Object-oriented programming and the extended finite-element method

The paper deals with the extended finite-element method (X-FEM) and its object-oriented implementation. The X-FEM, which belongs to the family of methods based on the partition of unity, is a numerical technique that extends the classical finite-element method approach by enriching the solution space with tailored functions. This permits the natural reproduction of many features associated with the underlying problem, such as the discontinuities, singularities, boundary layers and so on, while retaining the advantages of finite-element formulation. The implementation of the X-FEM, particularly its integration into an existing code, is a complex task. In this paper, a design of an object-oriented X-FEM toolkit will be presented, with particular attention paid to its generality, extensibility and easy integration.