RK sweeper #163
RK sweeper #163
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pancetta
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pancetta
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Could you move the test_order into the tests? Then it'll be picked up during CI testing.
with the new sweepers which avoids integration with both preconditioner and quadrature matrix. The nodes might be wrong, which would only show up in problems with time-dependent right hand sides.
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Please have a look at the stability plots at the bottom of https://github.com/Parallel-in-Time/pySDC/blob/8201e6e4e46d1866b506b6081065456b8d313aa2/pySDC/playgrounds/Runge_Kutta/Runge-Kutta-Methods.ipynb Are they what you would expect? I have no idea about RK methods and stability. In particular: Is implicit midpoint A-stable or did I make a mistake? |
LGTM. The plot for the explicit methods is somewhat hard to read, though. Could you highlight the region of stability? |
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And yes, implicit midpoint is A-stable, being a Gauss-Legendre method. |
collocation are given and I shaded the regions of stability in the plot
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Explicit Euler is unusually stable (entire left half plane). That's weird.. Any ideas why? |
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Where do you see this? Smells like you did implicit Euler by accident. |
Again in the last plot in https://github.com/Parallel-in-Time/pySDC/blob/a1bfc50fe1e15799d260e0b51362cb949dd78b75/pySDC/playgrounds/Runge_Kutta/Runge-Kutta-Methods.ipynb The stability region looks different than that of implicit Euler, though.. |
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New sweeper that takes a lower triangular Butcher tableau as input and does Runge-Kutta. I tried to eliminate unnecessary computations by forgoing the preconditioner, rather than setting preconditioner equal to the quadrature rule.
In the jupyter notebook there is a plot that confirms the order of a few RK schemes, but I have not made any further analysis and also implemented only few RK schemes.