P. Donescu et Ta. Laursen, A GENERALIZED OBJECT-ORIENTED APPROACH TO SOLVING ORDINARY AND PARTIAL-DIFFERENTIAL EQUATIONS USING FINITE-ELEMENTS, Finite elements in analysis and design, 22(1), 1996, pp. 93-107
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.