Hsin-Fang Chan¹, Chia-Ming Fan^1,2, Weichung Yeih¹

CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 125-142, 2011, DOI:10.3970/cmc.2011.024.125

Abstract The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the… More >

Chein-Shan Liu^1,2, Chung-Lun Kuo³, Dongjie Liu⁴

CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 105-124, 2011, DOI:10.3970/cmc.2011.024.105

Abstract The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmholtz equation and the modified Helmholtz equation, defined in annular domains are investigated. The outer boundary of the annulus is imposed by overspecified boundary data, and we seek unknown data on the inner boundary through the numerical solution by a spring-damping regularization method and its Lie-group shooting method (LGSM). Several numerical examples are examined to show that the LGSM can overcome the ill-posed behavior of inverse Cauchy problem against the disturbance from random noise, and the computational cost is very cheap. More >

L. Dong¹, S. N. Atluri²

CMC-Computers, Materials & Continua, Vol.24, No.1, pp. 61-104, 2011, DOI:10.3970/cmc.2011.024.061

Abstract A simple procedure to formulate efficient and stable hybrid/mixed finite elements is developed, for applications in macro- as well as micromechanics. In this method, the strain and displacement field are independently assumed. Instead of using two-field variational principles to enforce both equilibrium and compatibility conditions in a variational sense, the independently assumed element strains are related to the strains derived from the independently assumed element displacements, at a finite number of collocation points within the element. The element stiffness matrix is therefore derived, by simply using the principle of minimum potential energy. Taking the four-node plane isoparametric element as an… More >

Gregor Kosec¹, Miha Založnik², Božidar Šarler¹, Hervé Combeau²

CMC-Computers, Materials & Continua, Vol.22, No.2, pp. 169-196, 2011, DOI:10.3970/cmc.2011.022.169

Abstract The simulation of macrosegregation as a consequence of solidification of a binary Al-4.5%Cu alloy in a 2-dimensional rectangular enclosure is tackled in the present paper. Coupled volume-averaged governing equations for mass, energy, momentum and species transfer are considered. The phase properties are resolved from the Lever solidification rule, the mushy zone is modeled by the Darcy law and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the novel Local Radial Basis Function Collocation Method (LRBFCM).… More >

Wenqing Wang¹, Thomas Schnicke², Olaf Kolditz³

CMC-Computers, Materials & Continua, Vol.21, No.3, pp. 217-236, 2011, DOI:10.3970/cmc.2011.021.217

Abstract This work focuses on parallel finite element simulation of thermal hydraulic and mechanical (THM) coupled processes in porous media, which is a common phenomenon in geological applications such as nuclear waste repository and CO2 storage facilities. The Galerkin finite element method is applied to solve the derived partial differential equations. To deal with the coupling terms among the equations, the momentum equation is solved individually in a monolithic manner, and moreover their solving processes are incorporated into the solving processes of nonisothermal hydraulic equation and heat transport equation in a staggered manner. The computation task arising from the present method… More >

Zhao Huiming¹, Dong Zhengzhu¹, Chen Jiarui¹, Yang Min¹

CMC-Computers, Materials & Continua, Vol.21, No.3, pp. 209-216, 2011, DOI:10.3970/cmc.2011.021.209

Abstract The advantages of coupling of a natural boundary element method and a finite element method are introduced. Then we discuss the principle of the direct coupling of NBEM and FEM and its implementation. The comparison of the results between the direct coupling method and FEM proves that the direct coupling method is simple, feasible and valid in practice. More >

Zhuo-Jia Fu^1,2, Wen Chen¹, Qing-Hua Qin^2,3

CMC-Computers, Materials & Continua, Vol.21, No.3, pp. 187-208, 2011, DOI:10.3970/cmc.2011.021.187

Abstract This paper presents a hybrid finite element model (FEM) with a new type of general solution as interior trial functions, named as HGS-FEM. A variational functional corresponding to the proposed general solution is then constructed for deriving the element stiffness matrix of the proposed element model and the corresponding existence of extremum is verified. Then the assumed intra-element potential field is constructed by a linear combination of novel general solutions at the points on the element boundary under consideration. Furthermore, the independent frame field is introduced to guarantee the intra-element continuity. The present scheme inherits the advantages of hybrid Trefftz… More >

Chih-Wen Chang¹

CMC-Computers, Materials & Continua, Vol.21, No.2, pp. 87-106, 2011, DOI:10.3970/cmc.2011.021.087

Abstract We address a new numerical approach to deal with these multi-dimensional backward wave problems (BWPs) in this study. A fictitious time τ is utilized to transform the dependent variable u(x, y, z, t) into a new one by (1+τ)u(x, y, z, t)=: v(x, y, z, t, τ), such that the original wave equation is written as a new hyperbolic type partial differential equation in the space of (x, y, z, t, τ). Besides, a fictitious viscous damping coefficient can be employed to strengthen the stability of numerical integration of the discretized equations by using a group preserving scheme. Several numerical… More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.21, No.1, pp. 17-40, 2011, DOI:10.3970/cmc.2011.021.017

Abstract Only the left-boundary data of temperature and heat flux are used to estimate an unknown parameter function α(x) in T_t(x,t) = ∂(α(x)T_x)/∂x + h(x,t), as well as to recover the right-boundary data. When α(x) is given the above problem is a well-known inverse heat conduction problem (IHCP). This paper solves a mixed-type inverse problem as a combination of the IHCP and the problem of parameter identification, without needing to assume a function form of α(x) a priori, and without measuring extra data as those used by other methods. We use the one-step Lie-Group Adaptive Method (LGAM) for the semi-discretizations of… More >

Chih-Wen Chang¹

CMC-Computers, Materials & Continua, Vol.19, No.3, pp. 285-314, 2010, DOI:10.3970/cmc.2010.019.285

Abstract In this article, we propose a new numerical approach for solving these multi-dimensional nonlinear and nonhomogeneous backward heat conduction problems (BHCPs). A fictitious time t is employed to transform the dependent variable u(x, y, z, t) into a new one by (1+t)u(x, y, z, t)=: v(x, y, z, t, t), such that the original nonlinear and nonhomogeneous heat conduction equation is written as a new parabolic type partial differential equation in the space of (x, y, z, t, t). In addition, a fictitious viscous damping coefficient can be used to strengthen the stability of numerical integration of the discretized equations… More >