[petsc-users] TimeStepper norm problems. EMIL Please read this

[Lisandro Dalcin]

On 21 March 2015 at 17:32, Emil Constantinescu <emconsta at mcs.anl.gov> wrote:
> When -ts_theta_adapt is used, then it detects the instability as an error
> and reduces the step by a lot! wlte=1.24e+03 which means that the reduction
> should be severe but the controller tries 0.1*dt and that seems to pass but
> it "jig-saws" (take a look at the next attempted step), which means that it
> is likely unstable.

I think -ts_theta_adapt is seriously broken, I cannot make sense of
the way the error estimator is computed.

I have an alternative implementation of adaptivity in PetIGA in custom
Generalized-Alpha implementation. The adaptivity is not based on
embed-RK like for TSCN, but in storing a solution vector from the
previous step then estimate the LTE with backward differences. BTW,
this idea can be generalized to any second-order method at the cost of
tracking an extra solution vector and a bunch of Vec operations.

Emil, if you want to try my code to give it a try, it is very easy to
integrate, you just need to copy a file to your sources
(https://bitbucket.org/dalcinl/petiga/src/tip/src/tsalpha1.c) and add
a TSRegister() call after PetscInitialize(). Then you pass in the
command line -ts_type alpha1 -ts_alpha_adapt. You can also pass
-ts_alpha_radius 0.5 to add some high-frequency dissipation (the
default is 1.0, then the method is roughly equivalent to the midpoint
rule).

PS: I would like to put all this in PETSc, but before that, I need
help from you guys to make sure this method really makes sense. The
fact that this has worked very well for me in some problems is not
enough.

-- 
Lisandro Dalcin
============
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