Performance of a parallel mixed finite element implementation for fourth order clamped anisotropic plate bending problems in distributed memory environments

Abstract

The paper deals with a parallel implementation of a mixed finite element method of solution of a fourth order elliptic partial differential equation which in the particular case of aniso-/ortho-/isotropic plate bending problems gives a simultaneous approximation to the bending moment tensor field Ψ=(ψij)1⩽i,j⩽2 and the displacement field u. The parallel implementation has been done in Silicon Graphics Origin 3800, a 4 processor Intel Xeon Symmetric Multiprocessor and a beowulf cluster1 of four Intel Pentium III PCs. The indefinite linear system obtained after discretization using mixed finite element method is solved in parallel using direct (Schur's Complement approach) and iterative method (using Argonne National Laboratory's PETSc package). The numerical results obtained and the time, speed-up comparisons for the direct method and iterative methods for a few interesting examples are also given.