1c4762a1bSJed Brown! 2c4762a1bSJed Brown! Description: This example solves a nonlinear system in parallel with SNES. 3c4762a1bSJed Brown! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular 4c4762a1bSJed Brown! domain, using distributed arrays (DMDAs) to partition the parallel grid. 5c4762a1bSJed Brown! The command line options include: 6c4762a1bSJed Brown! -par <param>, where <param> indicates the nonlinearity of the problem 7c4762a1bSJed Brown! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81) 8c4762a1bSJed Brown! 9c4762a1bSJed Brown! 10c4762a1bSJed Brown 11c4762a1bSJed Brown! 12c4762a1bSJed Brown! -------------------------------------------------------------------------- 13c4762a1bSJed Brown! 14c4762a1bSJed Brown! Solid Fuel Ignition (SFI) problem. This problem is modeled by 15c4762a1bSJed Brown! the partial differential equation 16c4762a1bSJed Brown! 17c4762a1bSJed Brown! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1, 18c4762a1bSJed Brown! 19c4762a1bSJed Brown! with boundary conditions 20c4762a1bSJed Brown! 21c4762a1bSJed Brown! u = 0 for x = 0, x = 1, y = 0, y = 1. 22c4762a1bSJed Brown! 23c4762a1bSJed Brown! A finite difference approximation with the usual 5-point stencil 24c4762a1bSJed Brown! is used to discretize the boundary value problem to obtain a nonlinear 25c4762a1bSJed Brown! system of equations. 26c4762a1bSJed Brown! 27c4762a1bSJed Brown! -------------------------------------------------------------------------- 28c4762a1bSJed Brown 29c4762a1bSJed Brown program main 30c4762a1bSJed Brown#include <petsc/finclude/petscsnes.h> 31c4762a1bSJed Brown use petscdmda 32c4762a1bSJed Brown use petscsnes 33c4762a1bSJed Brown implicit none 34c4762a1bSJed Brown! 35c4762a1bSJed Brown! We place common blocks, variable declarations, and other include files 36c4762a1bSJed Brown! needed for this code in the single file ex5f.h. We then need to include 37c4762a1bSJed Brown! only this file throughout the various routines in this program. See 38c4762a1bSJed Brown! additional comments in the file ex5f.h. 39c4762a1bSJed Brown! 40c4762a1bSJed Brown#include "ex5f.h" 41c4762a1bSJed Brown 42c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 43c4762a1bSJed Brown! Variable declarations 44c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 45c4762a1bSJed Brown! 46c4762a1bSJed Brown! Variables: 47c4762a1bSJed Brown! snes - nonlinear solver 48c4762a1bSJed Brown! x, r - solution, residual vectors 49c4762a1bSJed Brown! its - iterations for convergence 50c4762a1bSJed Brown! 51c4762a1bSJed Brown! See additional variable declarations in the file ex5f.h 52c4762a1bSJed Brown! 53c4762a1bSJed Brown SNES snes 54c4762a1bSJed Brown Vec x,r 55c4762a1bSJed Brown PetscInt its,i1,i4 56c4762a1bSJed Brown PetscErrorCode ierr 57c4762a1bSJed Brown PetscReal lambda_max,lambda_min 58c4762a1bSJed Brown PetscBool flg 59c4762a1bSJed Brown DM da 60c4762a1bSJed Brown 61c4762a1bSJed Brown! Note: Any user-defined Fortran routines (such as FormJacobianLocal) 62c4762a1bSJed Brown! MUST be declared as external. 63c4762a1bSJed Brown 64c4762a1bSJed Brown external FormInitialGuess 65c4762a1bSJed Brown external FormFunctionLocal,FormJacobianLocal 66c4762a1bSJed Brown external MySNESConverged 67c4762a1bSJed Brown 68c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 69c4762a1bSJed Brown! Initialize program 70c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 71c4762a1bSJed Brown 72d8606c27SBarry Smith PetscCallA(PetscInitialize(ierr)) 73d8606c27SBarry Smith PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)) 74d8606c27SBarry Smith PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)) 75c4762a1bSJed Brown 76c4762a1bSJed Brown! Initialize problem parameters 77c4762a1bSJed Brown 78c4762a1bSJed Brown i1 = 1 79c4762a1bSJed Brown i4 = 4 80c4762a1bSJed Brown lambda_max = 6.81 81c4762a1bSJed Brown lambda_min = 0.0 82c4762a1bSJed Brown lambda = 6.0 83d8606c27SBarry Smith PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)) 84c4762a1bSJed Brown! