Department of Technical Mathematics and Informatics

Delft University of Technology

Mekelweg 4

2628 CD Delft

The Netherlands

Efficient computation of coarse grid matrices is important to the overall
efficiency of multigrid methods using Galerkin coarse grid approximation. A
way to compute coarse grid matrices efficiently (algorithm CALRAP) with the
non-zero pattern of coarse grid matrices determined by the algorithm STRURAP
is discussed for the 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 innermost loop of 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 algorithm is
presented for the case that the discretization matrix 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.

Contributed Februrary 4, 1994.