An algebraic multilevel parallelizable preconditioner for large-scale CFD problems

An efficient parallelizable preconditioner for solving large-scale CFD problems is presented. It is adapted to coarse-grain parallelism and can be used for both shared and distributed-memory parallel computers. The proposed preconditioner consists of two independent approximations of the system matrix. The first one is a block-diagonal, fully parallelizable approximation of the given system. The second matrix is coarser than the original one and is built using algebraic multi-grid methods. The preconditioner is used to compute the steady solution of the compressible Navier-Stokes equations for subsonic laminar flows, on shared-memory computers, for a moderate number of processors. The coupled two-level preconditioner is robust and has a large potential for parallelism. Interesting savings in computational time for parallel computations are obtained when comparing the two-level preconditioner with the well-known incomplete Gaussian factorization.