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Standard Test Problems (standard + test_problem)
Selected AbstractsA mixed finite element for plate bending with eight enhanced strain modesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2001Reinhard Piltner Abstract A low-order thick and thin plate bending element is derived using bilinear approximations for the transverse deflection, the two rotations and the thickness change. The stress,strain relationships from three-dimensional elasticity are used without any modifications. In order to avoid locking and to improve the accuracy of the results eight enhanced strain modes are used. For an efficient implementation of the mixed element, orthogonal stress and strain functions are utilized. Although the element is a low-order finite element the numerical results for a series of standard test problems are excellent. Copyright © 2001 John Wiley & Sons, Ltd. [source] Reduced modified quadratures for quadratic membrane finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2004Craig S. Long Abstract Reduced integration is frequently used in evaluating the element stiffness matrix of quadratically interpolated finite elements. Typical examples are the serendipity (Q8) and Lagrangian (Q9) membrane finite elements, for which a reduced 2 × 2 Gauss,Legendre integration rule is frequently used, as opposed to full 3 × 3 Gauss,Legendre integration. This ,softens' these element, thereby increasing accuracy, albeit at the introduction of spurious zero energy modes on the element level. This is in general not considered problematic for the ,hourglass' mode common to Q8 and Q9 elements, since this spurious mode is non-communicable. The remaining two zero energy modes occurring in the Q9 element are indeed communicable. However, in topology optimization for instance, conditions may arise where the non-communicable spurious mode associated with the elements becomes activated. To effectively suppress these modes altogether in elements employing quadratic interpolation fields, two modified quadratures are employed herein. For the Q8 and Q9 membrane elements, the respective rules are a five and an eight point rule. As compared to fully integrated elements, the new rules enhance element accuracy due to the introduction of soft, higher-order deformation modes. A number of standard test problems reveal that element accuracy remains comparable to that of the under-integrated counterparts. Copyright © 2004 John Wiley & Sons, Ltd. [source] Towards very high-order accurate schemes for unsteady convection problems on unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005R. Abgrall Abstract We construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the first class of methods, we interpolate the solution in the space,time element. We start by calculating the first-order node residuals, then we calculate the high-order cell residual, and modify the first-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order finite difference approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] Algebraic multigrid, mixed-order interpolation, and incompressible fluid flowNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2010R. Webster Abstract This paper presents the results of numerical experiments on the use of equal-order and mixed-order interpolations in algebraic multigrid (AMG) solvers for the fully coupled equations of incompressible fluid flow. Several standard test problems are addressed for Reynolds numbers spanning the laminar range. The range of unstructured meshes spans over two orders of problem size (over one order of mesh bandwidth). Deficiencies in performance are identified for AMG based on equal-order interpolations (both zero-order and first-order). They take the form of poor, fragile, mesh-dependent convergence rates. The evidence suggests that a degraded representation of the inter-field coupling in the coarse-grid approximation is the cause. Mixed-order interpolation (first-order for the vectors, zero-order for the scalars) is shown to address these deficiencies. Convergence is then robust, independent of the number of coarse grids and (almost) of the mesh bandwidth. The AMG algorithms used are reviewed. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||