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pySDC is a Python implementation of the spectral deferred correction (SDC) approach and its flavors, esp. the multilevel extension MLSDC and PFASST.

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This PR contains the Runge-Kutta sweeper base class for solving DAEs. Runge-Kutta methods for general DAEs $$0 = F(u, u', t)$$ read $$0 = F(u_0 + \Delta t \sum_{j=1}^m a_{i,j}...

Since more files were added to the ``DAE`` project ``README.rst`` got an update by adding the new files to the list there. Further, I added a section how to implement...

Turns out the base transfer class is not compatible with the diagonal sweepers. This is required for PFASSTER. I don't really know the underlying mathematics, so I just test that...

- [ ] [`Advection_ND_FD`](https://parallel-in-time.org/pySDC/coverage/d_91faa57f8583c837_AdvectionEquation_ND_FD_py.html): Dirichlet and higher dimensions - [ ] [`AllenCahn_MPIFFT`](https://parallel-in-time.org/pySDC/coverage/d_91faa57f8583c837_AllenCahn_MPIFFT_py.html): IMEX and `rand_circle` (do we need IMEX here?) - [ ] [`AllenCahn_Temp_MPIFFT`](https://parallel-in-time.org/pySDC/coverage/d_91faa57f8583c837_AllenCahn_Temp_MPIFFT_py.html): `rand_circle` (what about IMEX here?) -...

enhancement

I started looking into the transfer operators a little bit and noticed some issues. I will collect what I find here because I don't know if I have time to...

bug
help wanted

Mirror repository with Gitlab-Repo so that CI can use HPC-Resources. This is helpful e.g. for running GPU-Tests and/or for running Benchmarks. Tasks that should be done: - [x] Mirror with...

With #407 we have our first C/C++ source code shipping with pySDC. Looks like CodeQL does not like this (see failing action [here](https://github.com/Parallel-in-Time/pySDC/actions/runs/8506815602)). Possible troubleshoot: https://docs.github.com/en/code-security/code-scanning/troubleshooting-code-scanning/no-source-code-seen-during-build

The $\varepsilon$_-embedding method_ is a tool that can be used to get insights into the behavior of numerical methods when applied to stiff ODEs and DAEs. Assume we have a...

help wanted
question

To follow up on the discussion started in https://github.com/Parallel-in-Time/pySDC/commit/04fdedc56e52258fa88ea98aae5602d5944fc7c0#r138624434, @brownbaerchen @lisawim (and also centralize all that have been done on this topic, don't hesitate to complement the description ...) Workspace...

The files [problem_helper.py](https://github.com/Parallel-in-Time/pySDC/blob/729cb6913addd41d530ff3b54bb8292ff52ed77f/pySDC/helpers/problem_helper.py) and [buildFDMatrix.py](https://github.com/Parallel-in-Time/pySDC/blob/729cb6913addd41d530ff3b54bb8292ff52ed77f/pySDC/implementations/problem_classes/acoustic_helpers/buildFDMatrix.py) have the same purpose, only that the problem helper is more generic, tested and supposed to replace hardcoded finite difference stencils like in the file...

enhancement
good first issue