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check' 85c4762a1bSJed Brown if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then 86c4762a1bSJed Brown ierr = PETSC_ERR_ARG_OUTOFRANGE; SETERRA(PETSC_COMM_WORLD,ierr,'Lambda') 87c4762a1bSJed Brown endif 88c4762a1bSJed Brown 89c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 90c4762a1bSJed Brown! Create nonlinear solver context 91c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 92c4762a1bSJed Brown 93d8606c27SBarry Smith PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr)) 94c4762a1bSJed Brown 95c4762a1bSJed Brown! Set convergence test routine if desired 96c4762a1bSJed Brown 97d8606c27SBarry Smith PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)) 98c4762a1bSJed Brown if (flg) then 99d8606c27SBarry Smith PetscCallA(SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)) 100c4762a1bSJed Brown endif 101c4762a1bSJed Brown 102c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 103c4762a1bSJed Brown! Create vector data structures; set function evaluation routine 104c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 105c4762a1bSJed Brown 106c4762a1bSJed Brown! Create distributed array (DMDA) to manage parallel grid and vectors 107c4762a1bSJed Brown 108*60cf0239SBarry Smith! This really needs only the star-type stencil, but we use the box stencil temporarily. 109*60cf0239SBarry Smith 110*60cf0239SBarry Smith#if defined(PETSC_HAVE_FORTRAN_FREE_LINE_LENGTH_NONE) 111d8606c27SBarry Smith PetscCallA(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)) 112*60cf0239SBarry Smith#else 113*60cf0239SBarry Smith call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1, & 114*60cf0239SBarry Smith PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr) 115*60cf0239SBarry Smith#endif 116d8606c27SBarry Smith PetscCallA(DMSetFromOptions(da,ierr)) 117d8606c27SBarry Smith PetscCallA(DMSetUp(da,ierr)) 118c4762a1bSJed Brown 119c4762a1bSJed Brown! Extract global and local vectors from DMDA; then duplicate for remaining 120c4762a1bSJed Brown! vectors that are the same types 121c4762a1bSJed Brown 122d8606c27SBarry Smith PetscCallA(DMCreateGlobalVector(da,x,ierr)) 123d8606c27SBarry Smith PetscCallA(VecDuplicate(x,r,ierr)) 124c4762a1bSJed Brown 125c4762a1bSJed Brown! Get local grid boundaries (for 2-dimensional DMDA) 126c4762a1bSJed Brown 127*60cf0239SBarry Smith#if defined(PETSC_HAVE_FORTRAN_FREE_LINE_LENGTH_NONE) 128d8606c27SBarry Smith PetscCallA(DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)) 129*60cf0239SBarry Smith#else 130*60cf0239SBarry Smith call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, & 131*60cf0239SBarry Smith PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, & 132*60cf0239SBarry Smith PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr) 133*60cf0239SBarry Smith#endif 134d8606c27SBarry Smith PetscCallA(DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)) 135d8606c27SBarry Smith PetscCallA(DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)) 136c4762a1bSJed Brown 137c4762a1bSJed Brown! Here we shift the starting indices up by one so that we can easily 138c4762a1bSJed Brown! use the Fortran convention of 1-based indices (rather 0-based indices). 