Pengfei Zhu¹, Qinghui Zhang^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 107-127, 2020, DOI:10.32604/cmes.2020.09831

Abstract There are several difficulties in generalized/extended finite element methods (GFEM/XFEM) for moving interface problems. First, the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM. Second, they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes. Furthermore, time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time. This paper is devoted to proposing the stable and robust GFEM/XFEM with effi- cient time stepping schemes for the parabolic interface… More >

H. Theilig¹

Structural Durability & Health Monitoring, Vol.6, No.3&4, pp. 239-272, 2010, DOI:10.3970/sdhm.2010.006.239

Abstract The aim of this paper is to give an overview to some problems and solutions of the fracture analysis of 2D structures. It will be shown that the common computer-aided two-dimensional fatigue crack path simulation can be considerably improved in accuracy by using a predictor-corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method. Furthermore the paper presents an improved finite element technique for the calculation of stress intensity factors of mixed mode problems by the MVCCI Method. The procedure is devised to compute the separated strain energy release rates by using the convergence of two separate… More >

Vijay Kumar Gupta

The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.2, pp. 55-56, 2011, DOI:10.3970/icces.2011.020.055

Abstract Various applications of piezoelectric actuators have been explored over the years. One such application is use of piezoelectric actuators for shape control of structures. In this paper, steering of parabolic antenna by deforming the antenna surface using piezoelectric actuators has been explored. Optimization based on Genetic Algorithm is carried out to find out optimum location, length and applied electric field to the piezoelectric actuators to achieve desired steering of antenna. Constraints are included in the objective function using penalty approach. Shell finite element model is used to determine deformations induced by the actuators. As the wavelength is sufficiently smaller than… More >

Liqun Wang¹, Songming Hou², Liwei Shi^3,∗

CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 73-90, 2019, DOI:10.32604/cmes.2019.04581

Abstract In this paper, we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton’s method to handle nonlinearity. It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem. Numerical experiments show that our method is about second order accurate in the L^∞ norm. More >

Chein-Shan Liu¹, Chih-Wen Chang²

CMC-Computers, Materials & Continua, Vol.25, No.2, pp. 107-134, 2011, DOI:10.3970/cmc.2011.025.107

Abstract We consider two inverse problems for estimating radiative coefficients α(x) and α(x, y), respectively, in T_t(x, t) = T_xx(x, t)-α(x)T(x, t), and T_t(x, y, t) = T_xx(x, y, t) + T_yy(x, y, t)-α(x, y)T(x, y, t), where a are assumed to be continuous functions of space variables. A Lie-group adaptive method is developed, which can be used to find a at the spatially discretized points, where we only utilize the initial condition and boundary conditions, such as those for a typical direct problem. This point is quite different from other methods, which need the overspecified final time data. Three-fold advantages… 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 and analytical tests were carried… 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 >

S. Abbasbandy^1,2, V. Sladek³, A. Shirzadi¹, J. Sladek³

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.1, pp. 15-38, 2011, DOI:10.3970/cmes.2011.071.015

Abstract This paper deals with the development of a new method for solution of initial-boundary value problems governed by a couple of nonlinear diffusion equations occurring in the theory of self-organization in non-equilibrium systems. The time dependence is treated by linear interpolation using the finite difference method and the semi-discrete partial differential equations are considered in a weak sense by using the local integral equation method with approximating 2-d spatial variations of the field variables by the Moving Least Squares. The evaluation techniques are discussed and the applicability of the presented method is demonstrated on two illustrative examples with exact solutions… More >

G. C. Bourantas¹, E. D. Skouras^2,3,4, G. C. Nikiforidis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.043.001

Abstract The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis functions are constructed using the Moving Least Square (MLS) approximation. The weak-form description of PDEs is used in most MLS methods to circumvent problems related to the increased level of resolution necessary near natural (Neumann) boundary conditions (BCs), dislocations, or regions of steep gradients. Alternatively, one can adopt Radial Basis Function (RBF) approximation on the strong-form of PDEs using meshless PC methods, due to the delta function behavior (exact solution on nodes).… More >

M.Ganesh¹, D. Sheen²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 183-194, 2001, DOI:10.3970/cmes.2001.002.183

Abstract A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial-boundary value parabolic problems. The scheme is based on the method recently introduced in Sheen, Sloan, and Thomée (2000) for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows one to compute solutions in a wide range of time. Instead of using a standard time-marching method, which is not easily parallelizable, we take the Laplace transform in time of the parabolic problems. The resulting elliptic problems can be solved in parallel. Solutions are then computed by a discrete inverse Laplace transformation.… More >