Efficient a priori pivoting schemes for a sparse direct Gaussian equation solver for the mixed finite element formulation of the Navier-Stokes equations

摘要

A sparse direct solver for the Navier-Stokes is designed. The equation matrix is generated with a priori pivoting. The a priori pivoting is obtained by sorting the nodes prior to assembling the finite element matrix. Three ordering schemes of nodes are investigated. The nodes are sorted with respect to a point far away from the mesh, sequential ordering, the nodes are sorted with respect to the center of the mesh, circular ordering, and the node ordering is randomized, random ordering. The matrix is stored in two one dimensional vectors, containing the upper and lower triangular parts of the equation matrix. The addressing to the coefficient in the matrix is performed through addressing vectors. The complete structure of the equation matrix is obtained by symbolic factorization. The priori pivoting schemes are compared with regard to storage requirements and time efficiency.