R. Q. Rodríguez¹, A.F. Galvis¹, P. Sollero¹, E. L. Albuquerque²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 259-274, 2013, DOI:10.3970/cmes.2013.096.259

Abstract Over recent years the rapid evolution of the computational power has motivated the development of new numerical techniques to account for engineering solutions. The Boundary Element Method (BEM) has shown to be a powerful numeric tool for the analysis and solution of many physical and engineering problems. However, BEM fully populated and non-symmetric system matrices implies in higher memory requirements and solution times. This work analyze the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross Approximation - ACA, to multiple inclusion potential problems. The use of hierarchical format is aimed at More >

Sanderson L. Gonzaga de Oliveira¹, Mauricio Kischinhevsky², João Manuel R. S. Tavares³

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.2, pp. 119-141, 2013, DOI:10.3970/cmes.2013.095.119

Abstract A novel graph-based adaptive mesh refinement technique for triangular finite-volume discretizations in order to solve second-order partial differential equations is described. Adaptive refined meshes are built in order to solve timedependent problems aiming low computational costs. In the approach proposed, flexibility to link and traverse nodes among neighbors in different levels of refinement is admitted; and volumes are refined using an approach that allows straightforward and strictly local update of the data structure. In addition, linear equation system solvers based on the minimization of functionals can be easily used; specifically, the Conjugate Gradient Method. Numerical More >

Haitao Wang^1,2, Zhenhan Yao³

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.6, pp. 507-527, 2013, DOI:10.3970/cmes.2013.094.507

Abstract This paper presents the use of a three-dimensional time domain boundary element method (BEM) in conjunction with adaptive cross approximation method (ACA) for dynamic analyses of the HTR-PM nuclear island foundation. The advantage of this approach is that only foundation of the HTR-PM nuclear island and limited surfaces of the supporting half-space soil medium are modeled and analyzed in a direct time stepping scheme. In addition, the ACA can compress the BEM coefficient matrices at each time step efficiently, therefore allowing larger models to be analyzed compared with conventional BEMs. In order to discretize the More >

Y.M. Wang^1,2, Q. Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.1, pp. 17-45, 2013, DOI:10.3970/cmes.2013.093.017

Abstract A new kind of operator-orthogonal wavelet-based element is constructed based on the lifting scheme for adaptive analysis of thin plate bending problems. The operators of rectangular and skew thin plate bending problems and the sufficient condition for the operator-orthogonality of multilevel stiffness matrix are derived in the multiresolution finite element space. A new type of operator-orthogonal wavelets for thin plate bending problems is custom designed with high vanishing moments to be orthogonal with the scaling functions with respect to the operators of the problems, which ensures the independent solution of the problems in each scale. More >

Pratibhamoy Das¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.6, pp. 463-485, 2013, DOI:10.3970/cmes.2013.090.463

Abstract Adaptive mesh generation has become a valuable tool for the improvements of accuracy and efficiency of numerical solutions over fixed number of meshes. This paper gives an interpretation of the concept of equidistribution for singularly perturbed problems to obtain higher-order accuracy. We have used the post-processing Richardson extrapolation technique to improve the accuracy of the parameter uniform computed solution, obtained on a mesh which is adaptively generated by equidistributing a monitor function. Numerical examples demonstrate the high quality behavior of the computed solution. More >

P. Yuvaraj¹, A. Ramachandra Murthy², Nagesh R. Iyer³, Pijush Samui⁴, S.K. Sekar⁵

CMC-Computers, Materials & Continua, Vol.36, No.1, pp. 73-97, 2013, DOI:10.3970/cmc.2013.036.073

Abstract This paper presents Multivariate Adaptive Regression Splines (MARS) model to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (GF), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). This paper also presents the details of development of MARS model to predict failure load (Pmax) of high strength concrete (HSC) and ultra high strength concrete (UHSC) beam specimens. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described. Methodologies for evaluation of fracture energy, critical stress… More >

Cheng-Yu Ku^1,2,3, Weichung Yeih^1,2

CMC-Computers, Materials & Continua, Vol.31, No.3, pp. 173-200, 2012, DOI:10.3970/cmc.2012.031.173

Abstract In this paper, a dynamical Newton-like method with the adaptive stepsize based on the construction of a scalar homotopy function to transform a vector function of non-linear algebraic equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of the fictitious time-like function, we derived the adaptive stepsize using the dynamics of the residual vector. Based on the proposed dynamical Newton-like method, we can also derive the dynamical Newton method (DNM) and the dynamical Jacobian-inverse free method (DJIFM) with the transformation matrix as the inverse of the… More >

D. A. Hu^1,2,3, C. Liang¹, X. Han¹, Y. Z. Chen⁴, W. F. Xu⁴

CMC-Computers, Materials & Continua, Vol.29, No.2, pp. 155-168, 2012, DOI:10.3970/cmc.2012.029.155

Abstract Penetration process of concrete plate is simulated by 3D FE-SPH adaptive coupling algorithm, which is based on experimental research of projectile with 25mm diameter penetrates concrete target. In experiment, a high speed camera is used to record dynamic deformation process of concrete plate. Acceleration responses of concrete are obtained by acceleration sensor, which is pre-embedded in target plate. This experiment is also simulated by 3D FE-SPH adaptive coupling algorithm to verify the numerical model. Numerical model is approximated initially by FEM, and distorted elements are automatically converted into meshless particles to simulate damage, splash of More >

Jiun-Yu Wu^1,2, Hui-Ching Wang¹, Ming-I Char¹, Bo-Chen Tai¹

CMC-Computers, Materials & Continua, Vol.28, No.3, pp. 261-280, 2012, DOI:10.3970/cmc.2012.028.261

Abstract In this paper, we use the Local adaptive differential quadrature method (La-DQM) to solve multi-dimensional inverse scattering problem (ISP) of wave propagation. The La-DQM uses fictitious points to tackle the high-order differential equations with multi-boundary conditions and numerical results can be obtain directly in the calculation process. Six examples show the effectiveness and accuracy of the La-DQM in providing excellent estimates of unknown wave propagation from the given data. We think that the scheme is applicable to the ISP of wave propagation. Numerical results show that the La-DQM is powerful method for solving the inverse More >

Srinivasan Natesan¹, S. Gowrisankar²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 245-268, 2012, DOI:10.3970/cmes.2012.088.245

Abstract In this article, we propose a parameter-uniform computational technique to solve singularly perturbed parabolic initial-boundary-value problems exhibiting parabolic layers. The domain is discretized with a uniform mesh on the time direction and a nonuniform mesh obtained via equidistribution of a monitor function for the spatial variable. The numerical scheme consists of the implicit-Euler scheme for the time derivative and the classical central difference scheme for the spatial derivative. Truncation error, and stability analysis are carried out. Error estimates are derived, and numerical examples are presented. More >