Parallelization of the edge based stabilized finite element method

This paper presents a finite element formulation for solving multidimensional compressible flows. This method has been inspired by our experience with the SUPG, tile Finite Volume and tile discontinous-Galerkin methods. Our objective is to obtain a stable and accurate finite element formulation for multidimensional hyperbolic-parabolic problems with particular emphasis oil compressible flows. In tile proposed formulation, the upwinding effect is introduced by considering the flow characteristics along tile normal vectors to the element interfaces. Numerical tests performed so far are encouraging. It is expected that further numerical experiments and a theoretical analysis will lead to more insight into this promising formulation. The computational performance issue is addressed through a parallel implementation of the finite element data structure and tile iterative solver. PSPARLIB and MPI libraries are used for this purpose. The implicit parallel solver developed is based on the nonlinear version of GMRES and Additive Schwarz algorithms. Fairly good parallel performance is obtained.