Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.1, pp. 17-42, 2013, DOI:10.3970/cmes.2013.091.017

Abstract In the present paper, we propose a novel two-side equilibration method to properly reduce the condition number of a given non-singular matrix only through a few operations. Then, two different conditioners together with the conjugate gradient method (CGM) are developed, which can overcome the defect of CGM, being not vulnerable to noisy disturbance exerted on an ill-posed linear system. The twoside CGM (TSCGM) and the pre-conditioning CGM (PrCGM) are convergent fast and accurate in solving linear inverse problems and the linear Hilbert problem under a large random noise. More >

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 >

R. Djebali¹, M. El Ganaoui²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 179-202, 2011, DOI:10.3970/cmes.2011.071.179

Abstract The Lattice Boltzmann method (LBM) became, today, a powerful tool for simulating fluid flows. Its improvements for different applications and configurations offers more flexibility and results in several schemes such as in presence of external/internal forcing term. However, we look for the suitable model that gives correct informations, matches the hydrodynamic equations and preserves some features like coding easily, preserving computational cost, stability and accuracy. In the present work, high order incompressible models and equilibrium distribution functions for the advection-diffusion equations are analyzed. Boundary conditions, acceleration, stability and preconditioning with initial fields are underlined which permit to rigorously selecting two… More >

G.A. Gravvanis, K.M. Giannoutakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 35-44, 2008, DOI:10.3970/cmes.2008.032.035

Abstract A new parallel normalized optimized approximate inverse algorithm, based on the concept of the ``fish bone'' computational approach with cyclic distribution of the processors satisfying an antidiagonal data dependency, for computing classes of explicit approximate inverses, is introduced for symmetric multiprocessor systems. The parallel normalized explicit approximate inverses are used in conjunction with parallel normalized explicit preconditioned conjugate gradient square schemes, for the efficient solution of finite element sparse linear systems. The parallel design and implementation issues of the new proposed algorithms are discussed and the parallel performance is presented, using OpenMP. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.2, pp. 77-94, 2008, DOI:10.3970/cmes.2008.028.077

Abstract The method of fundamental solutions (MFS) is a truly meshless numerical method widely used in the elliptic type boundary value problems, of which the approximate solution is expressed as a linear combination of fundamental solutions and the unknown coefficients are determined from the boundary conditions by solving a linear equations system. However, the accuracy of MFS is severely limited by its ill-conditioning of the resulting linear equations system. This paper is motivated by the works of Chen, Wu, Lee and Chen (2007) and Liu (2007a). The first paper proved an equivalent relation of the Trefftz method and MFS for circular… More >

N. Laaroussi^1*, Y. Chihab¹, M. Garoum¹, L-V. Bénet², F. Lacroux³

FDMP-Fluid Dynamics & Materials Processing, Vol.11, No.4, pp. 354-365, 2015, DOI:10.3970/fdmp.2015.011.354

Abstract This study is based on the modeling of the air flow in the hall building including heating and air-conditioning systems. The building contains two converter stations “valves” considered as heat sources. Heat transfer in the hall is numerically simulated using the standard k-ε model of turbulence. For a very hot weather, this study aims to evaluate the local temperatures in the ambient air of the hall, with assuming running valves and air conditioning device in open loop with a 35°C inlet temperature. The study has shown that the air conditioning is efficient enough to maintain low level of temperature disparity.… More >