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Certain Sense (certain + sense)
Selected AbstractsEfficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003U. Langer Abstract This paper is concerned with the iterative solution of the boundary element equations arising from standard Galerkin boundary element discretizations of first-kind boundary integral operators of positive and negative order. We construct efficient preconditioners on the basis of so-called grey-box algebraic multigrid methods that are well adapted to the treatment of boundary element matrices. In particular, the coarsening is based on an auxiliary matrix that represents the underlying topology in a certain sense. This auxiliary matrix is additionally used for the construction of the smoothers and the transfer operators. Finally, we present the results of some numerical studies that show the efficiency of the proposed algebraic multigrid preconditioners. Copyright © 2003 John Wiley & Sons, Ltd. [source] Optimal modal reduction of vibrating substructuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003Paul E. Barbone Abstract A structure which consists of a main part and a number of attached substructures is considered. A ,model reduction' scheme is developed and applied to each of the discrete substructures. Linear undamped transient vibrational motion of the structure is assumed, with general external forcing and initial conditions. The goal is to replace each discrete substructure by another substructure with a much smaller number of degrees of freedom, while minimizing the effect this reduction has on the dynamic behaviour of the main structure. The approach taken here involves Ritz reduction and the Dirichlet-to-Neumann map as analysis tools. The resulting scheme is based on a special form of modal reduction, and is shown to be optimal in a certain sense, for long simulation times. The performance of the scheme is demonstrated via numerical examples, and is compared to that of standard modal reduction. Copyright © 2003 John Wiley & Sons, Ltd. [source] Z+ fading memory and extensions of input,output mapsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2001Irwin W. Sandberg Abstract An Erratum for this article has been published in the International Journal of Circuit Theory and Applications 30(4) 2002, 179. Much is known about time-invariant non-linear systems with inputs and outputs defined on Z+ that possess approximately-finite memory. For example, under mild additional conditions, they can be approximated arbitrarily well by the maps of certain interesting simple structures. An important fact that gives meaning to results concerning such systems is that the approximately-finite-memory condition is known to be often met. Here we consider the known proposition that if a causal time-invariant discrete-time input,output map H has fading memory on a set of bounded functions defined on all of the integers Z, then H can be approximated arbitrarily well by a finite Volterra series operator. We show that in a certain sense, involving the existence of extensions of system maps, this result too has wide applicability. Copyright © 2001 John Wiley & Sons, Ltd. [source] Existence of a weak solution to the Navier,Stokes equation in a general time-varying domain by the Rothe methodMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2009í Neustupa Abstract We assume that ,t is a domain in ,3, arbitrarily (but continuously) varying for 0,t,T. We impose no conditions on smoothness or shape of ,t. We prove the global in time existence of a weak solution of the Navier,Stokes equation with Dirichlet's homogeneous or inhomogeneous boundary condition in Q[0,,T) := {(x,,t);0,t,T, x,,t}. The solution satisfies the energy-type inequality and is weakly continuous in dependence of time in a certain sense. As particular examples, we consider flows around rotating bodies and around a body striking a rigid wall. Copyright © 2008 John Wiley & Sons, Ltd. [source] Optimality of greedy and sustainable policies in the management of renewable resourcesOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2003A. Rapaport Abstract We consider a discrete-time modelling of renewable resources, which regenerate after a delay once harvested. We study the qualitative behaviour of harvesting policies, which are optimal with respect to a discounted utility function over infinite horizon. Using Bellman's equation, we derive analytically conditions under which two types of policies (greedy and sustainable) are optimal, depending on the discount rate and the marginal utility. For this particular class of problems, we show also that the greedy policy is attractive in a certain sense. The techniques of proof lie on concavity, comparison of value functions and Lyapunov-like functions. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||