Parallel Incomplete Factorization Preconditioning of Rotated Linear Fem Systems

The recent efforts in development of efficient solution methods for nonconforming finite element systems are inspired by their importance for various applications in scientific computations and engineering. This study is focused on the implementation of rotated bilinear elements. A locally modified approximation of the global stiffness matrix is proposed allowing for: a) a stable MIC(0) factorization; and b) a scalable parallel implementation. An optimal condition number estimate is derived for the constructed sparse matrix approximation with respect to the original global stiffness matrix. The estimates of the parallel speed-up and the parallel efficiency as well as the presented parallel numerical tests demonstrate the potential of the PCG algorithm and the MPI code developed. Mathematical Subject Classification: 65F10, 65N30