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Minimum Principle (minimum + principle)
Selected AbstractsMinimum principle and related numerical scheme for simulating initial flow and subsequent propagation of liquefied groundINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2005Sami Montassar Abstract The problem of predicting the evolution of liquefied ground, modelled as a viscoplastic material, is addressed by combining a minimum principle for the velocity field, which characterizes such an evolution, and a time step integration procedure. Two different numerical schemes are then presented for the finite element implementation of this minimum principle, namely, the regularization technique and the decomposition-co-ordination method by augmented Lagrangian. The second method, which proves more accurate and efficient than the first, is finally applied to simulate the incipient flow failure and subsequent spreading of a liquefied soil embankment subject to gravity. The strong influence of liquefied soil residual shear strength on reducing the maximum amplitude of the ground displacement is particularly emphasized in such an analysis. Copyright © 2005 John Wiley & Sons, Ltd. [source] On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximantsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2010Adrian Rosolen Abstract We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright © 2009 John Wiley & Sons, Ltd. [source] Variational h -adaption in finite deformation elasticity and plasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007J. Mosler Abstract We ropose a variational h -adaption strategy in which the evolution of the mesh is driven directly by the governing minimum principle. This minimum principle is the principle of minimum potential energy in the case of elastostatics; and a minimum principle for the incremental static problem of elasto-viscoplasticity. In particular, the mesh is refined locally when the resulting energy or incremental pseudo-energy released exceeds a certain threshold value. In order to avoid global recomputes, we estimate the local energy released by mesh refinement by means of a lower bound obtained by relaxing a local patch of elements. This bound can be computed locally, which reduces the complexity of the refinement algorithm to O(N). We also demonstrate how variational h -refinement can be combined with variational r -refinement to obtain a variational hr -refinement algorithm. Because of the strict variational nature of the h -refinement algorithm, the resulting meshes are anisotropic and outperform other refinement strategies based on aspect ratio or other purely geometrical measures of mesh quality. The versatility and rate of convergence of the resulting approach are illustrated by means of selected numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] A review of reliable numerical models for three-dimensional linear parabolic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007I. Faragó Abstract The preservation of characteristic qualitative properties of different phenomena is a more and more important requirement in the construction of reliable numerical models. For phenomena that can be mathematically described by linear partial differential equations of parabolic type (such as the heat conduction, the diffusion, the pricing of options, etc.), the most important qualitative properties are: the maximum,minimum principle, the non-negativity preservation and the maximum norm contractivity. In this paper, we analyse the discrete analogues of the above properties for finite difference and finite element models, and we give a systematic overview of conditions that guarantee the required properties a priori. We have chosen the heat conduction process to illustrate the main concepts, but engineers and scientists involved in scientific computing can easily reformulate the results for other problems too. Copyright © 2006 John Wiley & Sons, Ltd. [source] Dialectica interpretation of well-founded induction,MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 3 2008Helmut Schwichtenberg Abstract From a classical proof that the gcd of natural numbers a1 and a2 is a linear combination of the two, we extract by Gödel's Dialectica interpretation an algorithm computing the coefficients. The proof uses the minimum principle. We show generally how well-founded recursion can be used to Dialectica interpret well-founded induction, which is needed in the proof of the minimum principle. In the special case of the example above it turns out that we obtain a reasonable extracted term, representing an algorithm close to Euclid's. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A simple PDE and Wiener-Hopf Riccati equations,COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2005Daniel W. Stroock We investigate the PDE (1.1), concentrating on the case when , < in which the boundary condition (1.1b) is not of Feller's type and we lose the minimum principle. Investigation of nonnegative solutions leads us to Wiener-Hopf theory and to a Riccati equation. A much-studied Markov chain analogue is developed further in the hope that it will illuminate all aspects of the PDE case. © 2005 Wiley Periodicals, Inc. [source] | ||||||||||