A parallel multiple front algorithm for p-adaptive finite element solution of viscous incompressible flows

A parallel multiple-front solution algorithm is developed for solving the linear systems arising from finite element discretization of boundary value problems and evolution problems such as those encountered in viscous incompressible hows. The basic substructuring approach and frontal algorithm on each subdomain are first modified to ensure stable factorization in situations where ill-conditioning may occur due to differing material properties or the use of high degree elements (p methods). The subdomain problems are reduced to the Schur's complement problems on the interfaces that may also include some of the internal unknowns that were not eliminated during the subdomain frontal factorization steps due to the absence of suitable pivots. We develop a recursive interface partitioning strategy for solving the global Schur's complement problem in parallel over a number of processors. The new algorithm is based on a graph theoretical representation of the subdomain interfaces.