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<p class="MsoNormal">Hello PETSc team,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I am currently using PETSc to improve the performance of a CFD solver by using it’s parallel linear solver. While doing so I ran across some scaling issues where performance increase ( measured as KSPSolve time using MPI_Wtime() function
) in the linear algebra operation was only 2 times while using 4 processes. So I tried to check the scaling of the example problem ex2f.F90 provided as a part of the PETSc package and ran across a similar issue there. Here is the issue, If I run the problem
on 1000 x 1000 2-D, five-point stencil with the exact solution set to 1.0, the scaling is perfect. But as soon as I change the exact solution to random values by using the flag -random_exact_sol (generally between 0 and 1), the scaling takes a major hit.
I have not changed the example code apart from increasing problem size and adding the time stamps before and after KSPSolve. Could you please let me know what I am missing (or) doing wrong here ? And I was also wondering if PETSc had an option to print out
the pre-conditioned matrix as changing the exact solution changes the RHS and hence might change the pre-conditioned matrix. I have provided below the exact code and the results from the 4 runs including the compilation part.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><b><u>Source Code: </u></b>(ex2f.F90 with time stamps and increased problem size)<o:p></o:p></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Description: Solves a linear system in parallel with KSP (Fortran code).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Also shows how to set a user-defined monitoring routine.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! -----------------------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> program main<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">#include <petsc/finclude/petscksp.h><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> use petscksp<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> implicit none<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Variable declarations<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Variables:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! ksp - linear solver context<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! ksp - Krylov subspace method context<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! pc - preconditioner context<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! x, b, u - approx solution, right-hand-side, exact solution vectors<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! A - matrix that defines linear system<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! its - iterations for convergence<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! norm - norm of error in solution<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! rctx - random number generator context<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Note that vectors are declared as PETSc "Vec" objects. These vectors<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! are mathematical objects that contain more than just an array of<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! double precision numbers. I.e., vectors in PETSc are not just<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! double precision x(*).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! However, local vector data can be easily accessed via VecGetArray().<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! See the Fortran section of the PETSc users manual for details.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscReal norm,t1,t2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscInt i,j,II,JJ,m,n,its<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscInt Istart,Iend,ione<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscErrorCode ierr<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscMPIInt rank,size<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscBool flg<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscScalar v,one,neg_one<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> Vec x,b,u<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> Mat A<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> KSP ksp<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscRandom rctx<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscViewerAndFormat vf,vzero<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! These variables are not currently used.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! PC pc<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! PCType ptype<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! PetscReal tol<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Note: Any user-defined Fortran routines (such as MyKSPMonitor)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! MUST be declared as external.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> external MyKSPMonitor,MyKSPConverged<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Beginning of program<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscInitialize(PETSC_NULL_CHARACTER,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (ierr .ne. 0) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> print*,'Unable to initialize PETSc'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> stop<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> m = 1000
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> n = 1000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> one = 1.0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> neg_one = -1.0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> ione = 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Compute the matrix and right-hand-side vector that define<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! the linear system, Ax = b.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Create parallel matrix, specifying only its global dimensions.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! When using MatCreate(), the matrix format can be specified at<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! runtime. Also, the parallel partitioning of the matrix is<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! determined by PETSc at runtime.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatCreate(PETSC_COMM_WORLD,A,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetFromOptions(A,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetUp(A,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Currently, all PETSc parallel matrix formats are partitioned by<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! contiguous chunks of rows across the processors. Determine which<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! rows of the matrix are locally owned.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatGetOwnershipRange(A,Istart,Iend,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Set matrix elements for the 2-D, five-point stencil in parallel.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - Each processor needs to insert only elements that it owns<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! locally (but any non-local elements will be sent to the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! appropriate processor during matrix assembly).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - Always specify global row and columns of matrix entries.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - Note that MatSetValues() uses 0-based row and column numbers<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! in Fortran as well as in C.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Note: this uses the less common natural ordering that orders first<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! all the unknowns for x = h then for x = 2h etc; Hence you see JH = II +- n<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! instead of JJ = II +- m as you might expect. The more standard ordering<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! would first do all variables for y = h, then y = 2h etc.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> do 10, II=Istart,Iend-1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> v = -1.0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> i = II/n<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> j = II - i*n<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (i.gt.0) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> JJ = II - n<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (i.lt.m-1) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> JJ = II + n<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (j.gt.0) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> JJ = II - 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (j.lt.n-1) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> JJ = II + 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> v = 4.0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatSetValues(A,ione,II,ione,II,v,INSERT_VALUES,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">10 continue<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Assemble matrix, using the 2-step process:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! MatAssemblyBegin(), MatAssemblyEnd()<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Computations can be done while messages are in transition,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! by placing code between these two statements.