We compare the performance on a concurrent computer of two domaindecomposition methods and a full-multigrid method for solving the Poisson equation on a square. Independent of the granularity of the computation, domain decomposition is almost always signi cantly slower than multigrid. Our largest computations use a multicomputer with 128 nodes to solve a problem on a 2048 2048 grid. In these co...

There are various techniques available to model the turbulence structure. Turbulence of incompressible water flow (without sediment) can be modelled completely using the Navier-Stokes equations. However for even a small part of a river channel, the size of the problem is many orders of magnitude larger than even the world’s largest super-computers can handle. This means that other techniques ar...

We consider multiple objective combinatorial optimization problems in which the first objective is of arbitrary type and the remaining objectives are either bottleneck or k-max objective functions. While the objective value of a bottleneck objective is determined by the largest cost value of any element in a feasible solution, the k-largest element defines the objective value of the k-max objec...

In this paper we study problems where one has to prove that certain graph parameter attains its maximum at the star and its minimum at the path among the trees on a fixed number of vertices. We give many applications of the socalled generalized tree shift which seems to be a powerful tool to attack the problems of the above mentioned kind. We show that the generalized tree shift increases the l...

For each positive integer n we use the concept of ‘admissible arrays on n symbols’ to define a set of positive integers Q(n) which is determined solely by number theoretical and combinatorial constraints and whose computation reduces to a finite problem. In earlier joint work with M. Scheutzow, it was shown that the set Q(n) is intimately connected to the set of periods of periodic points of cl...

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NS...

Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0-simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept of group of quotients [8]. To give the definition we first have to explain what is meant by a squar...