139c4762a1bSJed Brown 140c4762a1bSJed Brown xs = xs+1 141c4762a1bSJed Brown ys = ys+1 142c4762a1bSJed Brown gxs = gxs+1 143c4762a1bSJed Brown gys = gys+1 144c4762a1bSJed Brown 145c4762a1bSJed Brown ye = ys+ym-1 146c4762a1bSJed Brown xe = xs+xm-1 147c4762a1bSJed Brown gye = gys+gym-1 148c4762a1bSJed Brown gxe = gxs+gxm-1 149c4762a1bSJed Brown 150c4762a1bSJed Brown! Set function evaluation routine and vector 151c4762a1bSJed Brown 152d8606c27SBarry Smith PetscCallA(DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)) 153d8606c27SBarry Smith PetscCallA(DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)) 154d8606c27SBarry Smith PetscCallA(SNESSetDM(snes,da,ierr)) 155c4762a1bSJed Brown 156c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 157c4762a1bSJed Brown! Customize nonlinear solver; set runtime options 158c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 159c4762a1bSJed Brown 160c4762a1bSJed Brown! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>) 161c4762a1bSJed Brown 162d8606c27SBarry Smith PetscCallA(SNESSetFromOptions(snes,ierr)) 163c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 164c4762a1bSJed Brown! Evaluate initial guess; then solve nonlinear system. 165c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 166c4762a1bSJed Brown 167c4762a1bSJed Brown! Note: The user should initialize the vector, x, with the initial guess 168c4762a1bSJed Brown! for the nonlinear solver prior to calling SNESSolve(). In particular, 169c4762a1bSJed Brown! to employ an initial guess of zero, the user should explicitly set 170c4762a1bSJed Brown! this vector to zero by calling VecSet(). 171c4762a1bSJed Brown 172d8606c27SBarry Smith PetscCallA(FormInitialGuess(x,ierr)) 173d8606c27SBarry Smith PetscCallA(SNESSolve(snes,PETSC_NULL_VEC,x,ierr)) 174d8606c27SBarry Smith PetscCallA(SNESGetIterationNumber(snes,its,ierr)) 175c4762a1bSJed Brown if (rank .eq. 0) then 176c4762a1bSJed Brown write(6,100) its 177c4762a1bSJed Brown endif 178c4762a1bSJed Brown 100 format('Number of SNES iterations = ',i5) 179c4762a1bSJed Brown 180c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 181c4762a1bSJed Brown! Free work space. All PETSc objects should be destroyed when they 182c4762a1bSJed Brown! are no longer needed. 183c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 184c4762a1bSJed Brown 185d8606c27SBarry Smith PetscCallA(VecDestroy(x,ierr)) 186d8606c27SBarry Smith PetscCallA(VecDestroy(r,ierr)) 187d8606c27SBarry Smith PetscCallA(SNESDestroy(snes,ierr)) 188d8606c27SBarry Smith PetscCallA(DMDestroy(da,ierr)) 189d8606c27SBarry Smith PetscCallA(PetscFinalize(ierr)) 190c4762a1bSJed Brown end 191c4762a1bSJed Brown 192c4762a1bSJed Brown! --------------------------------------------------------------------- 193c4762a1bSJed Brown! 194c4762a1bSJed Brown! FormInitialGuess - Forms initial approximation. 195c4762a1bSJed Brown! 196c4762a1bSJed Brown! Input Parameters: 197c4762a1bSJed Brown! X - vector 198c4762a1bSJed Brown! 199c4762a1bSJed Brown! Output Parameter: 200c4762a1bSJed Brown! X - vector 201c4762a1bSJed Brown! 202c4762a1bSJed Brown! Notes: 203c4762a1bSJed Brown! This routine serves as a wrapper for the lower-level routine 204c4762a1bSJed Brown! "ApplicationInitialGuess", where the actual computations are 205c4762a1bSJed Brown! done using the standard Fortran style of treating the local 206c4762a1bSJed Brown! vector data as a multidimensional array over the local mesh. 207c4762a1bSJed Brown! This routine merely handles ghost point scatters and accesses 208c4762a1bSJed Brown! the local vector data via VecGetArray() and VecRestoreArray(). 