Hello Barry,
To answer your question, both the eigenvectors contain only two values: the
eigenvectors entries are different in the two eigenvectors but coherent with
the belonging of the entry to the sub-domains.
However, I was able to get the same behavior of the MatTestNullSpace using the
two ways of creating the null space.
To summarize the issue, I did:
- MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr, &nullspace)
(CASE 1)
- Vec* nsp;
VecDuplicateVecs(m_rhs, 1, &nsp);
VecSet(nsp[0],1.0);
VecNormalize(nsp[0], nullptr);
MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, 1, nsp, &nullspace); (CASE
2)
and then I tested with MatNullSpaceTest(nullspace, m_A, &isNullSpaceValid).
CASE 1 gave isNullSpaceValid=true but CASE 2 gave isNullSpaceValid=false.
I found the problem is the normalization of the Vec nsp[0].
Modifying CASE 2 like this:
Vec* nsp;
VecDuplicateVecs(m_rhs, 1, &nsp);
PetscInt N;
VecGetSize(nsp[0],&N);
VecSet(nsp[0],1.0 / N);
MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, 1, nsp, &nullspace);
I can get isNullSpaceValid= true even for CASE 2.
But most importantly, I can get isNullSpaceValid=true even creating the true
2-dimensional null space with explicit normalization (using the number of
non-zero entries sub-domain per sub-domain) and not VecNormalize:
MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, nConstants, constants,
&nullspace);
where nConstants=2 and constants[0] (constants[1]) has been set with 1/N0
(1/N1) in entries relative to sub-domain 0 (1).
I going to check which is the impact on CFD solution.
Any comment on this would be really appreciated.
Thank you all.
Marco Cisternino
-----Original Message-----
From: Barry Smith <[email protected]>
Sent: mercoledì 5 gennaio 2022 23:17
To: Marco Cisternino <[email protected]>
Cc: Jose E. Roman <[email protected]>; petsc-users <[email protected]>
Subject: Re: [petsc-users] Nullspaces
What do you get for the two eigenvectors ?
> On Jan 5, 2022, at 11:21 AM, Marco Cisternino <[email protected]>
> wrote:
>
> Hello Jose and Stefano.
> Thank you, Jose for your hints.
> I computed the two smallest eigenvalues of my operator and they are tiny but
> not zero.
> The smallest 0 eigenvalue is = (4.71506e-08, 0) with abs error =
> 3.95575e-07 The smallest 1 eigenvalue is = (1.95628e-07, 0) with abs
> error = 4.048e-07 As Stefano remarked, I would have expected much tinier
> values, closer to zero.
> Probably something is wrong in what I do:
> EPS eps;
> EPSCreate(PETSC_COMM_WORLD, &eps);
> EPSSetOperators( eps, matrix, NULL );
> EPSSetWhichEigenpairs(eps, EPS_SMALLEST_MAGNITUDE);
> EPSSetProblemType( eps, EPS_NHEP );
> EPSSetConvergenceTest(eps,EPS_CONV_ABS);
> EPSSetTolerances(eps, 1.0e-10, 1000);
> EPSSetDimensions(eps,2,PETSC_DEFAULT,PETSC_DEFAULT);
> EPSSetFromOptions( eps );
> EPSSolve( eps );
>
> Even commenting " EPSSetTolerances(eps, 1.0e-10, 1000);" and use default
> values, the results are exactly the same.
>
> Am I correctly computing the 2 smallest eigenvalues?
>
> They should be zeros but they are not. Any suggestions about how
> understanding why?
>
> In a previous email Mark remarked: "Also you say you divide by the cell
> volume. Maybe I am not understanding this but that is basically diagonal
> scaling and that will change the null space (ie, not a constant anymore)",
> therefore why does the null space built with
> MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, nullptr, &nullspace);
> passes the MatNullSpaceTest??
>
> Thank you all!
>
> Marco Cisternino
>
> -----Original Message-----
> From: Jose E. Roman <[email protected]>
> Sent: martedì 4 gennaio 2022 19:30
> To: Marco Cisternino <[email protected]>
> Cc: Stefano Zampini <[email protected]>; petsc-users
> <[email protected]>
> Subject: Re: [petsc-users] Nullspaces
>
> To compute more than one eigenpair, call
> EPSSetDimensions(eps,nev,PETSC_DEFAULT,PETSC_DEFAULT).
