Commit 4671111d authored by Davide Torlo's avatar Davide Torlo
Browse files

updated arxiv link

parent de837464
......@@ -13,7 +13,7 @@
"source": [
"This notebook is an extension of the original [Relaxation Runge--Kutta Notebook](https://github.com/ketch/RRK_rr) provided by D. Ketcheson and H. Ranocha on the work of H. Ranocha, M. Sayyari, L. Dalcin, M. Parsani and D. I. Ketcheson on [Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations](https://doi.org/10.1137/19M1263480).\n",
"\n",
"Here we use the Deferred Correction method as a Runge--Kutta method. The implementation of the Deferred Correction method as a Runge--Kutta method is included in [DeC.py](DeC.py) and explained in details in the work [Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes ](https://arxiv.org/search/?searchtype=author&query=Torlo%2C+D) by R. Abgrall, E. Le Mélédo, P. Öffner and D. Torlo."
"Here we use the Deferred Correction method as a Runge--Kutta method. The implementation of the Deferred Correction method as a Runge--Kutta method is included in [DeC.py](DeC.py) and explained in details in the work [Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes ](https://arxiv.org/abs/2106.05005) by R. Abgrall, E. Le Mélédo, P. Öffner and D. Torlo."
]
},
{
......
......@@ -3,10 +3,10 @@
[![License: MIT](https://img.shields.io/badge/License-MIT-success.svg)](https://opensource.org/licenses/MIT)
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 in [arXiv link](arxiv.org).
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 [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/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 [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.
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment