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 >

Montri Maleewong¹, Sirod Sirisup²

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 193-216, 2010, DOI:10.3970/cmes.2010.065.193

Abstract In this paper, we describe our investigation of an "on-line" POD-assisted projective integration method for solving a nonlinear PDE. Using the on-line method, we have computed the representative POD modes without assuming knowledge of the underlying slow manifold along the integration process. This approach is based on the "equation-free" framework where the governing PDE does not need to be projected onto the POD bases in order to build a reduced-order model. The main objectives of this study were to investigate the effectiveness of the method in reducing the computational time required for numerically solving a nonlinear PDE. Here, the one-dimensional… More >

Jun-Sheng Duan¹, Ai-Ping Guo²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 139-150, 2010, DOI:10.3970/cmes.2010.060.139

Abstract Adomian polynomials are constituted of reduced polynomials and derivatives of nonlinear operator. The reduced polynomials are independent of the form of the nonlinear operator. A recursive algorithm of the reduced polynomials is discovered and its symbolic implementation by the software Mathematica is given. As a result, a new and convenient algorithm for the Adomian polynomials is obtained. More >

Yunhua Li^1,2, Yunze Li³, Chieh-Li Chen⁴, Cha’o-Kuang Chen⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 1-14, 2010, DOI:10.3970/cmes.2010.058.001

Abstract Addressing the identification problem of the general Lagrange multiplier in the He's variational iteration method, this paper proposes a new kind of method based on Duhamel's principle for the dynamic system response analysis. In this method, we have constructed an analytical iteration formula in terms of the convolution for the residual error at the nth iteration, and have given a new interpretation to He's variational iteration method. The analysis illustrates that the computational result of this method is equal to that of He's variational iteration method on the assumption of considering the impulse response of the linear parts, or equal… More >