>
> To compute zero eigenvalues you may want to use an absolute convergence
> criterion, with EPSSetConvergenceTest(eps,EPS_CONV_ABS), but then a tolerance
> of 1e-12 is probably too small. You can try without this, anyway.
>
> Jose
>
>
>> El 4 ene 2022, a las 18:44, Marco Cisternino <[email protected]>
>> escribió:
>>
>> Hello Stefano and thank you for your support.
>> I never used SLEPc before but I did this:
>> right after the matrix loading from file I added the following lines to my
>> shared tiny code
>> MatLoad(matrix, v);
>>
>> EPS eps;
>> EPSCreate(PETSC_COMM_WORLD, &eps);
>> EPSSetOperators( eps, matrix, NULL );
>> EPSSetWhichEigenpairs(eps, EPS_SMALLEST_MAGNITUDE);
>> EPSSetProblemType( eps, EPS_NHEP );
>> EPSSetTolerances(eps, 1.0e-12, 1000);
>> EPSSetFromOptions( eps );
>> EPSSolve( eps );
>>
>> Vec xr, xi; /* eigenvector, x */
>> PetscScalar kr, ki; /* eigenvalue, k */
>> PetscInt j, nconv;
>> PetscReal error;
>> EPSGetConverged( eps, &nconv );
>> for (j=0; j<nconv; j++) {
>> EPSGetEigenpair( eps, j, &kr, &ki, xr, xi );
>> EPSComputeError( eps, j, EPS_ERROR_ABSOLUTE, &error );
>> std::cout << "The smallest eigenvalue is = (" << kr << ", " << ki <<
>> ") with error = " << error << std::endl;
>> }
>>
>> I launched using
>> mpirun -n 1 ./testnullspace -eps_monitor
>>
>> and the output is
>>
>> 1 EPS nconv=0 first unconverged value (error) -1499.29
>> (6.57994794e+01)
>> 2 EPS nconv=0 first unconverged value (error) -647.468
>> (5.39939262e+01)
>> 3 EPS nconv=0 first unconverged value (error) -177.157
>> (9.49337698e+01)
>> 4 EPS nconv=0 first unconverged value (error) 59.6771
>> (1.62531943e+02)
>> 5 EPS nconv=0 first unconverged value (error) 41.755
>> (1.41965990e+02)
>> 6 EPS nconv=0 first unconverged value (error) -11.5462
>> (3.60453662e+02)
>> 7 EPS nconv=0 first unconverged value (error) -6.04493
>> (4.60890030e+02)
>> 8 EPS nconv=0 first unconverged value (error) -22.7362
>> (8.67630086e+01)
>> 9 EPS nconv=0 first unconverged value (error) -12.9637
>> (1.08507821e+02)
>> 10 EPS nconv=0 first unconverged value (error) 7.7234
>> (1.53561979e+02) …
>> 111 EPS nconv=0 first unconverged value (error) -2.27e-08
>> (6.84762319e+00)
>> 112 EPS nconv=0 first unconverged value (error) -2.60619e-08
>> (4.45245528e+00)
>> 113 EPS nconv=0 first unconverged value (error) -5.49592e-09
>> (1.87798984e+01)
>> 114 EPS nconv=0 first unconverged value (error) -9.9456e-09
>> (7.96711076e+00)
>> 115 EPS nconv=0 first unconverged value (error) -1.89779e-08
>> (4.15471472e+00)
>> 116 EPS nconv=0 first unconverged value (error) -2.05288e-08
>> (2.52953194e+00)
>> 117 EPS nconv=0 first unconverged value (error) -2.02919e-08
>> (2.90090711e+00)
>> 118 EPS nconv=0 first unconverged value (error) -3.8706e-08
>> (8.03595736e-01)
>> 119 EPS nconv=1 first unconverged value (error) -61751.8
>> (9.58036571e-07) Computed 1 pairs The smallest eigenvalue is =
>> (-3.8706e-08, 0) with error = 4.9707e-07
>>
>> Am I using SLEPc in the right way at least for the first smallest
>> eigenvalue? If I’m on the right way I can find out how to compute the second
>> one.
>>
>> Thanks a lot
>>
>> Marco Cisternino
>
