FlowPy—A numerical solver for functional renormalization group equations

Abstract

FlowPy is a numerical toolbox for the solution of partial differential equations encountered in Functional Renormalization Group equations. This toolbox compiles flow equations to fast machine code and is able to handle coupled systems of flow equations with full momentum dependence, which furthermore may be given implicitly. Program summaryProgram title: FlowPyCatalogue identifier: AEPB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 4078No. of bytes in distributed program, including test data, etc.: 46,609Distribution format: tar.gzProgramming language: Python, C.Computer: PC or workstation.Operating system: Unix.RAM: approx. 40 MBClassification: 4.12, 11.1.External routines: Python, libpython, SciPy, NumPy, python-simpleparse.Nature of problem:In the study of functional renormalization group equations non-local integro-differential equations arise which furthermore can contain singular coefficient functions for the highest derivative and may only be given implicitly. Solving these equations beyond the simplest cases thus provides a numerical challenge.Solution method:A combination of numerical differentiation, integration, interpolation, and ODE solving.Restrictions:Due to the nature of FRG problems, computational effort (run time) will scale quadratically with the number of discretization points. Using more than at most a few hundred discretization points may be impractical.Running time:For the SUSY_QM example: ∼10 s for 10 support points, ∼5 min for 100 discretization points. For the momentum_dependent_wavefunction example: ∼40 min for 5 discretization points.