Solving quantum-mechanical problems on parallel systems

A general and very common procedure of computing matrix elements and solving the general symmetric eigenvalue problem is analyzed from the point of view of efficient utilization of computational resources in distributed memory environment. Although the impetus for this research originates in the quantum mechanics, the results may be useful in other areas of science dealing with the matrix eigenequation. The problem of solving the Schrodinger equation is reduced to two main building blocks: the evaluation of the matrix elements and the solution of the matrix eigenproblem. These two subproblems, which undergo parallelization in different ways, are analyzed in terms of the influence of the data distribution parameters on the efficiency. The choice of an optimum processor's grid and block size is up to the user and should be based on a careful numerical experiment. Sample results of such an experiment are presented. (C) 2000 Elsevier Science B.V. All rights reserved.