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Time Integration with NodalKernels #5883

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friedmud opened this issue Oct 28, 2015 · 4 comments
Closed

Time Integration with NodalKernels #5883

friedmud opened this issue Oct 28, 2015 · 4 comments
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C: Framework P: normal A defect affecting operation with a low possibility of significantly affects. T: defect An anomaly, which is anything that deviates from expectations.

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@friedmud
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NodalKernels were introduced in #5815 but they show issues with high order time integration. We need to get that figured out.

@friedmud friedmud added C: Framework T: defect An anomaly, which is anything that deviates from expectations. P: normal A defect affecting operation with a low possibility of significantly affects. labels Oct 28, 2015
@jwpeterson
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Specifically, BDF2 worked great but there were issues with Crank-Nicolson and the second-order Dirk scheme...

@friedmud
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Got it....

figure_1

It was what @permcody found in #5949

Man... DIRK has signficantly lower error! An order of magnitude lower than even Crank-Nicolson! 3 orders of magnitude lower than regular Backward Euler. Maybe I should use that thing more often!

What are the downsides to it?

@jwpeterson
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The error constant (vertical offset of the lines) strongly depends on the test problem and the higher derivatives (in time) of the true solution. So I wouldn't draw too many general conclusions from this one test problem. In that other plot I posted, for example, Crank-Nicolson had the lowest error of the second-order methods:

implicit_plot

The main drawback of the DIRK scheme is that it requires two solves per timestep, the benefit of the scheme over Crank-Nicolson is that it's L-stable (no ringing on stiff problems).

@friedmud
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Gotcha. Thanks John!

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Labels
C: Framework P: normal A defect affecting operation with a low possibility of significantly affects. T: defect An anomaly, which is anything that deviates from expectations.
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