[petsc-users] ARKIMEX produces incorrect values

[Barry Smith]

  Sure, random definitely is better. 

  Seems like worth putting in (at least debug mode) since it will catch nearly all incorrect uses of this functionality.

  Barry


> On Aug 31, 2020, at 10:23 AM, Jed Brown <jed at jedbrown.org> wrote:
> 
> Ed Bueler <elbueler at alaska.edu> writes:
> 
>>>>> I realize the ARKIMEX page does say "Methods with an explicit stage can
>>>>> only be used with ODE in which the stiff part G(t,X,Xdot) has the form
>> Xdot
>>>>> + Ghat(t,X)."  So my example does not do that.  Is there a way for
>>>>> ARKIMEX to detect that dG/d(Xdot) = I?
>>> 
>>>> Other than sampling its action on vectors?  Not really; it's user code.
>>> 
>>> Call TSComputeIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec Y,PetscBool
>>> imex) with Udot all 1 and rhsfunction turned off. Call again with Udot is
>>> zero, take the difference. If it does not return all 1 then you know the
>>> user has provided an unacceptable function?
> 
> That's weaker than sampling with random vectors.  For example, it would
> "accept" any case in which the matrix has row sum of 1, which is true
> for permutation matrices, arbitrary mass matrices (with appropriate
> scaling), etc.  It'd be more reliable to set Udot=random and check that
> the difference matches that random vector.
> 
>>> You could do this at the beginning of each TSSolve() for these picky
>>> methods in debug mode.
>> 
>> How about calling the IJacobian first with a=0 and then with a=1 and
>> subtracting matrices, to see if the result is the identity?
> 
> That's more precise (assuming the IJacobian does not depend on Udot),
> but significantly more expensive in memory and time.