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收集所有交通大學研究人員與學生個人或團體所發表之各項學術著作，涵蓋期刊論文、教師專書、學位論文等項。;;Collections of Publications of NCTU Researchers and Students Like Journal Papers and Thesis.

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Now showing 1 - 7 of 7

A two-stage least-squares finite element method for the stress-pressure-displacement elasticity equations
(1998-05-01)
Yang, SY
;
Chang, CL
;
應用數學系
;
Department of Applied Mathematics
A new stress-pressure-displacement formulation for the planar elasticity equations is proposed by introducing the auxiliary variables, stresses, and pressure. The resulting first-order system involves a nonnegative parameter that measures the material compressibility for the elastic body. A two-stage least-squares finite element procedure is introduced for approximating the solution to this system with appropriate boundary conditions. It is shown that the two-stage least-squares scheme is stable and, with respect to the order of approximation for smooth exact solutions, the rates of convergence of the approximations for all the unknowns are optimal both in the H-1-norm and in the L-2-norm. Numerical experiments with various values of the parameter are examined, which demonstrate the theoretical estimates. Among other things, computational results indicate that the behavior of convergence is uniform in the nonnegative parameter. (C) 1998 John Wiley & Sons, Inc.
On the convergence and stability of the standard least squares finite element method for first-order elliptic systems
(1998-07-01)
Yang, SY
;
應用數學系
;
Department of Applied Mathematics
A general framework of the theoretical analysis for the convergence and stability of the standard least squares finite element approximations to boundary value problems of first-order linear elliptic systems is established in a natural norm. With a suitable density assumption, the standard least squares method is proved to be convergent without requiring extra smoothness of the exact solutions. The method is also shown to be stable with respect to the natural norm. Some representative problems such as the grad-div type problems and the Stokes problem are demonstrated. (C) 1998 Published by Elsevier Science Inc. All rights reserved.
Three-dimensional simulation of the homeotropic to planar transition in cholesteric liquid crystals using the finite elements method
(2004-02-01)
Yao, IA
;
Wu, JJ
;
Chen, SH
;
光電工程學系
;
Department of Photonics
We investigated numerically the evolution of the director field in the homeotropic-planar transition of cholesteric liquid crystals bounded by parallel substrates. The simulation reproduces the observed relaxation from the homeotropic state to the long pitch transient planar state. The simulation agrees with the suggestion that the transient planar-planar transition occurs via a three-dimensional Helfrich-type deformation without the introduction of defect cores. On the basis of this understanding, we suggest improvements for increasing the speed of these transitions.
Study of the transient phenomenon during homeotropic to planar transition in cholesteric liquid crystal cells
(2004-04-01)
Yao, IA
;
Wu, JJ
;
Chen, SH
;
光電工程學系
;
Department of Photonics
The transient behavior of homeotropic-planar relaxation in surface stabilized cholesteric liquid crystals bounded by parallel substrates has been investigated both experimentally and numerically. By monitoring the evolution of transient transmittance, we observe that the homeotropic-planar relaxation after the electric field is switched off occurs via a transient planar state. The effect of bias waveform on the relaxation process is also studied. On the basis of this knowledge, we design a driving waveform to reduce the relaxation time.
Object-oriented programming of adaptive finite element and finite volume methods
(1996-10-01)
Liu, JL
;
Lin, IJ
;
Shih, MZ
;
Chen, RC
;
Hsieh, MC
This article describes an object-oriented implementation of the finite element method and the finite volume method in a unified adaptive system using the programming language C++. The system applies to various types of mathematical model problems. Traditionally, different numerical methods for different types of problems are implemented independently by procedural languages such as C and Fortran. Moreover, adaptive analysis programs are more complicated than nonadaptive programs. Nevertheless, these methods share many common properties such as linear system solvers, data structures, a posteriori error analyses, and refinement processes. Some advantageous features of object-oriented programming are demonstrated through the integration of these properties in the adaptive system. New data types of objects specific to adaptive methods are also introduced. The system is well-structured, extendable, and maintainable due mainly to the nature of encapsulation and inheritance of object-oriented programming.
Least-squares finite element methods for the elasticity problem
(1997-12-18)
Yang, SY
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A new first-order system formulation for the linear elasticity problem in displacement-stress form is proposed. The formulation is derived by introducing additional variables of derivatives of the displacements, whose combinations represent the usual stresses. Standard and weighted least-squares finite element methods are then applied to this extended system. These methods offer certain advantages such as that they need not satisfy the inf-sup condition which is required in the mixed finite element formulation, that a single continuous piecewise polynomial space can be used for the approximation of all the unknowns, that the resulting algebraic systems are symmetric and positive definite, and that accurate approximations of the displacements and the stresses can be obtained simultaneously. With displacement boundary conditions, it is shown that both methods achieve optimal rates of convergence in the H-1-norm and in the L-2-norm for all the unknowns. Numerical experiments with various Poisson ratios are given to demonstrate the theoretical error estimates.
Analysis of least squares finite element methods for a parameter-dependent first-order system
(1998-01-01)
Yang, SY
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A parameter-dependent first-order system arising from elasticity problems is introduced. The system corresponds to the 2D isotropic elasticity equations under a stress-pressure-displacement formulation in which the nonnegative parameter measures the material compressibility for the elastic body. Standard and weighted least squares finite element methods are applied to this system, and analyses for different values of the parameter are performed in a unified manner. The methods offer certain advantages such as they need not satisfy the Babuska-Brezzi condition, a single continuous piecewise polynomial space can be used for the approximation of all the unknowns, the resulting algebraic system is symmetric and positive definite, accurate approximations of all the unknowns can be obtained simultaneously, and, especially, computational results do not exhibit any significant numerical locking as the parameter tends to zero which corresponds to the incompressible elasticity problem (or equivalently, the Stokes problem). With suitable boundary conditions, it is shown that both methods achieve optimal rates of convergence in the H-1-norm and in the L-2-norm for all the unknowns. Numerical experiments with various values of the parameter are given to demonstrate the theoretical estimates.

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