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Manuscript Title: FIESTA 2: parallelizeable multiloop numerical calculations
Authors: A.V. Smirnov, V.A. Smirnov, M. Tentyukov
Program title: FIESTA2
Catalogue identifier: AECP_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 182(2011)790
Programming language: Wolfram Mathematica 6.0 (or higher) and C.
Computer: From a desktop PC to a supercomputer.
Operating system: Unix, Linux, Windows, Mac OS X.
Has the code been vectorised or parallelized?: Yes, the code has been parallelized for use on multi-kernel computers as well as clusters via Mathlink over the TCP/IP protocol.
The program can work successfully with a single processor, however, it is ready to work in a parallel environment and the use of multi-kernal processor and multi-processor computers significantly speeds up the calculation; on clusters the calculation speed can be improved even further.
RAM: Depends on the complexity of the problem
Keywords: Feynman diagrams, Sector decomposition, Numerical integration, Data-driven evaluation.
PACS: 02.60.jh, 02.70.Wz, 12.38.Bx.
Classification: 4.4, 4.12, 5, 6.5.

External routines: QLink [1], Cuba library [2], MPFR [3]

Does the new version supersede the previous version?: Yes

Nature of problem:
The sector decomposition approach to evaluating Feynman integrals falls apart into the sector decomposition itself, where one has to minimize the number of sectors; the pole resolution and epsilon expansion; and the numerical integration of the resulting expression.

Solution method:
The sector decomposition is based on a new strategy as well as on classical strategies such as Speer sectors. The sector decomposition, pole resolution and epsilon-expansion are performed in Wolfram Mathematica 6.0 or, preferably, 7.0 (enabling parallelization) [4]. The data is stored on hard disk via a special program, QLink [1]. The expression for integration is passed to the C-part of the code, that parses the string and performs the integration by one of the algorithms in the Cuba library package [2]. This part of the evaluation is perfectly parallelized on multi-kernel computers.

Reasons for new version:
  1. The first version of FIESTA had problems related to numerical instability, so for some classes of integrals it could not produce a result.
  2. The sector decomposition method can be applied not only for integral calculation.

Summary of revisions:
  1. New integrator library is used.
  2. New methods to deal with numerical instability (MPFR library).
  3. Parallelization in Mathematica.
  4. Parallelization on multiple computers via TCP-IP.
  5. New sector decomposition strategy (Speer sectors).
  6. Possibility of using FIESTA to for integral expansion.
  7. Possibility of using FIESTA to discover poles in d.
  8. New negative terms resolution strategies.

The complexity of the problem is mostly restricted by CPU time required to perform the evaluation of the integral

Running time:
Depends on the complexity of the problem

[1] http://qlink08.sourceforge.net, open source;
[2] http://www.feynarts.de/cuba/, open source;
[3] http://www.mpfr.org/, open source;
[4] http://www.wolfram.com/products/mathematica/index.html.