Jin Li¹, De-hao Yu^{2 3}

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.3&4, pp. 233-252, 2011, DOI:10.32604/cmes.2011.082.233

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 >

Yue-Ting Zhou¹, Xing Li², De-Hao Yu³, Kang Yong Lee^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.2, pp. 163-190, 2010, DOI:10.3970/cmes.2010.063.163

Abstract In this paper, a coupled crack/contact model is established for the composite material with arbitrary periodic cracks indented by periodic punches. The contact of crack faces is considered. Frictional forces are modeled to arise between the punch foundation and the composite material boundary. Kolosov-Muskhelisvili complex potentials with Hilbert kernels are constructed, which satisfy the continuity conditions of stress and displacement along the interface identically. The considered problem is reduced to a system of singular integral equations of first and second kind with Hilbert kernels. Bounded functions are defined so that singular integral equations of Hilbert type can be transformed to… More >

Chein-Shan Liu¹, Hong-Ki Hong¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 279-308, 2010, DOI:10.3970/cmes.2010.060.279

Abstract We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting ill-conditioned matrices, we add a vector equation into the given matrix equation for obtaining the left-inversion of matrix (and a similar vector equation for the right-inversion) and thus we obtain an over-determined system. The resulting two modifications of the MCGM, namely the… More >

Gu, M. H.¹, Young, D. L.^1,2, Fan, C. M.¹

CMC-Computers, Materials & Continua, Vol.11, No.3, pp. 185-208, 2009, DOI:10.3970/cmc.2009.011.185

Abstract A meshless numerical algorithm is developed for the solutions of one-dimensional wave equations in this paper. The proposed numerical scheme is constructed by the Eulerian-Lagrangian method of fundamental solutions (ELMFS) together with the D'Alembert formulation. The D'Alembert formulation is used to avoid the difficulty to constitute the linear algebraic system by using the ELMFS in dealing with the initial conditions and time-evolution. Moreover the ELMFS based on the Eulerian-Lagrangian method (ELM) and the method of fundamental solutions (MFS) is a truly meshless and quadrature-free numerical method. In this proposed wave model, the one-dimensional wave equation is reduced to an implicit… More >