Browsing by Author "Lin, IJ"

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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.
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.
On k-ary spanning trees of tournaments
(1999-03-01)
Lu, XY
;
Wang, DW
;
Chang, GJ
;
Lin, IJ
;
Wong, CK
It is well known that every tournament contains a Hamiltonian path, which can be restated as that every tournament contains a unary spanning tree. The purpose of this article is to study the general problem of whether a tournament contains a k-ary spanning tree. In particular, we prove that, for any fixed positive integer k, there exists a minimum number h(k) such that every tournament of order at least h(k) contains a k-ary spanning tree. The existence of a Hamiltonian path for any tournament is the same as h(1) = 1. We then show that h(2) = 4 and h(3) = 8. The values of h(k) remain unknown for k greater than or equal to 4. (C) 1999 John Wiley & Sons. Inc. J Graph Theory 30: 167-176, 1999.