THE DOMAIN COMPOSITION METHOD APPLIED TO POISSONS-EQUATION IN 2 DIMENSIONS

Domain composition, a recently described method for formulating contin uum field problems, removes certain restrictions on the construction o f finite element models such that it is possible to solve a finite ele ment problem without using a global compatible mesh. The domain compos ition method couples or otherwise constrains meshes in local regions t o obtain a solution equivalent to that produced by conventional finite element methods. In particular, the domain composition method enables finite element models to be formulated with overlapping elements. Sev eral advantages come from this, including an ability to automatically generate a finite element model from a solid geometric model, an abili ty to use a variety of element types in a single finite element model and an ability to exactly match element boundaries to the local geomet ry. This paper shows in detail a finite element formulation of Poisson 's equation using domain composition and presents certain key algorith ms that incorporate the domain composition method into well-establishe d finite element procedures.