On the algebraic construction of multilevel transfer operators

The basic idea of our new approach is to determine in a first step for each node those pairs of nodes which allow a good interpolation of the unknowns located at this node. These pairs of neighbor nodes (in some cases only on e node) are called parent nodes. This is done by solving a local minimizati on problem which, in addition, yields the interpolation and restriction coe fficients. The construction scheme has been generalized to systems of conve ction-diffusion-reaction equations using a point-block approach. After these suitable pairs of parent nodes have been determined. the nodes are labeled as C- and F-nodes such that each F-node can be interpolated usi ng one of these suitable pairs of parent nodes and the already computed coe fficients. Additionally, a simple heuristic algorithm tries to minimize the number of C-nodes and the number of non-zero entries in the coarse grid ma trix. The algorithm has been parallelized and shows mesh size independent converg ence for standard model problems. Realistic numerical experiments confirm t he efficiency of the presented algorithm.