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Create parallel vectors.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - Here, the parallel partitioning of the vector is determined by<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! PETSc at runtime. We could also specify the local dimensions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! if desired -- or use the more general routine VecCreate().<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - When solving a linear system, the vectors and matrices MUST<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! be partitioned accordingly. PETSc automatically generates<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! appropriately partitioned matrices and vectors when MatCreate()<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! and VecCreate() are used with the same communicator.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - Note: We form 1 vector from scratch and then duplicate as needed.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecSetFromOptions(u,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecDuplicate(u,b,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecDuplicate(b,x,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Set exact solution; then compute right-hand-side vector.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! By default we use an exact solution of a vector with all<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! elements of 1.0; Alternatively, using the runtime option<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! -random_sol forms a solution vector with random components.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-random_exact_sol',flg,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (flg) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscRandomSetFromOptions(rctx,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecSetRandom(u,rctx,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscRandomDestroy(rctx,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> else<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecSet(u,one,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatMult(A,u,b,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! View the exact solution vector if desired<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-view_exact_sol',flg,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (flg) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Create the linear solver and set various options<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Create linear solver context<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Set operators. Here the matrix that defines the linear system<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! also serves as the preconditioning matrix.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPSetOperators(ksp,A,A,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Set linear solver defaults for this problem (optional).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - By extracting the KSP and PC contexts from the KSP context,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! we can then directly directly call any KSP and PC routines<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! to set various options.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - The following four statements are optional; all of these<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! parameters could alternatively be specified at runtime via<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! KSPSetFromOptions(). All of these defaults can be<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! overridden at runtime, as indicated below.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! We comment out this section of code since the Jacobi<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! preconditioner is not a good general default.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! call KSPGetPC(ksp,pc,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! ptype = PCJACOBI<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! call PCSetType(pc,ptype,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! tol = 1.e-7<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Set user-defined monitoring routine if desired<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_ksp_monitor',flg,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (flg) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> vzero = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPMonitorSet(ksp,MyKSPMonitor,vzero,PETSC_NULL_FUNCTION,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Also use the default KSP monitor routine showing how it may be used from Fortran<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,vf,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPMonitorSet(ksp,KSPMonitorResidual,vf,PetscViewerAndFormatDestroy,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Set runtime options, e.g.,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! These options will override those specified above as long as<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! KSPSetFromOptions() is called _after_ any other customization<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! routines.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPSetFromOptions(ksp,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Set convergence test routine if desired<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_ksp_convergence',flg,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (flg) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPSetConvergenceTest(ksp,MyKSPConverged,0,PETSC_NULL_FUNCTION,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Solve the linear system<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> t1 = MPI_Wtime()<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPSolve(ksp,b,x,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> t2 = MPI_Wtime()<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> !x =A-1b<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Check solution and clean up<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Check the error<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecAXPY(x,neg_one,u,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecNorm(x,NORM_2,norm,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPGetIterationNumber(ksp,its,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (rank .eq. 0) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (norm .gt. 1.e-12) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> write(6,100) norm,its<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> else<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> write(6,110) its<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> write(6,111) t2 - t1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> 100 format('Norm of error ',e11.4,' iterations ',i5)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> 110 format('Norm of error < 1.e-12 iterations ',i5)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> 111 format('KSPSolve time: ',f10.3)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Free work space. All PETSc objects should be destroyed when they<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! are no longer needed.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPDestroy(ksp,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecDestroy(u,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecDestroy(x,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecDestroy(b,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MatDestroy(A,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Always call PetscFinalize() before exiting a program. This routine<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - finalizes the PETSc libraries as well as MPI<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - provides summary and diagnostic information if certain runtime<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! options are chosen (e.g., -log_view). See PetscFinalize()<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! manpage for more information.