A GENERALIZED OBJECT-ORIENTED APPROACH TO SOLVING ORDINARY AND PARTIAL-DIFFERENTIAL EQUATIONS USING FINITE-ELEMENTS

This paper presents a new method of designing an object-oriented finit e element program. In contrast to the traditional structured programmi ng approach and some earlier object-oriented approaches designed only for solving specific problems, this approach adopts a very general str ucture originating from the weak form of the initial/boundary value pr oblem. A coherent system of classes, representing concepts used in fin ite element methods, has been designed such that their instantiation d iscretizes the continuous problem into algebraic or differential equat ions. The discrete equations are further solved using a chain of insta nces of numerical methods, thus providing support for a flexible and p roblem-optimized code.The proposed approach is applied to a series of test problems from elasto-plasticity, heat transfer and fluid dynamics , and appears to be easily adaptable to a large range of problems.