209c4762a1bSJed Brown! 210c4762a1bSJed Brown subroutine FormInitialGuess(X,ierr) 211c4762a1bSJed Brown use petscsnes 212c4762a1bSJed Brown implicit none 213c4762a1bSJed Brown 214c4762a1bSJed Brown#include "ex5f.h" 215c4762a1bSJed Brown 216c4762a1bSJed Brown! Input/output variables: 217c4762a1bSJed Brown Vec X 218c4762a1bSJed Brown PetscErrorCode ierr 219c4762a1bSJed Brown 220c4762a1bSJed Brown! Declarations for use with local arrays: 221c4762a1bSJed Brown PetscScalar lx_v(0:1) 222c4762a1bSJed Brown PetscOffset lx_i 223c4762a1bSJed Brown 224c4762a1bSJed Brown ierr = 0 225c4762a1bSJed Brown 226c4762a1bSJed Brown! Get a pointer to vector data. 227c4762a1bSJed Brown! - For default PETSc vectors, VecGetArray() returns a pointer to 228c4762a1bSJed Brown! the data array. Otherwise, the routine is implementation dependent. 229c4762a1bSJed Brown! - You MUST call VecRestoreArray() when you no longer need access to 230c4762a1bSJed Brown! the array. 231c4762a1bSJed Brown! - Note that the Fortran interface to VecGetArray() differs from the 232c4762a1bSJed Brown! C version. See the users manual for details. 233c4762a1bSJed Brown 234d8606c27SBarry Smith PetscCall(VecGetArray(X,lx_v,lx_i,ierr)) 235c4762a1bSJed Brown 236c4762a1bSJed Brown! Compute initial guess over the locally owned part of the grid 237c4762a1bSJed Brown 238d8606c27SBarry Smith PetscCall(InitialGuessLocal(lx_v(lx_i),ierr)) 239c4762a1bSJed Brown 240c4762a1bSJed Brown! Restore vector 241c4762a1bSJed Brown 242d8606c27SBarry Smith PetscCall(VecRestoreArray(X,lx_v,lx_i,ierr)) 243c4762a1bSJed Brown 244c4762a1bSJed Brown return 245c4762a1bSJed Brown end 246c4762a1bSJed Brown 247c4762a1bSJed Brown! --------------------------------------------------------------------- 248c4762a1bSJed Brown! 249c4762a1bSJed Brown! InitialGuessLocal - Computes initial approximation, called by 250c4762a1bSJed Brown! the higher level routine FormInitialGuess(). 251c4762a1bSJed Brown! 252c4762a1bSJed Brown! Input Parameter: 253c4762a1bSJed Brown! x - local vector data 254c4762a1bSJed Brown! 255c4762a1bSJed Brown! Output Parameters: 256c4762a1bSJed Brown! x - local vector data 257c4762a1bSJed Brown! ierr - error code 258c4762a1bSJed Brown! 259c4762a1bSJed Brown! Notes: 260c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 261c4762a1bSJed Brown! 262c4762a1bSJed Brown subroutine InitialGuessLocal(x,ierr) 263c4762a1bSJed Brown use petscsnes 264c4762a1bSJed Brown implicit none 265c4762a1bSJed Brown 266c4762a1bSJed Brown#include "ex5f.h" 267c4762a1bSJed Brown 268c4762a1bSJed Brown! Input/output variables: 269c4762a1bSJed Brown PetscScalar x(xs:xe,ys:ye) 270c4762a1bSJed Brown PetscErrorCode ierr 271c4762a1bSJed Brown 272c4762a1bSJed Brown! Local variables: 273c4762a1bSJed Brown PetscInt i,j 274c4762a1bSJed Brown PetscReal temp1,temp,one,hx,hy 275c4762a1bSJed Brown 276c4762a1bSJed Brown! Set parameters 277c4762a1bSJed Brown 278c4762a1bSJed Brown ierr = 0 279c4762a1bSJed Brown one = 1.0 280c4762a1bSJed Brown hx = one/((mx-1)) 281c4762a1bSJed Brown hy = one/((my-1)) 282c4762a1bSJed Brown temp1 = lambda/(lambda + one) 283c4762a1bSJed Brown 284c4762a1bSJed Brown do 20 j=ys,ye 285c4762a1bSJed Brown temp = (min(j-1,my-j))*hy 286c4762a1bSJed Brown do 10 i=xs,xe 287c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 288c4762a1bSJed Brown x(i,j) = 0.0 289c4762a1bSJed Brown else 290c4762a1bSJed Brown x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp))) 291c4762a1bSJed Brown endif 292c4762a1bSJed Brown 10 continue 293c4762a1bSJed Brown 20 continue 294c4762a1bSJed Brown 295c4762a1bSJed Brown return 296c4762a1bSJed Brown end 297c4762a1bSJed Brown 298c4762a1bSJed Brown! --------------------------------------------------------------------- 299c4762a1bSJed Brown! 