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

[Kaushik Kulkarni]

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
  .
  .
  .

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.
>>> >
>>> > C​an 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
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