CMES-Vol. 71, No. 4, 2011

Open Access

ARTICLE

Finite Element Approximate Inverse Preconditioning for solving 3D Biharmonic Problems on Shared Memory Systems
G.A. Gravvanis¹, K.M. Giannoutakis²
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 305-330, 2011, DOI:10.3970/cmes.2011.071.305
Abstract In this paper we present parallel explicit approximate inverse matrix techniques for solving sparse linear systems on shared memory systems, which are derived using the finite element method for biharmonic equations in three space variables. Our approach for solving such equations is by considering the biharmonic equation as a coupled equation approach (pair of Poisson equation), using a FE approximation scheme, yielding an inner-outer iteration method. Additionally, parallel approximate inverse matrix algorithms are introduced for the efficient solution of sparse linear systems, based on an anti-diagonal computational approach that eliminates the data dependencies. Parallel explicit preconditioned conjugate gradient-type schemes in… More >

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The Superconvergence of Certain Two-Dimensional Cauchy Principal Value Integrals
Jin Li ¹, De-hao Yu ²
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 331-346, 2011, DOI:10.3970/cmes.2011.071.331
Abstract The composite rectangle (midpoint) rule for the computation of multi-dimensional singular integrals is discussed, and the superconvergence results is obtained. When the local coordinate is coincided with certain priori known coordinates, we get the convergence rate one order higher than the global one. At last, numerical examples are presented to illustrate our theoretical analysis which agree with it very well. More >

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Computation of Nonlinear Schrödinger Equation on an Open Waveguide Terminated by a PML
Jianxin Zhu¹, Zheqi Shen¹
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 347-362, 2011, DOI:10.3970/cmes.2011.071.347
Abstract It is known that the perfectly matched layer (PML) is a powerful tool to truncate the unbounded domain. Recently, the PML technique has been introduced in the computation of nonlinear Schrödinger equations (NSE), in which the nonlinearity is separated by some efficient time-splitting methods. A major task in the study of PML is that the original equation is modified by a factor c which varies fast inside the layer. And a large number of grid points are needed to capture the profile of c in the discretization. In this paper, the possibility is discussed for using some nonuniform finite difference… More >

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A novel MLPG-Finite-Volume Mixed Method for Analyzing Stokesian Flows & Study of a new Vortex Mixing Flow
Ruben Avila¹, Zhidong Han², Satya N. Atluri³
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 363-396, 2011, DOI:10.3970/cmes.2011.071.363
Abstract The two dimensional steady state Stokes equations are solved by using a novel MLPG-Mixed Finite Volume method, that is based on the independent meshless interpolations of the deviatoric velocity strain tensor, the volumetric velocity strain tensor, the velocity vector and the pressure. The pressure field directly obtained from this method does not suffer from the malady of checker-board patterns. Numerical simulations of the flow field, and trajectories of passive fluid elements in a new complex Stokes flow are also presented. The new flow geometry consists of three coaxial cylinders two of smaller diameter, that steadily rotate independently, inside a third… More >

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