General matrix interative solver

[Julian]

I'm using '-ksp_type cg' now to solve the symmetric matric...But then do I
need to store all the non-zero elements of a symmetric matrix ? i.e. A[i,j]
as well as A[j,i] ?

Shouldn't I be able to store just the upper or lower triangle or the matrix
? Is that possible with petsc ?

Julian.


> -----Original Message-----
> From: owner-petsc-users at mcs.anl.gov 
> [mailto:owner-petsc-users at mcs.anl.gov] On Behalf Of Julian
> Sent: Wednesday, October 11, 2006 12:37 PM
> To: petsc-users at mcs.anl.gov
> Subject: RE: General matrix interative solver
> 
> 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.
> > > > >
> > > > >
> > > > 
> > > > 
> > > 
> > > 
> > 
> 
>