the proposed scheme can be extended straightforwardly from one-dimensional to multi-dimensional problems without much difficulty and complication. To investigate the computational performances of the proposed scheme five numerical examples are considered: (i) dispersion of Gaussian concentration distribution in one-dimensional uniform flow; (ii) one-dimensional viscous Burgers equation; (iii) pure advection of Gaussian concentration distribution in two-dimensional uniform flow; (iv) pure advection of Gaussian concentration distribution in two-dimensional rigid-body rotating flow; and (v) three-dimensional diffusion in a shear flow. In comparison not only with the QUICKEST scheme, the fully time-centred implicit QUICK scheme and the fully time-centred implicit TCSD scheme for one-dimensional problem but also with the ADI-QUICK scheme, the ADI-TCSD scheme and the MOSQUITO scheme for two-dimensional problems, the proposed scheme shows convincing computational performances. Copyright © 2001 John Wiley & Sons, Ltd. [source] A dual mortar approach for 3D finite deformation contact with consistent linearizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010Alexander Popp Abstract In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal,dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source] Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loadingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009J. J. Muñoz Abstract Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr,Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization problem using specific algorithms for Second-Order Conic Program (SOCP). From the stress field at the lower bound and the velocities at the upper bound, we construct a novel error estimate based on elemental and edge contributions to the bound gap. These contributions are employed in an adaptive remeshing strategy that is able to reproduce fan-type mesh patterns around points with discontinuous surface loading. The solution of this type of problems is analysed in detail, and from this study some additional meshing strategies are also described. We particularise the resulting formulation and strategies to two-dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature. Copyright © 2008 John Wiley & Sons, Ltd. [source] Slope stability analysis based on elasto-plastic finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005H. Zheng Abstract The paper deals with two essential and related closely processes involved in the finite element slope stability analysis in two-dimensional problems, i.e. computation of the factors of safety (FOS) and location of the critical slide surfaces. A so-called ,,v inequality, sin ,,1 , 2v is proved for any elasto-plastic material satisfying Mohr,Coulomb's yield criterion. In order to obtain an FOS of high precision with less calculation and a proper distribution of plastic zones in the critical equilibrium state, it is stated that the Poisson's ratio v should be adjusted according to the principle that the ,,v inequality always holds as reducing the strength parameters c and ,. While locating the critical slide surface represented by the critical slide line (CSL) under the plane strain condition, an initial value problem of a system of ordinary differential equations defining the CSL is formulated. A robust numerical solution for the initial value problem based on the predictor,corrector method is given in conjunction with the necessary and sufficient condition ensuring the convergence of solution. A simple example, the kinematic solution of which is available, and a challenging example from a hydraulic project in construction are analysed to demonstrate the effectiveness of the proposed procedures. Copyright © 2005 John Wiley & Sons, Ltd. [source] Generalization of robustness test procedure for error estimators.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005Part II: test results for error estimators using SPR Abstract In this part of the paper we shall use the formulation given in the first part to assess the quality of recovery-based error estimators using two recovery methods, i.e. superconvergent patch recovery (SPR) and recovery by equilibrium in patches (REP). The recovery methods have been shown to be asymptotically robust and superconvergent when applied to two-dimensional problems. In this study we shall examine the behaviour of the recovery methods on several three-dimensional mesh patterns for patches located either inside or at boundaries. This is performed by first finding an asymptotic finite element solution, irrespective of boundary conditions at far ends of the domain, and then applying the recovery methods. The test procedure near kinked boundaries is explained in a step-by-step manner. The results are given in a series of tables and figures for various cases of three-dimensional mesh patterns. It has been experienced that the full superconvergent property is generally lost due to presence of boundary layer solution and the definition of the recoveries near boundaries though the results of the robustness test is still within an acceptable range. Copyright © 2005 John Wiley & Sons, Ltd. [source] Accuracy of Galerkin finite elements for groundwater flow simulations in two and three-dimensional triangulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2001Christian Cordes Abstract In standard finite element simulations of groundwater flow the correspondence between hydraulic head gradients and groundwater fluxes is represented by the stiffness matrix. In two-dimensional problems the use of linear triangular elements on Delaunay triangulations guarantees a stiffness matrix of type M. This implies that the local numerical fluxes are physically consistent with Darcy's law. This condition is fundamental to avoid the occurrence of local maxima or minima, and is of crucial importance when the calculated flow field is used in contaminant transport simulations or pathline evaluation. In three spatial dimensions, the linear Galerkin approach on tetrahedra does not lead to M -matrices even on Delaunay meshes. By interpretation of the Galerkin approach as a subdomain collocation scheme, we develop a new approach (OSC, orthogonal subdomain collocation) that is shown to produce M -matrices in three-dimensional Delaunay triangulations. In case of heterogeneous and anisotropic coefficients, extra mesh properties required for M -stiffness matrices will also be discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Two-dimensional unsteady heat conduction analysis with heat generation by triple-reciprocity BEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001Yoshihiro Ochiai Abstract If the initial temperature is assumed to be constant, a domain integral is not needed to solve unsteady heat conduction problems without heat generation using the boundary element method (BEM).However, with heat generation or a non-uniform initial temperature distribution, the domain integral is necessary. This paper demonstrates that two-dimensional problems of unsteady heat conduction with heat generation and a non-uniform initial temperature distribution can be solved approximately without the domain integral by the triple-reciprocity boundary element method. In this method, heat generation and the initial temperature distribution are interpolated using the boundary integral equation. Copyright © 2001 John Wiley & Sons, Ltd. [source] A new stable space,time formulation for two-dimensional and three-dimensional incompressible viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001Donatien N'dri Abstract A space,time finite element method for the incompressible Navier,Stokes equations in a bounded domain in ,d (with d=2 or 3) is presented. The method is based on the time-discontinuous Galerkin method with the use of simplex-type meshes together with the requirement that the space,time finite element discretization for the velocity and the pressure satisfy the inf,sup stability condition of Brezzi and Babu,ka. The finite element discretization for the pressure consists of piecewise linear functions, while piecewise linear functions enriched with a bubble function are used for the velocity. The stability proof and numerical results for some two-dimensional problems are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Algebraic multigrid and 4th-order discrete-difference equations of incompressible fluid flowNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2010R. Webster Abstract This paper investigates the effectiveness of two different Algebraic Multigrid (AMG) approaches to the solution of 4th-order discrete-difference equations for incompressible fluid flow (in this case for a discrete, scalar, stream-function field). One is based on a classical, algebraic multigrid, method (C-AMG) the other is based on a smoothed-aggregation method for 4th-order problems (SA-AMG). In the C-AMG case, the inter-grid transfer operators are enhanced using Jacobi relaxation. In the SA-AMG case, they are improved using a constrained energy optimization of the coarse-grid basis functions. Both approaches are shown to be effective for discretizations based on uniform, structured and unstructured, meshes. They both give good convergence factors that are largely independent of the mesh size/bandwidth. The SA-AMG approach, however, is more costly both in storage and operations. The Jacobi-relaxed C-AMG approach is faster, by a factor of between 2 and 4 for two-dimensional problems, even though its reduction factors are inferior to those of SA-AMG. For non-uniform meshes, the accuracy of this particular discretization degrades from 2nd to 1st order and the convergence factors for both methods then become mesh dependent. Copyright © 2009 John Wiley & Sons, Ltd. [source] | |||||||||||||