A parallelizable element-by-element multilevel block ILU preconditioner

We consider a new element-by-element algebraic multilevel block-ILU preconditioner for linear systems with an underlying element structure. The multilevel block-ILU factorization is formed in an element-by-element fashion. The resulting preconditioner has a high degree of inherent parallelism and uses BLAS3 and LAPACK routines during construction. The resulting algorithm also resembles the multifrontal method well. Our numerical experiments demonstrate the effectiveness of the preconditioner relative to ARMS and ILUT on some problems from computational fluid dynamics.status: publishe