學術出版;;Publications

Permanent URI for this communityhdl:11536/1

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.

Browse

🏛️國立陽明交通大學機構典藏

Search Results

Now showing 1 - 10 of 28

Magneto-optical response of layers of semiconductor quantum dots and nanorings
(2005-06-01)
Voskoboynikov, O
;
Wijers, CMJ
;
Liu, JL
;
Lee, CP
;
應用數學系
In this paper a comparative theoretical study was made of the magneto-optical response of square lattices of nanoobjects (dots and rings). Expressions for both the polarizability of the individual objects as their mutual electromagnetic interactions (for a lattice in vacuum) was derived. The quantum-mechanical part of the derivation is based upon the commonly used envelope function approximation. The description is suited to investigate the optical response of these layers in a narrow region near the interband transitions onset, particularly when the contribution of individual level pairs can be separately observed. A remarkable distinction between clearly quantum-mechanical and classical electromagnetic behavior was found in the shape and volume dependence of the polarizability of the dots and rings. This optical response of a single plane of quantum dots and nanorings was explored as a function of frequency, magnetic field, and angle of incidence. Although the reflectance of these layer systems is not very strong, the ellipsometric angles are large. For these isolated dot-ring systems they are of the order of magnitude of degrees. For the ring systems a full oscillation of the optical Bohm-Ahronov effect could be isolated. Layers of dots do not display any remarkable magnetic field dependence. Both type of systems, dots and rings, exhibit an outspoken angular-dependent dichroism of quantum-mechanical origin.
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.
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.
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.
A posteriori finite element error analysis for symmetric positive differential equations
(1999-01-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
Based on the solution of local weak residual problems, conforming and nonconforming error estimators are presented and analyzed for finite element solutions of symmetric positive differential equations in the sense of Friedrichs. These estimators are devised to treat the Friedrichs system in a general setting in terms of application (hyperbolic as well as mixed-type problems), approximation (h-, p and hp-version finite element methods), implementation (no local boundary conditions and no flux jumps across element boundaries) and a posteriori error analysis (very moderate conditions on the system and on the approximation). Three model problems of the Friedrichs system, namely, the neutron transport equation, the forward-backward heat equation and the Tricomi problem are used to illustrate the applicability of the weak residual error estimation.
A unified analysis of a weighted least squares method for first-order systems
(1998-06-01)
Yang, SY
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A unified analysis of a weighted least squares finite element method (WLSFEM) for approximating solutions of a large class of first-order differential systems is proposed. The method exhibits several advantageous features. For example, the trial and test functions are not required to satisfy the boundary conditions. Its discretization results in symmetric and positive definite algebraic systems with condition number O(h(-2) + w(2)). And a single piecewise polynomial finite element space may be used for all test and trial functions. Asymptotic convergence of the least squares approximations with suitable weights is established in a natural norm without requiring extra smoothness of the solutions. If instead, the solutions are sufficiently regular, a priori error estimates can be derived under two suitable assumptions which are related respectively to the symmetric positive systems of Friedrichs and first-order Agmon-Douglis-Nirenberg (ADN) elliptic systems. Numerous model problems fit into these two important systems. Some selective examples are examined and verified in the unified framework. (C) 1998 Published by Elsevier Science Inc. All rights reserved.
A posteriori finite element error analysis for symmetric positive differential equations
(1999-01-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
Based on the solution of local weak residual problems, conforming and nonconforming error estimators are presented and analyzed for finite element solutions of symmetric positive differential equations in the sense of Friedrichs. These estimators are devised to treat the Friedrichs system in a general setting in terms of application (hyperbolic as well as mixed-type problems), approximation (h-, p and hp-version finite element methods), implementation (no local boundary conditions and no flux jumps across element boundaries) and a posteriori error analysis (very moderate conditions on the system and on the approximation). Three model problems of the Friedrichs system, namely, the neutron transport equation, the forward-backward heat equation and the Tricomi problem are used to illustrate the applicability of the weak residual error estimation.
A posteriori boundary element error estimation
(1999-06-15)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
An a posteriori error estimator is presented for the boundary element method in a general framework. It is obtained by solving local residual problems for which a local concept is introduced to accommodate the fact that integral operators are nonlocal operators. The estimator is shown to have an upper and a lower bound by the constant multiples of the exact error in the energy norm for Symm's and hypersingular integral equations. Numerical results are also given to demonstrate the effectiveness of the estimator for these equations. It can be used for adaptive h, p, and hp methods. (C) 1999 Elsevier Science B.V. All rights reserved.
A nonconforming weak residual error estimator for elliptic partial differential equations
(1999-09-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
A nonconforming weak residual error estimator is presented and analyzed for finite element solutions of linear elliptic partial differential equations. The treatment of the flux jumps across element edges is of special interest. The estimator is obtained by solving local residual problems which do not explicitly involve the jumps and do not require boundary conditions. The estimator handles both interior and edge residuals on each element by a suitable construction of the basis functions for the local problems. Together with the previous conforming estimator, the weak residual error estimation, without the flux jumps, can thus be applied to both odd- and even-order finite element approximations.
An a posteriori finite element error analysis for the Stokes equations
(2000-02-01)
Jou, J
;
Liu, JL
;
應用數學系
;
Department of Applied Mathematics
Conforming and nonconforming error estimators are presented and analyzed for the mixed finite element approximation of the Stokes problem. The estimators are obtained by solving local Poisson-type problems that do not involve boundary conditions, compatibility and balancing conditions, incompressibility constraint, or flux jumps across inter-element boundaries. The estimators are bounded from above and below by constant multiples of the actual error in an energy-like norm and can be used in adaptive h, p, and hp computations. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 65N15; 65N30.

學術出版;;Publications

Browse

Filters

Settings

Sort By

Results per page

🏛️國立陽明交通大學機構典藏

Search Results