[petsc-users] TimeStepper norm problems. EMIL Please read this
Emil Constantinescu
emconsta at mcs.anl.gov
Sat Mar 21 09:32:33 CDT 2015
I haven't been able to compile and run. But here are a few quick notes.
The problem appears to be very stiff.
Theta and theta_endpoint are defining different methods:
1) -ts_type beuler OR -ts_theta_theta 1.0: is backward Euler
u(t + h) = u(t) + h*A(t+h)*u(t+h)
2) -ts_theta_theta 0.5: is the implicit midpoint rule
u(t + h) = u(t) + h*[A(t+h/2)*(u(t+h)+u(t))/2]
3) -ts_type cn OR -ts_theta_theta 0.5 -ts_theta_endpoint: is
Crank-Nicholson/trapezoidal
u(t + h) = u(t) + h/2[A(t+h)*u(t+h) + A(t)*u(t)]
Note that the last two are different. -ts_type theta -ts_theta_theta .5
is different from -ts_type cn. They the same linear stability properties
if A(t)=A; but not if A depends on t.
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'll try to build the example to get more insight.
Emil
On 3/20/15 10:57 PM, Barry Smith wrote:
>
> Andrew,
>
> I'm afraid Emil will have to take a look at this and explain it. The -ts_type beuler and -ts_type theta -ts_theta_theta .5 are stable but the -ts_type cn is not stable. It turns out that -ts_type cn is equivalent to -ts_type theta -ts_theta_theta .5 -ts_theta_endpoint and somehow this endpoint business (which I don't understand) is causing a problem. Meanwhile if I add -ts_theta_adapt to the endpoint one it becomes stable ? Anyways all cases are displayed below.
>
> Emil,
>
> What's up with this? Does the endpoint business have a bug or can it not be used for this problem (the matrix A is a function of t.)
>
> Barry
>
>
> $ ./ex2 -ts_type cn
> t: 0 step: 0 norm-1: 0
> t: 0.01 step: 1 norm-1: 0
> t: 0.02 step: 2 norm-1: 1
> t: 0.03 step: 3 norm-1: 3
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type theta
> t: 0 step: 0 norm-1: 0
> t: 0.01 step: 1 norm-1: 0
> t: 0.02 step: 2 norm-1: 0
> t: 0.03 step: 3 norm-1: 0
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type theta -ts_theta_theta .5
> t: 0 step: 0 norm-1: 0
> t: 0.01 step: 1 norm-1: 0
> t: 0.02 step: 2 norm-1: 0
> t: 0.03 step: 3 norm-1: 0
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type theta -ts_theta_theta .5 -ts_theta_endpoint
> t: 0 step: 0 norm-1: 0
> t: 0.01 step: 1 norm-1: 0
> t: 0.02 step: 2 norm-1: 1
> t: 0.03 step: 3 norm-1: 3
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type theta -ts_theta_theta .5 -ts_theta_endpoint -ts_theta_adapt
> t: 0 step: 0 norm-1: 0
> t: 0.01 step: 1 norm-1: 0
> t: 0.02 step: 2 norm-1: 0
> t: 0.03 step: 3 norm-1: 0
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type theta -ts_theta_theta .5 -ts_theta_endpoint -ts_theta_adapt -ts_monitor
> 0 TS dt 0.01 time 0
> t: 0 step: 0 norm-1: 0
> 0 TS dt 0.01 time 0
> 1 TS dt 0.1 time 0.01
> t: 0.01 step: 1 norm-1: 0
> 1 TS dt 0.1 time 0.01
> 2 TS dt 0.1 time 0.02
> t: 0.02 step: 2 norm-1: 0
> 2 TS dt 0.1 time 0.02
> 3 TS dt 0.1 time 0.03
> t: 0.03 step: 3 norm-1: 0
> 3 TS dt 0.1 time 0.03
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type theta -ts_theta_theta .5 -ts_theta_endpoint -ts_theta_adapt -ts_monitor -ts_adapt_monitor
> 0 TS dt 0.01 time 0
> t: 0 step: 0 norm-1: 0
> 0 TS dt 0.01 time 0
> TSAdapt 'basic': step 0 accepted t=0 + 1.000e-02 wlte= 0 family='theta' scheme=0:'(null)' dt=1.000e-01
> 1 TS dt 0.1 time 0.01
> t: 0.01 step: 1 norm-1: 0
> 1 TS dt 0.1 time 0.01
> TSAdapt 'basic': step 1 rejected t=0.01 + 1.000e-01 wlte=1.24e+03 family='theta' scheme=0:'(null)' dt=1.000e-02
> TSAdapt 'basic': step 1 accepted t=0.01 + 1.000e-02 wlte= 0 family='theta' scheme=0:'(null)' dt=1.000e-01
> 2 TS dt 0.1 time 0.02
> t: 0.02 step: 2 norm-1: 0
> 2 TS dt 0.1 time 0.02
> TSAdapt 'basic': step 2 rejected t=0.02 + 1.000e-01 wlte=1.24e+03 family='theta' scheme=0:'(null)' dt=1.000e-02
> TSAdapt 'basic': step 2 accepted t=0.02 + 1.000e-02 wlte= 0 family='theta' scheme=0:'(null)' dt=1.000e-01
> 3 TS dt 0.1 time 0.03
> t: 0.03 step: 3 norm-1: 0
> 3 TS dt 0.1 time 0.03
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type beuler
> t: 0 step: 0 norm-1: 0
> t: 0.01 step: 1 norm-1: 0
> t: 0.02 step: 2 norm-1: 0
> t: 0.03 step: 3 norm-1: 0
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
> $ ./ex2 -ts_type euler
> t: 0 step: 0 norm-1: 0
> t: 0.01 step: 1 norm-1: 0
> t: 0.02 step: 2 norm-1: 0
> t: 0.03 step: 3 norm-1: 0
> ~/Src/petsc/test-dir (barry/more-tchem-work *=) arch-debug
>
>
>> On Mar 20, 2015, at 10:18 PM, Andrew Spott <ansp6066 at colorado.edu> wrote:
>>
>> here are the data files.
