[petsc-users] TimeStepper norm problems.

[Andrew Spott]

I have a fairly simple problem that I’m trying to timestep:


u’ = A(t) u


I’m using the crank-nicholson method, which I understand (for this problem) to be:


u(t + h) = u(t) + h/2[A(t+h)*u(t+h) + A(t)*u(t)]
or
[1 - h/2 * A(t+1)] u(t+1) = [1 + h/2 * A(t)] u(t)


When I attempt to timestep using PETSc, the norm of `u` blows up.  When I do it directly (using the above), the norm of `u` doesn’t blow up.


It is important to note that the solution generated after the first step is identical for both, but the second step for Petsc has a norm of ~2, while for the directly calculated version it is ~1.  The third step for petsc has a norm of ~4, while the directly calculated version it is still ~1.


I’m not sure what I’m doing wrong.


PETSc code is taken out of the manual and is pretty simple:


        TSCreate( comm, &ts );
        TSSetProblemType( ts, TS_LINEAR);
        TSSetType( ts, TSCN );
        TSSetInitialTimeStep( ts, 0, 0.01 );
        TSSetDuration( ts, 5, 0.03 );
        TSSetFromOptions( ts );
        TSSetRHSFunction( ts, NULL, TSComputeRHSFunctionLinear, NULL );
        TSSetRHSJacobian( ts, A, A, func, &cntx );
        TSSolve( ts, psi0 );


`func` just constructs A(t) at the time given.  The same code for calculating A(t) is used in both calculations, along with the same initial vector psi0, and the same time steps.


Let me know what other information is needed.  I’m not sure what could be the problem.  `func` doesn’t touch U at all (should it?).


-Andrew
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