Efficient Algorithm for the Computation of Galerkin Coarse Grid Approximation forthe Incompressible Navier-Stokes Equations

摘要

A way to compute coarse grid matrices efficiently (algorithm CALRAP) with the nonzero pattern of coarse grid matrices determined by the algorithm STRURAP is discussed for operator independent prolongations and restrictions with boundary modifications, assuming that the discretization matrix on the finest grid is derived from a scalar partial differential equation. By means of partition of grids, the computation of coarse grid matrices near boundaries is well treated in the same way as for interior grid points, with neither introducing 'if-then' statements nor distinguishing between interior and boundary cases in the inner most loop of the algorithm CALRAP, which is expected to give an efficient computation of coarse grid matrices. Quasi ALGOL descriptions of the two algorithms are developed, which can be used as predesigns for practical FORTRAN codes. A generalization of the algorithms is presented for the case that the discretization matrix is derived from a set of partial differential equations, particularly the incompressible Navier-Stokes equations, discretized on a staggered grid. A quasi ALGOL description of the generalization is also given.