>>
>> dipole_matrix.dat:
>> https://www.dropbox.com/s/2ahkljzt6oo9bdr/dipole_matrix.dat?dl=0
>>
>> energy_eigenvalues_vector.dat
>> https://www.dropbox.com/s/sb59q38vqvjoypk/energy_eigenvalues_vector.dat?dl=0
>>
>> -Andrew
>>
>>
>>
>> On Fri, Mar 20, 2015 at 7:25 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>
>> Data files are needed
>>
>> PetscViewerBinaryOpen( PETSC_COMM_WORLD, "hamiltonian/energy_eigenvalues_vector.dat", FILE_MODE_READ, &view );
>> VecLoad( H0, view );
>> PetscViewerBinaryOpen( PETSC_COMM_WORLD, "hamiltonian/dipole_matrix.dat", FILE_MODE_READ, &view );
>>
>> BTW: You do not need to call Mat/VecAssembly on Mats and Vecs after they have been loaded.
>>
>> Barry
>>
>>
>>> On Mar 20, 2015, at 6:39 PM, Andrew Spott <ansp6066 at colorado.edu> wrote:
>>>
>>> Sorry it took so long, I wanted to create a “reduced” case (without all my parameter handling and other stuff…)
>>>
>>> https://gist.github.com/spott/aea8070f35e79e7249e6
>>>
>>> The first section does it using the time stepper. The second section does it by explicitly doing the steps. The output is:
>>>
>>> //first section, using TimeStepper:
>>> t: 0 step: 0 norm-1: 0
>>> t: 0.01 step: 1 norm-1: 0
>>> t: 0.02 step: 2 norm-1: 0.999995
>>> t: 0.03 step: 3 norm-1: 2.99998
>>>
>>> //Second section, using explicit code.
>>> t: 0.01 norm-1: 0
>>> t: 0.02 norm-1: 0
>>> t: 0.02 norm-1: 2.22045e-16
>>>
>>>
>>>
>>> On Fri, Mar 20, 2015 at 4:45 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>>
>>> Andrew,
>>>
>>> Send your entire code. It will be easier and faster than talking past each other.
>>>
>>> Barry
>>>
>>>> On Mar 20, 2015, at 5:00 PM, Andrew Spott <ansp6066 at colorado.edu> wrote:
>>>>
>>>> I’m sorry, I’m not trying to be difficult, but I’m not following.
>>>>
>>>> The manual states (for my special case):
>>>> • u ̇ = A(t)u. Use
>>>>
>>>> TSSetProblemType(ts,TS LINEAR); TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,NULL); TSSetRHSJacobian(ts,A,A,YourComputeRHSJacobian,&appctx);
>>>>
>>>> where YourComputeRHSJacobian() is a function you provide that computes A as a function of time. Or use ...
>>>> My `func` does this. It is 7 lines:
>>>>
>>>> context* c = static_cast<context*>( G_u );
>>>> PetscScalar e = c->E( t_ );
>>>> MatCopy( c->D, A, SAME_NONZERO_PATTERN );
>>>> MatShift( A, e );
>>>> MatDiagonalSet( A, c->H0, INSERT_VALUES);
>>>> MatShift( A, std::complex<double>( 0, -1 ) );
>>>> return 0;
>>>>
>>>> SHOULD `func` touch U? If so, what should `func` do to U? I thought that the RHSJacobian function was only meant to create A, since dG/du = A(t) (for this special case).
>>>>
>>>> -Andrew
>>>>
>>>>
>>>>
>>>> On Fri, Mar 20, 2015 at 3:26 PM, Matthew Knepley <knepley at gmail.com> wrote:
>>>>
>>>> On Fri, Mar 20, 2015 at 3:09 PM, Andrew Spott <ansp6066 at colorado.edu> wrote:
>>>> So, it doesn’t seem that zeroing the given vector in the function passed to TSSetRHSJacobian is the problem. When I do that, it just zeros out the solution.
>>>>
>>>> I would think you would zero the residual vector (if you add to it to construct the residual, as in FEM methods), not the solution.
>>>>
>>>> The function that is passed to TSSetRHSJacobian has only one responsibility — to create the jacobian — correct? In my case this is A(t). The solution vector is given for when you are solving nonlinear problems (A(t) also depends on U(t)). In my case, I don’t even look at the solution vector (because my A(t) doesn’t depend on it).
>>>>
>>>> Are you initializing the Jacobian to 0 first?
>>>>
>>>> Thanks,
>>>>
>>>> Matt
>>>>
>>>> Is this the case? or is there some other responsibility of said function?
>>>>
>>>> -Andrew
>>>>
>>>>> Ah ha!
>>>>>
>>>>> The function passed to TSSetRHSJacobian needs to zero the solution vector?
>>>>>
>>>>> As a point, this isn’t mentioned in any documentation that I can find.
>>>>>
>>>>> -Andrew
>>>>
>>>> On Friday, Mar 20, 2015 at 2:17 PM, Matthew Knepley <knepley at gmail.com>, wrote:
>>>> This sounds like a problem in your calculation function where a Vec or Mat does not get reset to 0, but it does in your by hand code.
>>>>
>>>> Matt
>>>>
>>>> On Mar 20, 2015 2:52 PM, "Andrew Spott" <ansp6066 at colorado.edu> wrote:
>>>> 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
>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>
>>>
>>>
>>
>>
>>
>
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