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

[Dave May]

Nope - welcome to finite precision arithmetic. What's the condition number?

On Tue, 11 Apr 2017 at 14:07, Kaushik Kulkarni <kaushikggg at gmail.com> wrote:

> 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.
> >
> > 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
>
>
>
>
> --
> 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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