Ju’e Yang¹, Hongying Huang², Dehao Yu³

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.4, pp. 347-366, 2012, DOI:10.3970/cmes.2012.085.347

Abstract In this paper, a new domain decomposition method is suggested for the stationary Stokes equations on unbounded domain and its convergence is proved. We draw an artificial boundary to make the domain into two parts: one is bounded, in which we use the mixed finite element method; the other is unbounded, in which we apply the natural boundary reduction. Then we change the sub-problem on the unbounded domain onto a one in a bounded domain and we use the Dirichlet to Neumann(DtN) alternating algorithm to solve the resulting mixed system. The theoretical results as well as the numerical examples show… More >

D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 311-352, 2012, DOI:10.3970/cmes.2012.083.311

Abstract In this study, local moving least square - one dimensional integrated radial basis function network (LMLS-1D-IRBFN) method is presented and demonstrated with the solution of time-dependent problems such as Burgers' equation, unsteady flow past a square cylinder in a horizontal channel and unsteady flow past a circular cylinder. The present method makes use of the partition of unity concept to combine the moving least square (MLS) and one-dimensional integrated radial basis function network (1D-IRBFN) techniques in a new approach. This approach offers the same order of accuracy as its global counterpart, the 1D-IRBFN method, while the system matrix is more… More >

Ju’e Yang¹, Dehao Yu²

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.3, pp. 311-330, 2011, DOI:10.3970/cmes.2011.073.311

Abstract In this paper, we introduce a domain decomposition method with non-matching grids for a certain nonlinear interface problem in unbounded domains. To solve this problem, we discuss a new coupling of finite element method(FE) and natural boundary element(NBE). We first derive the optimal energy error estimate of finite element approximation to the coupled FEM-NBEM problem. Then we use a dual basis multipier on the interface to provide the numerical analysis with non-matching grids.Finally, we give some numerical examples further to confirm our theoretical results. More >

O. Allix¹, P. Kerfriden¹, P. Gosselet¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.3, pp. 271-292, 2010, DOI:10.3970/cmes.2010.055.271

Abstract We present numerical enhancements of a multiscale domain decomposition strategy based on a LaTIn solver and dedicated to the computation of the debounding in laminated composites. We show that the classical scale separation is irrelevant in the process zones, which results in a drop in the convergence rate of the strategy. We show that performing nonlinear subresolutions in the vicinity of the front of the crack at each prediction stage of the iterative solver permits to restore the effectiveness of the method. More >

Dan Gordon¹, Rachel Gordon²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 23-46, 2009, DOI:10.3970/cmes.2009.053.023

Abstract Linear systems with very large off-diagonal elements and discontinuous coefficients (LODC systems) arise in some modeling cases, such as those involving heterogeneous media. Such problems are usually solved by domain decomposition methods, but these can be difficult to implement on unstructured grids or when the boundaries between subdomains have a complicated geometry. Gordon and Gordon have shown that Björck and Elfving's (sequential) CGMN algorithm and their own block-parallel CARP-CG are very robust and efficient on strongly convection dominated cases (but without discontinuous coefficients). They have also shown that scaling the equations by dividing each equation by the L2-norm of its… More >

M. Patrício¹, R. Mattheij¹, G. de With²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 69-94, 2009, DOI:10.3970/cmes.2009.041.069

Abstract In this paper the effect of the local structure of a highly heterogeneous composite material on the parameters that characterise crack propagation is analysed. The evaluation of stress intensity factors is discussed. A hybrid approach based on domain decomposition and homogenisation methods is employed to obtain accurate solutions with reduced computational complexity. More >

A. Takei¹, S. Yoshimura¹, H. Kanayama²

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 63-82, 2009, DOI:10.3970/cmes.2009.040.063

Abstract This paper describes a large-scale finite element analysis (FEA) for a high-frequency electromagnetic field of Maxwell equations including the displacement current. A stationary Helmholtz equation for the high-frequency electromagnetic field analysis is solved by considering an electric field and an electric scalar potential as unknown functions. To speed up the analysis, the hierarchical domain decomposition method (HDDM) is employed as a parallel solver. In this study, the Parent-Only type (Parallel processor mode: P-mode) of the HDDM is employed. In the P-mode, Parent processors perform the entire FEA. In this mode, all CPUs can be used without idling in an environment… More >