Finite element analysis of solidification using object-oriented and parallel techniques

This paper describes an implementation in C++ and in parallel of an explicit nite element formulation for the solution of transient heat conduction problems with phase change. The scheme requires a very small timestep because of its conditional stability, but, as no matrix inversion is required, the cost per timestep is an order of magnitude lower than for a conventional scheme. The principles of using object-oriented techniques for general nite element programming are brie y ex- plained, while the advantages for parallel processing are described in detail, including the classes used to perform message passing. An example is given showing the performance of the scheme on two completely di erent parallel machines: a shared memory Silicon Graphics Power Challenge, and a distributed memory Cray T3D. The results indicate that the program scales e ciently for large meshes