viernes, 23 de octubre de 2009
HSL_MI20: An efficient AMG preconditioner for finite element problems in 3D
Algebraic multigrid (AMG) is one of the most effective iterative methods for the solution of large, sparse linear systems obtained from the discretization of second-order scalar elliptic self-adjoint partial differential equations. It can also be used as a preconditioner for Krylov subspace methods. In this communication, we report on the design and development of a robust, effective and portable Fortran 95 implementation of the classical Ruge-Stüben AMG, which is available as package HSL_MI20 within the HSL mathematical software library. The routine can be used as a 'black-box' preconditioner, but it also offers the user a range of options and parameters. Proper tuning of these parameters for a particular application can significantly enhance the performance of an AMG-preconditioned Krylov solver. This is illustrated using a number of examples arising in the unstructured finite element discretization of the diffusion, the convection-diffusion, and the Stokes equations, as well as transient thermal convection problems associated with the Boussinesq approximation of the Navier-Stokes equations in 3D. Copyright © 2009 John Wiley & Sons, Ltd.
Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms
This paper investigates the extended finite element method (XFEM)-GA detection algorithm proposed by Rabinovich et al. (Int. J. Numer. Meth. Engng 2007; 71(9):1051-1080; Int. J. Numer. Meth. Engng 2009; 77(3):337-359) on elastostatic problems with different types of flaws. This algorithm is designed for non-destructive assessment of structural components. Trial flaws are modeled using the XFEM as the forward problem and genetic algorithms (GAs) are employed as the optimization method to converge to the true flaw location and size. The main advantage of the approach is that XFEM alleviates the need for re-meshing the domain at every new iteration of the inverse solution process and GAs have proven to be robust and efficient optimization techniques in particular for this type of problems.In this paper the XFEM-GA methodology is applied to elastostatic problems where flaws are considered as straight cracks, circular holes and non-regular-shaped holes. Measurements are obtained from strain sensors that are attached to the surface of the structure at specific locations and provide the target solution to the GA. The results show convergence robustness and accuracy provided that a sufficient number of sensors are employed and sufficiently large flaws are considered. Copyright © 2009 John Wiley & Sons, Ltd.
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