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call PetscFinalize(ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> end<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! --------------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! MyKSPMonitor - This is a user-defined routine for monitoring<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! the KSP iterative solvers.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Input Parameters:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! ksp - iterative context<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! n - iteration number<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! rnorm - 2-norm (preconditioned) residual value (may be estimated)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! dummy - optional user-defined monitor context (unused here)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> subroutine MyKSPMonitor(ksp,n,rnorm,dummy,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> use petscksp<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> implicit none<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> KSP ksp<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> Vec x<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscErrorCode ierr<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscInt n,dummy<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscMPIInt rank<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscReal rnorm<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Build the solution vector<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call KSPBuildSolution(ksp,PETSC_NULL_VEC,x,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Write the solution vector and residual norm to stdout<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! - Note that the parallel viewer PETSC_VIEWER_STDOUT_WORLD<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! handles data from multiple processors so that the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! output is not jumbled.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (rank .eq. 0) write(6,100) n<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (rank .eq. 0) write(6,200) n,rnorm<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">100 format('iteration ',i5,' solution vector:')<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">200 format('iteration ',i5,' residual norm ',e11.4)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> ierr = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> end<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! --------------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! MyKSPConverged - This is a user-defined routine for testing<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! convergence of the KSP iterative solvers.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! Input Parameters:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! ksp - iterative context<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! n - iteration number<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! rnorm - 2-norm (preconditioned) residual value (may be estimated)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! dummy - optional user-defined monitor context (unused here)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> subroutine MyKSPConverged(ksp,n,rnorm,flag,dummy,ierr)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> use petscksp<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> implicit none<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> KSP ksp<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscErrorCode ierr<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscInt n,dummy<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> KSPConvergedReason flag<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> PetscReal rnorm<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> if (rnorm .le. .05) then<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> flag = 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> else<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> flag = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> endif<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> ierr = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"> end<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!/*TEST<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! test:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! nsize: 2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! test:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! suffix: 2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! nsize: 2<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">! args: -pc_type jacobi -my_ksp_monitor -ksp_gmres_cgs_refinement_type refine_always<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%">!TEST*/<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#2F5597;mso-style-textfill-fill-color:#2F5597;mso-style-textfill-fill-alpha:100.0%"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><u>Output:<o:p></o:p></u></b></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console";color:#1CA800">snarayanan1@USLN38
</span><span style="font-size:9.0pt;font-family:"Lucida Console";color:#C0A000">/cygdrive/c/sidarth/petsc-test/scaling_test<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">$ make ex2f<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">/home/snarayanan1/petsc-release/lib/petsc/bin/win32fe/win32fe ifort -MT -O3 -fpp -MT -O3 -fpp -I/home/snarayanan1/petsc-release/include -I/home/snarayanan1/petsc-release/arch-ci-mswin-opt-impi/include
-I/cygdrive/c/PROGRA~2/Intel/oneAPI/mpi/2021.5.0/include ex2f.F90 -L/cygdrive/c/cygwin64/home/snarayanan1/petsc-release/arch-ci-mswin-opt-impi/lib -L/cygdrive/c/PROGRA~2/Intel/oneAPI/mkl/2022.0.0/lib/intel64 -lpetsc mkl_intel_lp64_dll.lib mkl_sequential_dll.lib
mkl_core_dll.lib /cygdrive/c/PROGRA~2/Intel/oneAPI/mpi/2021.5.0/lib/release/impi.lib Gdi32.lib User32.lib Advapi32.lib Kernel32.lib Ws2_32.lib -o ex2f<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console""><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console";color:#1CA800">snarayanan1@USLN38
</span><span style="font-size:9.0pt;font-family:"Lucida Console";color:#C0A000">/cygdrive/c/sidarth/petsc-test/scaling_test<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">$ $PETSC_DIR/lib/petsc/bin/petscmpiexec -n 1 ex2f.exe<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">Norm of error 0.1214E+02 iterations 2571<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">KSPSolve time: 104.949<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console""><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console";color:#1CA800">snarayanan1@USLN38
</span><span style="font-size:9.0pt;font-family:"Lucida Console";color:#C0A000">/cygdrive/c/sidarth/petsc-test/scaling_test<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">$ $PETSC_DIR/lib/petsc/bin/petscmpiexec -n 2 ex2f.exe<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">Norm of error 0.1221E+02 iterations 1821<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">KSPSolve time: 47.139<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console""><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console";color:#1CA800">snarayanan1@USLN38
</span><span style="font-size:9.0pt;font-family:"Lucida Console";color:#C0A000">/cygdrive/c/sidarth/petsc-test/scaling_test<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">$ $PETSC_DIR/lib/petsc/bin/petscmpiexec -n 1 ex2f.exe -random_exact_sol<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">Norm of error 0.8541E+02 iterations 1003<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">KSPSolve time: 40.853<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console""><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console";color:#1CA800">snarayanan1@USLN38
</span><span style="font-size:9.0pt;font-family:"Lucida Console";color:#C0A000">/cygdrive/c/sidarth/petsc-test/scaling_test<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">$ $PETSC_DIR/lib/petsc/bin/petscmpiexec -n 2 ex2f.exe -random_exact_sol<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">Norm of error 0.8562E+02 iterations 1191<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:9.0pt;font-family:"Lucida Console"">KSPSolve time: 31.745<o:p></o:p></span></p>
<p class="MsoNormal"><b><u><o:p><span style="text-decoration:none"> </span></o:p></u></b></p>
<p class="MsoNormal"><b><u><o:p><span style="text-decoration:none"> </span></o:p></u></b></p>
<p class="MsoNormal">Thank You,<br>
Sidarth Narayanan<o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:9.0pt">Electronics Thermal Management Intern<o:p></o:p></span></i></p>
<p class="MsoNormal"><i><span style="font-size:9.0pt">Altair Engineering Inc.<o:p></o:p></span></i></p>
<p class="MsoNormal"><i><span style="font-size:9.0pt">Troy, MI<o:p></o:p></span></i></p>
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