Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations

TL;DR

Kranc is a Mathematica-based suite that automates the conversion of tensorial PDE systems into parallelized C or Fortran code, aiding physicists and mathematicians in rapid prototyping and efficient code generation for numerical relativity.

Contribution

It introduces a novel Mathematica toolkit that seamlessly translates complex tensorial PDEs into optimized parallel code integrated with the Cactus framework.

Findings

Successfully generates parallelized code for Einstein equations

Demonstrates efficiency and performance in numerical relativity simulations

Facilitates rapid prototyping of complex PDE systems

Abstract

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.