Implementation of a novel element-by-element finite element method on the hypercube Original Research Article

This paper discusses an implementation of a novel element-by-element finite element method recently proposed by Layton and Rabier [5] on the Hypercube. The algorithm uses element matrices, thereby avoiding the assembly of the global stiffness matrix. In addition, the elemental stiffness matrix calculations decouple from ech other, making the algorithm completely parallel. Experimental results are presented and found to support the rapid convergence results of [5]. The method makes good use of all the processors. On meshes with over 500 elements, sample runs show that the percentage of communication time to total processing time is at most 10%, even on 16 processors.