Computational Aspects of the Calculation of the Leading Divergence of a Particle?Particle Ladder

Abstract

In order to isolate the leading divergence of a particle-particle ladder graph, we wish to study the most positive eigenvalue, and its eigenfunction, of the operator describing the addition of one rung. We discuss issues of computational efficiency associated with the setting up and solving of the resulting eigenvalue problem, with an emphasis on the use of inherent symmetries to reduce the size of the problem, and the choice of machine and algorithms appropriate for the calculation. In particular, we compare various load-balancing techniques for a problem involving a large number of independent integrals, requiring greatly differing amounts of computer time, which we have implemented on an Intel Paragon massively parallel supercomputer. We find that a stack-based parallel adaptive integration algorithm performs significantly better than a more natural recursive implementation when load-balancing is a priority.