Commit 42156741 authored by Davide Torlo's avatar Davide Torlo
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updated the python notebook with the arxiv version

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In this repository we provide a *Python* and a *Julia* implementation of the RDeC method: an arbitrarily high order accurate time integration method that allows to preserve (or dissipate) entropies for ODEs and simple hyperbolic PDEs. This repository provides the code used in the work **Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes** by R. Abgrall, E. Le Mélédo, P. Offner and D. Torlo available at this [arXiv link](https://arxiv.org/abs/2106.05005).
In the [python notebook](Notebooks/python/Relaxation Runge--Kutta tests for inner-product norms.ipynb) there is an extension of the [notebook](https://github.com/ketch/RRK_rr) proposed by H. Ranocha, M. Sayyari, L. Dalcin, M. Parsani and D. I. Ketcheson. There the DeC is written into a Runge--Kutta form and it is used to solve the same tests proposed by the original relaxation Runge--Kutta work.
In the [python notebook](Notebooks/python/RelaxationDeC.ipynb) there is an extension of the [notebook](https://github.com/ketch/RRK_rr) proposed by H. Ranocha, M. Sayyari, L. Dalcin, M. Parsani and D. I. Ketcheson. There the DeC is written into a Runge--Kutta form and it is used to solve the same tests proposed by the original relaxation Runge--Kutta work. The file with the DeC related functions, including the passage to Runge--Kutta methods is [here](Notebooks/python/DeC.py).
In the [Julia notebook](Notebooks/julia/RelaxationDeC.ipynb) an implementation of the relaxation DeC, without recurring to a Runge--Kutta algorithm, is provided, in particular in [Relaxation DeC implementation](Notebooks/julia/DeC.jl). In this notebook only energy conservative/dispersive tests are considered. We test the convergence of RDeC up to 8th order in this notebook.
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