> On Aug 29, 2017, at 10:31 PM, Jed Brown <[email protected]> wrote: > > 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.
True, but if this is for theoretical studies of convergence and not optimal performance it is easier. For example you do this and see the convergence is much better with coloring than without and then conclude it is worth spending the time to do it properly within an SOR framework. Barry > >> 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 >>> >>>
