General matrix interative solver

[Julian]

Barry,

I tried sending the commands from a file for now... And once I used
'-ksp_type cg', I got pretty much the same performance as that of the
inhouse code !
Now, I'll try the performance with larger cases...

Thanks for your help!

Julian.


> -----Original Message-----
> From: owner-petsc-users at mcs.anl.gov 
> [mailto:owner-petsc-users at mcs.anl.gov] On Behalf Of Barry Smith
> Sent: Wednesday, October 11, 2006 11:25 AM
> To: petsc-users at mcs.anl.gov
> Subject: RE: General matrix interative solver
> 
> 
>   PetscOptionsSetValue() but recommend putting them on the 
> command line or in a file (pass the name of the file into 
> PetscInitialize()). Having to recompile for every option is 
> too painful.
> 
>    Barry
> 
> 
> On Wed, 11 Oct 2006, Julian wrote:
> 
> > Hong,
> > 
> > The times are for the solution process alone and the 
> initial guess is 
> > the same, i.e. zero.
> > 
> > As for the algorithm, they are probably different. 
> > Can you tell me how to pass 'runtime options' like -help 
> and -ksp_view 
> > from within the code... I mean, at compile time.
> > 
> > thanks
> > 
> > > 
> > > Julian,
> > > 
> > > When comparing the inhouse solver and petsc solver, you need make 
> > > sure
> > > 
> > > 1. Timings are collected for solution process. The matrix 
> and vector
> > >    assembly should be excluded.
> > > 2. They should use same iterative algorithm. By default, 
> petsc uses
> > >    gmres with restart=30 and ilu(0) preconditioner. Petsc supports
> > >    symmetric matrices, e.g., runtime option '-ksp_type cg 
> -pc_type 
> > > icc'
> > >    might give better performance
> > > 3. They should start from same intial guess. By default, petsc
> > >    initial guess is zero.
> > > 
> > > You can use '-ksp_view' to see what algorithm and options 
> are used 
> > > in petsc.
> > > 
> > > Hong
> > > 
> > > On Wed, 11 Oct 2006, Julian wrote:
> > > 
> > > > Hello,
> > > >
> > > > I implemented the iterative sparse matrix solver in PetSc
> > > into my FEM
> > > > code recently. I compared the results from a problem with 1317 
> > > > unknowns. I used a direct solver to obtain the reference
> > > solution. I
> > > > have another in-house sparse iterative solver that I have
> > > been using
> > > > so far. It was written by someone else but I have access to
> > > the source for that solver.
> > > > I find the 'error norm' in the solution by taking the
> > > square root of
> > > > the sum of the squares of the absolute differences between the 
> > > > solution from the direct solver and the iterative solver. I am 
> > > > ignoring the numerical zeros in the solutions when doing this.
> > > > I find that in order to get same order of the error 
> norm (1e-13) 
> > > > as the in-house iterative solver, the petsc solver takes a much 
> > > > longer time and larger number of iterations. While the inhouse 
> > > > solver took less than one second, the petsc solver took 13 
> > > > seconds. The inhouse solver took 476 iterations whereas 
> the petsc 
> > > > solver took
> > > 4738 iterations.
> > > > I'm guessing this has to do with different setting of 
> the solver 
> > > > in petsc such as the preconditioner etc.
> > > > Can you tell me what the different settings are? And how to
> > > tweak them
> > > > so that I can atleast get as good as a performance as the
> > > inhouse code ?
> > > > Given below is how I have implemented the petsc solver:
> > > >
> > > > /////initialization
> > > >     PetscInitializeNoArguments();
> > > >         Assert( mat = (double*)malloc(sizeof(Mat)) );
> > > >     MatCreateSeqAIJ(PETSC_COMM_SELF, L, L,
> > > >       PETSC_DEFAULT, PETSC_NULL, (Mat*)mat);
> > > >
> > > > ////// this is the function I use to populate the matrix 
> > > > MatSetValue(*(Mat*)mat, ii, jj, value, ADD_VALUES);
> > > >
> > > > ////// this is how I actaully solve the matrix
> > > >   MatAssemblyBegin(*(Mat*)mat, MAT_FINAL_ASSEMBLY);
> > > >   MatAssemblyEnd(*(Mat*)mat, MAT_FINAL_ASSEMBLY);
> > > >
> > > >   double iter_error = 1e-10;
> > > >   int max_iter_num = 10000;
> > > >   int num_of_iter;
> > > >
> > > >         Vec rhs, x;
> > > >     VecCreateSeqWithArray(PETSC_COMM_SELF, L, b, &rhs);
> > > >     VecDuplicate(rhs, &x);
> > > >
> > > >     KSP ksp;
> > > >     KSPCreate(PETSC_COMM_SELF, &ksp);
> > > >     KSPSetTolerances(ksp, iter_error, PETSC_DEFAULT,
> > > >       PETSC_DEFAULT, max_iter_num);
> > > >     KSPSetFromOptions(ksp);
> > > >     KSPSetOperators(ksp, *(Mat*)mat, *(Mat*)mat,
> > > >       SAME_PRECONDITIONER);
> > > >     KSPSolve(ksp,rhs,x);
> > > >
> > > >     PetscReal r_norm;
> > > >     KSPGetResidualNorm(ksp, &r_norm);
> > > >     KSPGetIterationNumber(ksp, &num_of_iter);
> > > >
> > > >         cout << "max_iter_num\t" << max_iter_num << endl;
> > > >         cout << "iter_error\t" << iter_error << endl;
> > > >
> > > >         cout << "Matrix solver step " << num_of_iter << ",
> > > residual " 
> > > > << r_norm << ".\n";
> > > >
> > > >         PetscScalar *p;
> > > >     VecGetArray(x, &p);
> > > >     for(int i=0; i<L; i++) {
> > > >         b[i] = p[i];
> > > >     }
> > > >     VecRestoreArray(x, &p);
> > > >
> > > >     KSPDestroy(ksp);
> > > >     VecDestroy(rhs);
> > > >     VecDestroy(x);
> > > >
> > > > cout <<"Iterations for convergence="<< num_of_iter << " -
> > > Residual Norm = "
> > > > << r_norm << endl;
> > > >
> > > >
> > > >
> > > > If this is not the typical method to be used to solve 
> this kind of 
> > > > problem, please let me know what functions I should use.
> > > > I should mention that the inhouse code is for symmetric
> > > matrices and
> > > > from what I understand, the petsc solver works for general
> > > unsymmetric matrices.
> > > > But I think for iterative solvers, it should still give 
> around the 
> > > > same performance.
> > > > I tested the solvers against some other problems as well, and I 
> > > > got the same performance.. In some cases, no matter how many
> > > iterations it
> > > > goes through, the petsc solver would not go below a certain
> > > error norm
> > > > whereas the inhouse solver would get almost exactly the
> > > same answer as
> > > > the direct solver solution. I'm thinking the petsc 
> solver should 
> > > > be able to solve this problem just as easily. It would be
> > > great if anyone
> > > > could help me figure out the appropriate settings I should
> > > use in the petsc solver.
> > > >
> > > > Thanks,
> > > > Julian.
> > > >
> > > >
> > > 
> > > 
> > 
> > 
>