[petsc-users] TimeStepper norm problems. EMIL Please read this
Andrew Spott
ansp6066 at colorado.edu
Sun Mar 22 21:23:26 CDT 2015
Thanks! Let me know if I can do anything to help.
-Andrew
—
Andrew
On Sun, Mar 22, 2015 at 8:21 PM, Emil Constantinescu <emconsta at mcs.anl.gov>
wrote:
> Hi Andrew,
> I can reproduce this issue and I agree that there is something wrong.
> I'll look into it.
> Emil
> On 3/22/15 3:29 PM, Andrew Spott wrote:
>> So, I’m now even more confused.
>>
>> I’m attempting to solve an equation that looks like this:
>>
>> u’ = -i(H0 + e(t) D) u
>>
>> Where H0 is a purely real diagonal matrix, D is an off-diagonal block
>> matrix, and e(t) is a function of time (The schrödinger equation in the
>> energy basis).
>>
>> I’ve rewritten the e(t) function in my code to just return 0.0. So the
>> new equation is just u’ = -iH0 u. The matrix is time independent and
>> diagonal (I’ve checked this). H0[0] ~= -.5 (with no imaginary
>> component). and u(t=0) = [1,0,0,0,..]
>>
>> This problem SHOULD be incredibly simple: u’ = i (0.5) u.
>>
>> However, I’m still getting the same blowup with the TS.:
>>
>> //with e(t) == 0
>> //TS
>> t: 0 step: 0 norm-1: 0
>> t: 0.01 step: 1 norm-1: 0
>> t: 0.02 step: 2 norm-1: 0.9999953125635765
>> t: 0.03 step: 3 norm-1: 2.999981250276277
>> //Hand rolled
>> t: 0.01 norm-1: 0 ef 0
>> t: 0.02 norm-1: 0 ef 0
>> t: 0.03 norm-1: -1.110223024625157e-16 ef 0
>> ——————————————————————————————
>> //with e(t) != 0
>> //TS
>> t: 0 step: 0 norm-1: 0
>> t: 0.01 step: 1 norm-1: 0
>> t: 0.02 step: 2 norm-1: 0.9999953125635765
>> t: 0.03 step: 3 norm-1: 2.999981250276277
>> //Hand rolled
>> t: 0.01 norm-1: 0 ef 9.474814647559372e-11
>> t: 0.02 norm-1: 0 ef 7.57983838406065e-10
>> t: 0.03 norm-1: -1.110223024625157e-16 ef 2.558187954267552e-09
>>
>> I’ve updated the gist.
>>
>> -Andrew
>>
>>
>>
>> On Fri, Mar 20, 2015 at 9:57 PM, Barry Smith <bsmith at mcs.anl.gov
>> <mailto:bsmith at mcs.anl.gov>> 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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