300c4762a1bSJed Brown! FormFunctionLocal - Computes nonlinear function, called by 301c4762a1bSJed Brown! the higher level routine FormFunction(). 302c4762a1bSJed Brown! 303c4762a1bSJed Brown! Input Parameter: 304c4762a1bSJed Brown! x - local vector data 305c4762a1bSJed Brown! 306c4762a1bSJed Brown! Output Parameters: 307c4762a1bSJed Brown! f - local vector data, f(x) 308c4762a1bSJed Brown! ierr - error code 309c4762a1bSJed Brown! 310c4762a1bSJed Brown! Notes: 311c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 312c4762a1bSJed Brown! 313c4762a1bSJed Brown! 314c4762a1bSJed Brown subroutine FormFunctionLocal(info,x,f,da,ierr) 315c4762a1bSJed Brown#include <petsc/finclude/petscdmda.h> 316c4762a1bSJed Brown use petscsnes 317c4762a1bSJed Brown implicit none 318c4762a1bSJed Brown 319c4762a1bSJed Brown#include "ex5f.h" 320c4762a1bSJed Brown DM da 321c4762a1bSJed Brown 322c4762a1bSJed Brown! Input/output variables: 323c4762a1bSJed Brown DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE) 324c4762a1bSJed Brown PetscScalar x(gxs:gxe,gys:gye) 325c4762a1bSJed Brown PetscScalar f(xs:xe,ys:ye) 326c4762a1bSJed Brown PetscErrorCode ierr 327c4762a1bSJed Brown 328c4762a1bSJed Brown! Local variables: 329c4762a1bSJed Brown PetscScalar two,one,hx,hy 330c4762a1bSJed Brown PetscScalar hxdhy,hydhx,sc 331c4762a1bSJed Brown PetscScalar u,uxx,uyy 332c4762a1bSJed Brown PetscInt i,j 333c4762a1bSJed Brown 334c4762a1bSJed Brown xs = info(DMDA_LOCAL_INFO_XS)+1 335c4762a1bSJed Brown xe = xs+info(DMDA_LOCAL_INFO_XM)-1 336c4762a1bSJed Brown ys = info(DMDA_LOCAL_INFO_YS)+1 337c4762a1bSJed Brown ye = ys+info(DMDA_LOCAL_INFO_YM)-1 338c4762a1bSJed Brown mx = info(DMDA_LOCAL_INFO_MX) 339c4762a1bSJed Brown my = info(DMDA_LOCAL_INFO_MY) 340c4762a1bSJed Brown 341c4762a1bSJed Brown one = 1.0 342c4762a1bSJed Brown two = 2.0 343c4762a1bSJed Brown hx = one/(mx-1) 344c4762a1bSJed Brown hy = one/(my-1) 345c4762a1bSJed Brown sc = hx*hy*lambda 346c4762a1bSJed Brown hxdhy = hx/hy 347c4762a1bSJed Brown hydhx = hy/hx 348c4762a1bSJed Brown 349c4762a1bSJed Brown! Compute function over the locally owned part of the grid 350c4762a1bSJed Brown 351c4762a1bSJed Brown do 20 j=ys,ye 352c4762a1bSJed Brown do 10 i=xs,xe 353c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 354c4762a1bSJed Brown f(i,j) = x(i,j) 355c4762a1bSJed Brown else 356c4762a1bSJed Brown u = x(i,j) 357c4762a1bSJed Brown uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j)) 358c4762a1bSJed Brown uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1)) 359c4762a1bSJed Brown f(i,j) = uxx + uyy - sc*exp(u) 360c4762a1bSJed Brown endif 361c4762a1bSJed Brown 10 continue 362c4762a1bSJed Brown 20 continue 363c4762a1bSJed Brown 364d8606c27SBarry Smith PetscCall(PetscLogFlops(11.0d0*ym*xm,ierr)) 365c4762a1bSJed Brown 366c4762a1bSJed Brown return 367c4762a1bSJed Brown end 368c4762a1bSJed Brown 369c4762a1bSJed Brown! --------------------------------------------------------------------- 370c4762a1bSJed Brown! 371c4762a1bSJed Brown! FormJacobianLocal - Computes Jacobian matrix, called by 372c4762a1bSJed Brown! the higher level routine FormJacobian(). 373c4762a1bSJed Brown! 374c4762a1bSJed Brown! Input Parameters: 375c4762a1bSJed Brown! x - local vector data 376c4762a1bSJed Brown! 