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scikit-finite-diff, a new tool for PDE solving

Nicolas Cellier; Christian Ruyer-Quil

Scikit-FDiff is a new tool, written in pure Python, that focus on reducing the time between the developpement of the mathematical model and the numerical solving.

It allows an easy and automatic finite difference discretization, thanks to a symbolic processing that can deal with systems of multi-dimensional partial differential equation with complex boundary conditions.

Using finite differences and the method of lines, it allows the transformation of the original PDE into an ODE, provinding a fast computation of the temporal evolution vector and the Jacobian matrix. The later is pre-computed in a symbolic way and sparsed by nature. It can be evaluated with as few computational ressources as possible, allowing the use of implicit and explicit solvers at a reasoneable cost.

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  • Cellier, N (2018). Optimisation d'échangeurs à films ruisselants.

  • LeVeque, R J (2002). Finite Volume Methods for Hyperbolic Problems.

  • Meurer, Aaron and al. (2017). SymPy: symbolic computing in Python.

  • Rang, Joachim (2015). Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs.

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