Keywords: object oriented programming, boundary element method.

The adequacy of the concepts of object oriented programming (OOP) for implementation of numerical analysis programs based on the finite element method (FEM) has been demonstrated by several works. The early investigations on the possibilities of application of OOP to finite element programming were justified because FEM has been the most used computational method for solving a wide range of numerical problems in science and engineering. As a consequence, many researchers have proposed object oriented models for FEM which have shown that OOP improves code readability, modularity, and reusability.

In addition to FEM, the boundary element method (BEM) has become an important numerical method in science and engineering. BEM is mainly attractive because the dimensionality of a problem analysed by the method is decreased to one, usually only the boundary discretization of the body being analysed is required, which results in smaller equations systems. Furthermore, there are specific cases in which BEM can be more appropriately applied than FEM, e.g. to analysis of problems with semi-infinite domains.

This paper presentes a first approach to object oriented boundary element programming applied to elastostatic solid analysis. The implementation is based on the class library of OSW [1,2], a toolkit for development of C++ applications for analysis and visualization of structural models.

Eleven new classes for BEM analysis have been created and added into the OSW Class Libray (OCL); no original class has been modified. The functionality of the most important classes making up the proposed implementation is described in the paper. The discussion is only limited to the analysis capabilities of the BEM code, leaving aside any pre-processing and post-processing resources.

The BEM classes introduced in the paper has two main purposes. The first one is that they can be effectively employed in, or at least serve as inspiration to, the development of numerical applications based on BEM. In this sense, the next step of research will be to extend the functionality of OSW boundary element classes in order to support dynamic and nonlinear analysis. As a consequence, new classes will be created and, possibly, already existent classes will be modified. The second objective is to provide an object oriented framework for developing of modeling applications based on FEM/BEM coupling.

Because of the employment of object oriented techniques such as encapsulation, inheritance, and polymorphism, the code listed in paper can be more easily expanded by creating derived classes from the BEM classes and overloading the inherited virtual methods. Improvements on the proposed implementation can include new types of elements, internal cells or solvers, or the use of other integration schemes or fundamental solutions.

1

P.A. Pagliosa, J.B. Paiva, "OSW: a toolkit for object oriented structural modeling", in Developments in Engineering Computational Technology, ed. B.H.V. Topping, Civil-Comp Press, 151-166, 2000. doi:10.4203/ccp.68.7.6

2

P.A. Pagliosa, J.B. Paiva, "A toolkit for building object oriented structural modeling applications", submitted to Computer and Structures, 2002.

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