377c4762a1bSJed Brown! Output Parameters: 378c4762a1bSJed Brown! jac - Jacobian matrix 379c4762a1bSJed Brown! jac_prec - optionally different preconditioning matrix (not used here) 380c4762a1bSJed Brown! ierr - error code 381c4762a1bSJed Brown! 382c4762a1bSJed Brown! Notes: 383c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 384c4762a1bSJed Brown! 385c4762a1bSJed Brown! Notes: 386c4762a1bSJed Brown! Due to grid point reordering with DMDAs, we must always work 387c4762a1bSJed Brown! with the local grid points, and then transform them to the new 388c4762a1bSJed Brown! global numbering with the "ltog" mapping 389c4762a1bSJed Brown! We cannot work directly with the global numbers for the original 390c4762a1bSJed Brown! uniprocessor grid! 391c4762a1bSJed Brown! 392c4762a1bSJed Brown! Two methods are available for imposing this transformation 393c4762a1bSJed Brown! when setting matrix entries: 394c4762a1bSJed Brown! (A) MatSetValuesLocal(), using the local ordering (including 395c4762a1bSJed Brown! ghost points!) 396c4762a1bSJed Brown! by calling MatSetValuesLocal() 397c4762a1bSJed Brown! (B) MatSetValues(), using the global ordering 398c4762a1bSJed Brown! - Use DMDAGetGlobalIndices() to extract the local-to-global map 399c4762a1bSJed Brown! - Then apply this map explicitly yourself 400c4762a1bSJed Brown! - Set matrix entries using the global ordering by calling 401c4762a1bSJed Brown! MatSetValues() 402c4762a1bSJed Brown! Option (A) seems cleaner/easier in many cases, and is the procedure 403c4762a1bSJed Brown! used in this example. 404c4762a1bSJed Brown! 405c4762a1bSJed Brown subroutine FormJacobianLocal(info,x,A,jac,da,ierr) 406c4762a1bSJed Brown use petscsnes 407c4762a1bSJed Brown implicit none 408c4762a1bSJed Brown 409c4762a1bSJed Brown#include "ex5f.h" 410c4762a1bSJed Brown DM da 411c4762a1bSJed Brown 412c4762a1bSJed Brown! Input/output variables: 413c4762a1bSJed Brown PetscScalar x(gxs:gxe,gys:gye) 414c4762a1bSJed Brown Mat A,jac 415c4762a1bSJed Brown PetscErrorCode ierr 416c4762a1bSJed Brown DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE) 417c4762a1bSJed Brown 418c4762a1bSJed Brown! Local variables: 419c4762a1bSJed Brown PetscInt row,col(5),i,j,i1,i5 420c4762a1bSJed Brown PetscScalar two,one,hx,hy,v(5) 421c4762a1bSJed Brown PetscScalar hxdhy,hydhx,sc 422c4762a1bSJed Brown 423c4762a1bSJed Brown! Set parameters 424c4762a1bSJed Brown 425c4762a1bSJed Brown i1 = 1 426c4762a1bSJed Brown i5 = 5 427c4762a1bSJed Brown one = 1.0 428c4762a1bSJed Brown two = 2.0 429c4762a1bSJed Brown hx = one/(mx-1) 430c4762a1bSJed Brown hy = one/(my-1) 431c4762a1bSJed Brown sc = hx*hy 432c4762a1bSJed Brown hxdhy = hx/hy 433c4762a1bSJed Brown hydhx = hy/hx 434c4762a1bSJed Brown 435c4762a1bSJed Brown! Compute entries for the locally owned part of the Jacobian. 436c4762a1bSJed Brown! - Currently, all PETSc parallel matrix formats are partitioned by 437c4762a1bSJed Brown! contiguous chunks of rows across the processors. 438c4762a1bSJed Brown! - Each processor needs to insert only elements that it owns 439c4762a1bSJed Brown! locally (but any non-local elements will be sent to the 440c4762a1bSJed Brown! appropriate processor during matrix assembly). 441c4762a1bSJed Brown! - Here, we set all entries for a particular row at once. 442c4762a1bSJed Brown! - We can set matrix entries either using either 443c4762a1bSJed Brown! MatSetValuesLocal() or MatSetValues(), as discussed above. 