適應性方法的物件導向程式設計

Abstract

本論文使用物件導向程式語言發展出一套結合適應性計算與有限元素法， 有限體積法，和最小平方有限元素法的數值計算軟體，用以求得一般變分 問題的數值解。此軟體命名為 AdaptC++ ，其基本的部分包括精確化策略 ，不規則網格的資料結構，數值解法，線性方程組解法和弱剩餘誤差估計 。 AdaptC++ 展現了物件導向程式語言運用在複雜度較高之適應性方法上 的價值，並且達成了適應性技術的可重用性和可擴充性。此外，本論文提 出一些適應性過程上的新演算法。最後，以二維的 driven cavity flow 問題來顯示 AdaptC++ 基本特色—親和的使用環境，抽象的資料結構，功 能的多重選擇，和上述適應性的性能。 An object-oriented code in C++, dubbed by AdaptC++, for the solution analysis on a class of general variational problems is developed in connection with finite element, finite volume, and least-squares finite element methods. Basic components constituting the code are refinement strategies, data structures of unstructured mesh, numerical solvers, linear system solvers, and weak residual error estimators. The code shows the merit of the object-oriented programming (OOP) in handling complex programming tasks and promises the use of OOP in adaptive technology. Along with the development, some new algorithms in terms of adaptive process and OOP are proposed. A model problem of 2-D driven cavity flow is given to demonstrate, among other things, the fundamental features of the code - user friendly environment, abstract data structure, multiple choice of tasks, and above all the remarkable performance of adaptivity.