[petsc-users] Solving NON-Diagonally dominant sparse system

Tue Apr 11 07:07:32 CDT 2017

But anyway since I am starting off with the exact solution itself,
shouldn't the norm should be zero independent of the conditioning?

On Tue, Apr 11, 2017 at 11:57 AM, Dave May <dave.mayhem23 at gmail.com> wrote:

>
>
> On Tue, 11 Apr 2017 at 07:28, Kaushik Kulkarni <kaushikggg at gmail.com>
> wrote:
>
>> A strange behavior I am observing is:
>> Problem: I have to solve A*x=rhs, and currently I am currently trying to
>> solve for a system where I know the exact solution. I have initialized the
>> exact solution in the Vec x_exact.
>>
>> MatMult(A, x_exact, dummy);// Storing the value of A*x_exact in dummy
>> VecAXPY(dummy, -1.0, rhs); // dummy = dummy -rhs
>> VecNorm(dummy, NORM_INFINITY, &norm_val); // norm_val = ||dummy||, which
>> gives us the residual norm
>> PetscPrintf(PETSC_COMM_SELF, "Norm = %f\n", norm_val); // Printing the
>> norm.
>>
>> // Starting with the linear solver
>> KSPCreate(PETSC_COMM_SELF, &ksp);
>> KSPSetOperators(ksp, A, A);
>> KSPSetFromOptions(ksp);
>> KSPSolve(ksp,rhs,x_exact); // Solving the system A*x= rhs, with the given
>> initial input x_exact. So the result will also be stored in x_exact
>>
>> On running with -pc_type lu -pc_factor_mat_solver_package superlu
>> -ksp_monitor I get the following output:
>> Norm = 0.000000
>>   0 KSP Residual norm 4.371606462669e+04
>>   1 KSP Residual norm 5.850058113796e+02
>>   2 KSP Residual norm 5.832677911508e+02
>>   3 KSP Residual norm 1.987386549571e+02
>>   4 KSP Residual norm 1.220006530614e+02
>>   .
>>   .
>>   .
>>
>
> The default KSP is left preconditioned GMRES. Hence the above iterates
> report the preconditioned residual. If your operator is singular, and LU
> generated garbage, the preconditioned residual can be very different to the
> true residual.
>
> To see the true residual, use
> -ksp_monitor_true_residual
>
> Alternatively, use a right preconditioned KSP method, e.g.
> -ksp_type fgmres
> (or -ksp_type gcr)
> With these methods, you will see the true residual with just -ksp_monitor
>
>
> Thanks
>   Dave
>
>
>
>
>>
>> Since the initial guess is the exact solution should'nt the first
>> residual itself be zero and converge in one iteration.
>>
>> Thanks,
>> Kaushik
>>
>>
>> On Tue, Apr 11, 2017 at 10:08 AM, Kaushik Kulkarni <kaushikggg at gmail.com>
>> wrote:
>>
>> Thank you for the inputs.
>> I tried Barry' s suggestion to use SuperLU, but the solution does not
>> converge and on doing -ksp_monitor -ksp_converged_reason. I get the
>> following error:-
>> 240 KSP Residual norm 1.722571678777e+07
>> Linear solve did not converge due to DIVERGED_DTOL iterations 240
>> For some reason it is diverging, although I am sure that for the given
>> system a unique solution exists.
>>
>> Thanks,
>> Kaushik
>>
>> On Tue, Apr 11, 2017 at 1:04 AM, Xiaoye S. Li <xsli at lbl.gov> wrote:
>>
>> If you need to use SuperLU_DIST, the pivoting is done statically, using
>> maximum weighted matching, so the small diagonals are usually taken care as
>> well. It is not as good as partial pivoting, but works most of the time.
>>
>> Sherry
>>
>> On Mon, Apr 10, 2017 at 12:07 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>
>>
>>    I would suggest using ./configure --download-superlu and then when
>> running the program -pc_type lu -pc_factor_mat_solver_package superlu
>>
>>    Note that this is SuperLU, it is not SuperLU_DIST.  Superlu uses
>> partial pivoting for numerical stability so should be able to handle the
>> small or zero diagonal entries.
>>
>>     Barry
>>
>> > On Apr 10, 2017, at 1:17 PM, Kaushik Kulkarni <kaushikggg at gmail.com>
>> wrote:
>> >
>> > Hello,
>> > I am trying to solve a 2500x2500 sparse matrix. To get an idea about
>> the matrix structure I have added a file matrix.log which contains the
>> output of MatView() and also the output of Matview_draw in the image file.
>> >
>> > From the matrix structure it can be seen that Jacobi iteration won't
>> work and some of the diagonal entries being very low(of the order of 1E-16)
>> LU factorization would also fail.
>> >
>> > Can someone please suggest what all could I try next, in order to make
>> the solution converge?
>> >
>> > Thanks,
>> > Kaushik
>> > 
>> > --
>> > Kaushik Kulkarni
>> > Fourth Year Undergraduate
>> > Department of Mechanical Engineering
>> > Indian Institute of Technology Bombay
>> > Mumbai, India
>> > https://kaushikcfd.github.io/About/
>> > +91-9967687150
>> > <matrix.log><matrix_pattern.png>
>>
>>
>>
>>
>>
>> --
>> Kaushik Kulkarni
>> Fourth Year Undergraduate
>> Department of Mechanical Engineering
>> Indian Institute of Technology Bombay
>> Mumbai, India
>> https://kaushikcfd.github.io/About/
>> +91-9967687150
>>
>>
>>
>>
>> --
>> Kaushik Kulkarni
>> Fourth Year Undergraduate
>> Department of Mechanical Engineering
>> Indian Institute of Technology Bombay
>> Mumbai, India
>> https://kaushikcfd.github.io/About/
>> +91-9967687150
>>
>

-- 
Kaushik Kulkarni
Fourth Year Undergraduate
Department of Mechanical Engineering
Indian Institute of Technology Bombay
Mumbai, India
https://kaushikcfd.github.io/About/
+91-9967687150
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