444c4762a1bSJed Brown! - Note that MatSetValues() uses 0-based row and column numbers 445c4762a1bSJed Brown! in Fortran as well as in C. 446c4762a1bSJed Brown 447c4762a1bSJed Brown do 20 j=ys,ye 448c4762a1bSJed Brown row = (j - gys)*gxm + xs - gxs - 1 449c4762a1bSJed Brown do 10 i=xs,xe 450c4762a1bSJed Brown row = row + 1 451c4762a1bSJed Brown! boundary points 452c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 453c4762a1bSJed Brown! Some f90 compilers need 4th arg to be of same type in both calls 454c4762a1bSJed Brown col(1) = row 455c4762a1bSJed Brown v(1) = one 456d8606c27SBarry Smith PetscCall(MatSetValuesLocal(jac,i1,row,i1,col,v,INSERT_VALUES,ierr)) 457c4762a1bSJed Brown! interior grid points 458c4762a1bSJed Brown else 459c4762a1bSJed Brown v(1) = -hxdhy 460c4762a1bSJed Brown v(2) = -hydhx 461c4762a1bSJed Brown v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j)) 462c4762a1bSJed Brown v(4) = -hydhx 463c4762a1bSJed Brown v(5) = -hxdhy 464c4762a1bSJed Brown col(1) = row - gxm 465c4762a1bSJed Brown col(2) = row - 1 466c4762a1bSJed Brown col(3) = row 467c4762a1bSJed Brown col(4) = row + 1 468c4762a1bSJed Brown col(5) = row + gxm 469d8606c27SBarry Smith PetscCall(MatSetValuesLocal(jac,i1,row,i5,col,v, INSERT_VALUES,ierr)) 470c4762a1bSJed Brown endif 471c4762a1bSJed Brown 10 continue 472c4762a1bSJed Brown 20 continue 473d8606c27SBarry Smith PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)) 474d8606c27SBarry Smith PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)) 475c4762a1bSJed Brown if (A .ne. jac) then 476d8606c27SBarry Smith PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)) 477d8606c27SBarry Smith PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)) 478c4762a1bSJed Brown endif 479c4762a1bSJed Brown return 480c4762a1bSJed Brown end 481c4762a1bSJed Brown 482c4762a1bSJed Brown! 483c4762a1bSJed Brown! Simple convergence test based on the infinity norm of the residual being small 484c4762a1bSJed Brown! 485c4762a1bSJed Brown subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr) 486c4762a1bSJed Brown use petscsnes 487c4762a1bSJed Brown implicit none 488c4762a1bSJed Brown 489c4762a1bSJed Brown SNES snes 490c4762a1bSJed Brown PetscInt it,dummy 491c4762a1bSJed Brown PetscReal xnorm,snorm,fnorm,nrm 492c4762a1bSJed Brown SNESConvergedReason reason 493c4762a1bSJed Brown Vec f 494c4762a1bSJed Brown PetscErrorCode ierr 495c4762a1bSJed Brown 496d8606c27SBarry Smith PetscCall(SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)) 497d8606c27SBarry Smith PetscCall(VecNorm(f,NORM_INFINITY,nrm,ierr)) 498c4762a1bSJed Brown if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS 499c4762a1bSJed Brown 500c4762a1bSJed Brown end 501c4762a1bSJed Brown 502c4762a1bSJed Brown!/*TEST 503c4762a1bSJed Brown! 504c4762a1bSJed Brown! build: 505c4762a1bSJed Brown! requires: !complex !single 506c4762a1bSJed Brown! 507c4762a1bSJed Brown! test: 508c4762a1bSJed Brown! nsize: 4 5098f8b3c79SStefano Zampini! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short \ 5108f8b3c79SStefano Zampini! -ksp_gmres_cgs_refinement_type refine_always 511c4762a1bSJed Brown! 512c4762a1bSJed Brown! test: 513c4762a1bSJed Brown! suffix: 2 514c4762a1bSJed Brown! nsize: 4 515c4762a1bSJed Brown! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 516c4762a1bSJed Brown! 517c4762a1bSJed Brown! test: 518c4762a1bSJed Brown! suffix: 3 519c4762a1bSJed Brown! nsize: 3 520c4762a1bSJed Brown! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 521c4762a1bSJed Brown! 522c4762a1bSJed Brown! test: 523c4762a1bSJed Brown! suffix: 6 524c4762a1bSJed Brown! nsize: 1 525c4762a1bSJed Brown! args: -snes_monitor_short -my_snes_convergence 526c4762a1bSJed Brown! 527c4762a1bSJed Brown!TEST*/ 528