CMES-Vol. 84, No. 4, 2012

Open Access

ARTICLE

Hybrid Parallelism of Multifrontal Linear Solution Algorithm with Out Of Core Capability for Finite Element Analysis
Min Ki Kim¹, Seung Jo Kim²
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 297-332, 2012, DOI:10.3970/cmes.2012.084.297
Abstract Hybrid parallelization of multifrontal solution method and its parallel performances in a multicore distributed parallel computing architecture are represented in this paper. To utilize a state-of-the-art multicore computing architecture, parallelization of the multifrontal method for a symmetric multiprocessor machine is required. Multifrontal method is easier to parallelize than other direct solution methods because the solution procedure implies that the elimination of unknowns can be executed simultaneously. This paper focuses on the multithreaded parallelism and mixing distributed algorithm and multithreaded algorithm together in a unified software. To implement the hybrid parallelized algorithm in a distributed shared memory environment, two innovative ideas… More >

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ARTICLE

A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation
Ali Shokri¹, Mehdi Dehghan¹
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 333-358, 2012, DOI:10.3970/cmes.2012.084.333
Abstract The Ginzburg-Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg-Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numerical results we use a predictor-corrector scheme. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the accuracy and efficiency of the presented method. More >

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An hp Adaptive Strategy to Compute the Vibration Modes of a Fluid-Solid Coupled System
M.G. Armentano¹, C. Padra², R. Rodríguez³, M. Scheble²
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 359-382, 2012, DOI:10.3970/cmes.2012.084.359
Abstract In this paper we propose an hp finite element method to solve a two-dimensional fluid-structure vibration problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We use a residual-type a posteriori error indicator to guide an hp adaptive algorithm. Since the tubes are allowed to be different, the weak formulation is a non-standard generalized eigenvalue problem. This feature is inherited by the algebraic system obtained by the discretization process. We introduce an algebraic technique to solve this particular spectral problem. We report several numerical tests which allow… More >

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A Globally Optimal Iterative Algorithm to Solve an Ill-Posed Linear System
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 383-404, 2012, DOI:10.3970/cmes.2012.084.383
Abstract An iterative algorithm based on the critical descent vector is proposed to solve an ill-posed linear system: Bx = b. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value α_c in the critical descent vector u = α_cr + B^Tr is derived, which renders the largest convergence rate as to be the globally optimal iterative algorithm (GOIA) among all the numerically iterative algorithms with the descent vector having the form u = αr + B^Tr to solve the ill-posed linear problems. Some numerical examples are used to reveal… More >

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