Barry Smith <[email protected]> writes:

>   Ok, you should be using the BAIJ matrix it supports point-block Jacobi and 
> point-block Gauss-Seidel.
>
>    We do not have a red-black Jacobi/Gauss-Seidel but you could easily add 
> it. You will add it, not by using a any shell objects but by adding 
> functionality to the PCPBJACOBI code in PETSc which is in 
> src/ksp/pc/impls/pbjacobi/pbjacobi.c
>
>    First you will need to add a routine to supply the colors (make it general 
> for any number of colors since the code is basically the same as for only two 
> colors) call it say
>
>    PCPBJacobiSetColors(PC pc,PetscInt number of colors, PetscInt 
> *sizeofeachcolor, PetscInt **idsforeachcolor);
>   
>   you will have to add additional fields in PC_PBJacobi to contain this 
> information.
>
>   Then copy the static PetscErrorCode PCApply_PBJacobi_N(PC pc,Vec x,Vec y)  
> for your block size N (for example 3) and modify it to do what you want, so 
> for example 
>
> static PetscErrorCode PCApply_PBJacobi_2_Color(PC pc,Vec x,Vec y)
> {
>   PC_PBJacobi     *jac = (PC_PBJacobi*)pc->data;
>   PetscErrorCode  ierr;
>   PetscInt        i,m = jac->mbs;
>   const MatScalar *diag = jac->diag;
>   PetscScalar     x0,x1,*yy;
>   const PetscScalar *xx;
>
>   PetscFunctionBegin;
>   if (!jac->b) {
>      ierr = VecDuplicate(x,&jac->b);
>      ierr = VecDuplicate(x,&jac->work);
>   }
>
>   ierr = VecCopy(x,b);CHKERRQ(ierr);
>   for (j=0; j<jac->numberofcolors; j++) {
>
>   ierr = VecGetArrayRead(b,&xx);CHKERRQ(ierr);
>   ierr = VecGetArray(y,&yy);CHKERRQ(ierr);
>
>   for (i=0; i<jac->sizeofeachcolor[j]; i++) {
>     ii = jac->idsforeachcolor[j][i];
>     diag = jac->diag + 4*ii;
>     x0        = xx[2*ii]; x1 = xx[2*ii+1];
>     yy[2*ii]   = diag[0]*x0 + diag[2]*x1;
>     yy[2*ii+1] = diag[1]*x0 + diag[3]*x1;
>   }
>   ierr = VecRestoreArrayRead(b,&xx);CHKERRQ(ierr);
>   ierr = VecRestoreArray(y,&yy);CHKERRQ(ierr);
>
>   /* update residual */
>   if (i < jac->sizeofeachcolor[j]-1) {
>      ierr = MatMult(pc->matrix,y,work2);
>      ierr = VecAYPX(b,-1,work1);
>   }
>   }

Why this way instead of adding the functionality to SOR?  This global
residual update is horribly inefficient compared to merely computing the
residual on each color.

>   PetscFunctionReturn(0);
> }
>
>   Finally in PCSetUp_PBJacobi() you would set the apply function pointer to 
> the "color" version if the user has provided the coloring information.
>
>   Pretty simple.
>
>   Barry
>
>
>> On Aug 29, 2017, at 6:47 PM, Ben Yee <[email protected]> wrote:
>> 
>> I'm solving a coupled set of equations, so each "block" corresponds to a set 
>> of unknowns for a particular spatial cell.  The matrix is structured such 
>> that all of the unknowns for a given spatial cell have adjacent global 
>> matrix indices (i.e., they're next to each other in the global solution 
>> vector).  Effectively, I want to do red-black Gauss Seidel, but with blocks. 
>>  Alternatively, it's the same as applying block Jacobi for all the red cells 
>> and then applying block Jacobi for all the black cells.
>> 
>> The color of the block is determined from the geometry of the problem which 
>> is stored in various structures in the code I'm working on, independent of 
>> petsc.  (Physically, I generally have a nice 3d cartesian spatial grid and 
>> the coloring is just a checkerboard in that case.)
>> 
>> The reason I want to do this is for research purposes.  I've implemented my 
>> own interpolation matrices for PCMG, and, in my simpler 1d codes and 
>> convergence analyses, I've found that doing a red-black smoothing 
>> significantly improved convergence for my particular problem (though I'm 
>> aware that this generally leads to poor cache efficiency).
>> 
>> On Aug 29, 2017 7:33 PM, "Barry Smith" <[email protected]> wrote:
>> 
>>   Ben,
>> 
>>    Please explain more what you mean by "a red-black block Jacobi smoother". 
>> What is your matrix structure? What are the blocks? How do you decide which 
>> ones are which color?  Why do you wish to use some a smoother.
>> 
>>   Barry
>> 
>> > On Aug 29, 2017, at 6:19 PM, Ben Yee <[email protected]> wrote:
>> >
>> > Hi,
>> >
>> > For the smoother in PCMG, I want to use a red-black block Jacobi smoother. 
>> >  Is this available with the existing PETSc options?  If so, how do I 
>> > designate which blocks are red and which are black?
>> >
>> > If it is not possible, what would be the best way to implement this?  
>> > Would I use KSPRICHARDSON+PCSHELL?
>> >
>> > Thanks!
>> >
>> > --
>> > Ben Yee
>> >
>> > NERS PhD Candidate, University of Michigan
>> > B.S. Mech. & Nuclear Eng., U.C. Berkeley
>> 
>> 

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