Determination of stripe structures for finite element matrics

Stripe structures were introduced by the author [Parallel Computing, to appear] as a means for the inclusion of the nonzero elements of a sparse matrix into a regular pattern which allows for efficient parallel manipulation. In this paper the stripe structures of stiffness matrices resulting from irregular domains covered by regular grids are analyzed. It is proved that the nonzero elements in these matrices may be covered by very few stripes and that these stripes may be nonoverlapping if the nodes of the grids are numbered appropriately. The exact number of stripes, which is independent of the size of the problem, is derived for different types of grids and different numbering schemes. The stripe structures of some irregular grids are also examined.