Solving quantum-mechanical problems on parallel systems

A general and very common procedure of computing matrix elements and solvin g the general symmetric eigenvalue problem is analyzed from the point of vi ew of efficient utilization of computational resources in distributed memor y environment. Although the impetus for this research originates in the qua ntum mechanics, the results may be useful in other areas of science dealing with the matrix eigenequation. The problem of solving the Schrodinger equa tion is reduced to two main building blocks: the evaluation of the matrix e lements 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 ch oice of an optimum processor's grid and block size is up to the user and sh ould be based on a careful numerical experiment. Sample results of such an experiment are presented. (C) 2000 Elsevier Science B.V. All rights reserve d.