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Collocation Scheme (collocation + scheme)
Selected AbstractsMeshfree point collocation method for elasticity and crack problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004Sang-Ho Lee Abstract A generalized diffuse derivative approximation is combined with a point collocation scheme for solid mechanics problems. The derivatives are obtained from a local approximation so their evaluation is computationally very efficient. This meshfree point collocation method has other advantages: it does not require special treatment for essential boundary condition nor the time-consuming integration of a weak form. Neither the connectivity of the mesh nor differentiability of the weight function is necessary. The accuracy of the solutions is exceptional and generally exceeds that of element-free Galerkin method with linear basis. The performance and robustness are demonstrated by several numerical examples, including crack problems. Copyright © 2004 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] Analysis of incompressible miscible displacement in porous media by characteristics collocation methodNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2006Ning Ma Abstract Miscible displacement of one incompressible fluid by another in a porous medium is modelled by a coupled system of two partial differential equations. The pressure equation is elliptic, whereas the concentration equation is parabolic but normally convection-dominated. In this article, the collocation scheme is used to approximate the pressure equation and another characteristics collocation scheme to treat concentration equation. Existence and uniqueness of solutions of the algorithm are proved. Optimal order error estimate is demonstrated. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source] Level-Sets fields, placement and velocity based formulations of contact-impact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2007Hachmi Ben Dhia Abstract By introducing unknown Sign -like fields of Level-Sets type, the Signorini-Moreau dynamic contact conditions are set merely as boundary equations. From this setting, a continuous hybrid weak,strong formulation for dynamic contact between deformable solids is derived and a new Lagrangian formulation (we call stabilized) generalizing both the classical and augmented ones is obtained. Friction phenomena are treated similarly. In the global problem, the irregular Sign -like fields stand for the intrinsic contact unknown ones. This problem is discretized by means of time, space and collocation schemes. Some numerical experimentations are carried out, showing the potential of our developments. Copyright © 2006 John Wiley & Sons, Ltd. [source] A high-order mass-lumping procedure for B-spline collocation method with application to incompressible flow simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2003O. Botella Abstract This paper presents new developments of the staggered spline collocation method for cost-effective solution to the incompressible Navier,Stokes equations. Maximal decoupling of the velocity and the pressure is obtained by using the fractional step method of Gresho and Chan, allowing the solution to sparse elliptic problems only. In order to preserve the high-accuracy of the B-spline method, this fractional step scheme is used in association with a sparse approximation to the inverse of the consistent mass matrix. Such an approximation is constructed from local spline interpolation method, and represents a high-order generalization of the mass-lumping technique of the finite-element method. A numerical investigation of the accuracy and the computational efficiency of the resulting semi-consistent spline collocation schemes is presented. These schemes generate a stable and accurate unsteady Navier,Stokes solver, as assessed by benchmark computations. Copyright © 2003 John Wiley & Sons, Ltd. [source] |