[petsc-users] Changing nonzero structure and Jacobian coloring

[Ellen M. Price]

Thanks for the reply, Barry! Unfortunately, this is a particle code
(SPH, specifically), so the particle neighbors, which influence the
properties, change over time; the degrees of freedom is a constant, as
is the particle number. Any thoughts, given the new info? Or should I
stick with explicit integration? I've seen explicit used most commonly,
but, as I mentioned before, the optimal timestep that gives the error
bounds I need is just too small for my application, and the only other
thing I can think to try is to throw a lot more cores at the problem and
wait.

Ellen


On 10/15/19 4:14 PM, Smith, Barry F. wrote:
> 
>   So you have a fixed "mesh" and fixed number of degrees of freedom for the entire time but the dependency on the function value at each particular point on the neighbor points changes over time?
> 
>   For example, if you are doing upwinding and the direction changes when you used to use values from the right you now use values from the left?
> 
>    Independent of the coloring, just changing the locations in the matrix where the entries are nonzero is expensive and painful. So what I would do is build the initial Jacobian nonzero structure to contain all possible connections, color that and then use that for the entire computation. At each time step you will be working with some zero entries in the Jacobian but that is ok, it is simpler and ultimately probably faster than trying to keep changing the nonzero structure to "optimize" and only treat truly nonzero values. 
> 
>    For "stencil" type discretizations (finite difference, finite value) what I describe should be fine. But if you problem is completely different (I can't imagine how) and the Jacobian changes truly dramatically in structure then what I suggest may not be appropriate but you'll need to tell us your problem in that case so we can make suggestions.
> 
>    Barry
> 
> 
> 
>> On Oct 15, 2019, at 2:56 PM, Ellen M. Price via petsc-users <petsc-users at mcs.anl.gov> wrote:
>>
>> Hi PETSc users!
>>
>> I have a problem that I am integrating with TS, and I think an implicit
>> method would let me take larger timesteps. The Jacobian is difficult to
>> compute, but, more importantly, the nonzero structure is changing with
>> time, so even if I use coloring and finite differences to compute the
>> actual values, I will have to update the coloring every time the
>> Jacobian recomputes.
>>
>> Has anyone done this before, and/or is there a correct way to tell TS to
>> re-compute the coloring of the matrix before SNES actually computes the
>> entries? Is this even a good idea, or is the coloring so expensive that
>> this is foolish (in general -- I know the answer depends on the problem,
>> but there may be a rule of thumb)?
>>
>> Thanks,
>> Ellen Price
>