Publications [#56564] of Tod A Laursen

Papers Published

1. Donescu, Pompiliu and Laursen, Tod A., Generalized object-oriented approach to solving ordinary and partial differential equations using finite elements, Finite Elements in Analysis and Design, vol. 22 no. 1 (1996), pp. 93 - 107 [0168-874X(95)00061-W]
   (last updated on 2007/04/06)

   Abstract:
   This paper presents a new method of designing an object-oriented finite element program. In contrast to the traditional structured programming approach and some earlier object-oriented approaches designed only for solving specific problems, this approach adopts a very general structure originating from the weak from of the initial/boundary value problem. A coherent system of classes, representing concepts used in finite element methods, has been designed such that their instantiation discretizes the continuous problem into algebraic or differential equations. The discrete equations are further solved using a chain of instances of numerical methods, thus providing support for a flexible and problem-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.

   Keywords:
   Object oriented programming;Finite element method;Mathematical programming;Problem solving;Boundary value problems;Optimization;Algebra;Numerical methods;Structured programming;