Subproject A2: Parallelization of Algebraic Program Systems

Project leader:
Prof. Dr. Johann Kühn, Institute of Theoretical Particle Physics, Karlsruhe Institute of Technology (KIT) and
Prof. Dr. Matthias Steinhauser, Institute of Theoretical Particle Physics, Karlsruhe Institute of Technology (KIT)

Short Summary:

In modern theoretical particle physics computer algebra systems (CAS) are indispensable. They are very important tools for the manipulation of formulae. The main focus of this project is the further development of ParFORM and TFORM, the parallel versions of FORM designed to handle huge algebraic expressions. In particular, the combination of the two different parallelization concepts is considered. In addition we develop in this project efficient programs for the reduction of Feynman integrals to master integrals and their numerical evaluation.


The symbolic manipulation of complicated formulae has a long tradition in particle physics. Computer algebra systems (CAS) have been used already quite early in order to evaluate, e.g., traces over γ matrices. Among the first CAS there are REDUCE and SCHOONSCHIP, the latter has been designed by M. Veltman. Afterwards Mathematica, Maple and others have been developed which are still in use nowadays. However, their field of application is limited to small and medium sized problems since it is not possible to work with very large intermediate expressions. On the other hand, there are quite a lot of problems which produce intermediate expression of the order of a few hundred giga bytes up tera bytes to be manipulated by the CAS. The only CAS currently available in order to cope with such tasks is FORM.

Although FORM is very powerful, there are many important physical applications where even FORM requires several weeks or even months of CPU time. Furthermore the resources as far as CPU speed, memory and disk space are concerned are often not sufficient. An obvious solution is the parallelization of FORM which makes simultaneously available the resources of several computers and furthermore significantly reduces the wall clock time.

In recent years two concepts for parallel versions of FORM have been successfully implemented: ParFORM, essentially based on MPI (message passing interface), and TFORM which uses threads for the parallelization and has been developed in the current funding period. Both programs run stable, show a good speedup and are complete in the sense that all programs written for the serial version of FORM can now be used with ParFORM and TFORM}. For the next funding period we aim at the combination of both parallelization concepts allowing for the efficient use of clusters build from multi-core nodes. Furthermore, an improvement of the speedup behaviour is on the agenda.

In this project there are also activities concerned with the reduction of families of Feynman integrals to a small set of basis elements (master integrals) and their numerical evaluation. These two topics are covered in two program packages, FIRE and FIESTA, which have been published within this project. In the next period we plan to rewrite FIRE in C++ and to extend FIESTA to additional kinematical regions.

Last Change : 14th June 2011