[petsc-users] How to simplify the nonzero structure of the jacobian matrix.

[Xuefei (Rebecca) Yuan]

Hello all,

This is a test for np=1 case of the nonzero structure of the jacobian matrix. The jacobian matrix is created via 

ierr = DMDACreate2d(comm,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX, parameters.mxfield, parameters.myfield, PETSC_DECIDE, PETSC_DECIDE, 4, 2, 0, 0, &da);CHKERRQ(ierr);

ierr = DMCreateMatrix(DMMGGetDM(dmmg), MATAIJ, &jacobian);CHKERRQ(ierr);

After creation of the jacobian matrix, 

		ierr = MatAssemblyBegin(jacobian, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
		ierr = MatAssemblyEnd(jacobian, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

		PetscViewer viewer;
	        char fileName[120];
        	sprintf(fileName, "jacobian_after_creation.m");CHKERRQ(ierr);
        	
        	FILE * fp;
		
		ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,fileName,&viewer);CHKERRQ(ierr);
        	ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
		ierr = MatView (jacobian, viewer); CHKERRQ (ierr);  
        	ierr = PetscFOpen(PETSC_COMM_WORLD,fileName,"a",&fp);	CHKERRQ(ierr);
        	ierr = PetscViewerASCIIPrintf(viewer,"spy((spconvert(zzz)));\n");CHKERRQ(ierr);
        	ierr = PetscFClose(PETSC_COMM_WORLD,fp);CHKERRQ(ierr);
        	PetscViewerDestroy(&viewer);

I took a look at the structure of the jacobian by storing it in the matlab format, the matrix has 5776 nonzeros entries, however, those values are all zeros at the moment as I have not insert or add any values into it yet, the structure shows: (the following figure shows a global replacement of 0.0 by 1.0 for those 5776 numbers) 

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Inside the FormJacobianLocal() function, I have selected the index to pass to the nonzero values to jacobian, for example, 

 ierr = MatSetValuesStencil(jacobian, 1, &row, 6, col, v, INSERT_VALUES);CHKERRQ(ierr);

where

                    col[0].i = column[4].i;
                    col[1].i = column[5].i;
                    col[2].i = column[6].i;
                    col[3].i = column[9].i;
                    col[4].i = column[10].i;
                    col[5].i = column[12].i;


                    col[0].j = column[4].j;
                    col[1].j = column[5].j;
                    col[2].j = column[6].j;
                    col[3].j = column[9].j;
                    col[4].j = column[10].j;
                    col[5].j = column[12].j;

                    col[0].c = column[4].c;
                    col[1].c = column[5].c;
                    col[2].c = column[6].c;
                    col[3].c = column[9].c;
                    col[4].c = column[10].c;
                    col[5].c = column[12].c;
			
                    v[0] = value[4];
                    v[1] = value[5];
                    v[2] = value[6];
                    v[3] = value[9];
                    v[4] = value[10];
                    v[5] = value[12];

and did not pass the zero entries into the jacobian matrix. However,  after inserting or adding all values to the matrix, by the same routine above to take a look at the jacobian matrix in matlab format, the matrix still has 5776 nonzeros, in which 1075 numbers are nonzeros, and the other 4701 numbers are all zeros. The spy() gives

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for the true nonzero structures. 

But the ksp_view will give the nonzeros number as 5776, instead of 1075:

  linear system matrix = precond matrix:
  Matrix Object:  Mat_0x84000000_1   1 MPI processes
    type: seqaij
    rows=100, cols=100
    total: nonzeros=5776, allocated nonzeros=5776

It is a waste of memory to have all those values of zeros been stored in the jacobian. 

Is there anyway to get rid of those zero values in jacobian and has the only nonzero numbers stored in jacobian? In such a case, the ksp_view will tell that total:  nonzeros=1075.

Thanks very much!

Have a nice weekend!

Cheers,

Rebecca