Abstract:The eigenvalue problem is one of the most recurring numerical task in scientific and engineering disciplines. For example, Shell Model or RPA calculations, that are fundamental tools for the study of many-body systems, consist, from a numerically point of view, in solving an eigenvalue problem. The matrix to be diagonalized, is typically the representation of the Hamiltonian operator in a finite basis. A common problem is that the dimensions of the matrix increase very rapidly with the size of the studied physical system. Therefore, the critical points in the diagonalization methods are the amount of needed memory and the time spent in the diagonalization process. Standard methods are often not suited and alternative approaches have to be used. In recent years, parallel eigensolvers, which use parallel computers technology, have been developed. SLEPC, is a free software library for the solution of large sparse eigenvalue problems. It allows to choose different algorithm of diagonalization, such as Lanczos, Arnoldi etc., and to use parallel distributed-memory strategies, where the data of the problem are distributed across the available processors. In order to study SLEPC library features, we have tested it in the study of a schematic physical model (Picket-Fence), paying particular attention to its parallel efficiency. Good results have been obtained (see figure). In the near future we plan to use Grid infrastructure, together with parallel libraries, to the study of collective properties of large size many-body systems.
<BR><BR><B>Software requirements</B>: F77 and F90 compiler, PETSC and SLEPC library^