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! -------------------------------------------------------------------------- 28*dfbbaf82SBarry Smith module ex5fmodule 29*dfbbaf82SBarry Smith use petscsnes 30*dfbbaf82SBarry Smith use petscdmda 31*dfbbaf82SBarry Smith#include <petsc/finclude/petscsnes.h> 32*dfbbaf82SBarry Smith#include <petsc/finclude/petscdm.h> 33*dfbbaf82SBarry Smith#include <petsc/finclude/petscdmda.h> 34*dfbbaf82SBarry Smith PetscInt xs,xe,xm,gxs,gxe,gxm 35*dfbbaf82SBarry Smith PetscInt ys,ye,ym,gys,gye,gym 36*dfbbaf82SBarry Smith PetscInt mx,my 37*dfbbaf82SBarry Smith PetscMPIInt rank,size 38*dfbbaf82SBarry Smith PetscReal lambda 39*dfbbaf82SBarry Smith end module ex5fmodule 40c4762a1bSJed Brown 41c4762a1bSJed Brown program main 42*dfbbaf82SBarry Smith use ex5fmodule 43c4762a1bSJed Brown implicit none 44c4762a1bSJed Brown 45c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 46c4762a1bSJed Brown! Variable declarations 47c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 48c4762a1bSJed Brown! 49c4762a1bSJed Brown! Variables: 50c4762a1bSJed Brown! snes - nonlinear solver 51c4762a1bSJed Brown! x, r - solution, residual vectors 52c4762a1bSJed Brown! its - iterations for convergence 53c4762a1bSJed Brown! 54c4762a1bSJed Brown! See additional variable declarations in the file ex5f.h 55c4762a1bSJed Brown! 56c4762a1bSJed Brown SNES snes 57c4762a1bSJed Brown Vec x,r 58c4762a1bSJed Brown PetscInt its,i1,i4 59c4762a1bSJed Brown PetscErrorCode ierr 60c4762a1bSJed Brown PetscReal lambda_max,lambda_min 61c4762a1bSJed Brown PetscBool flg 62c4762a1bSJed Brown DM da 63c4762a1bSJed Brown 64c4762a1bSJed Brown! Note: Any user-defined Fortran routines (such as FormJacobianLocal) 65c4762a1bSJed Brown! MUST be declared as external. 66c4762a1bSJed Brown 67c4762a1bSJed Brown external FormInitialGuess 68c4762a1bSJed Brown external FormFunctionLocal,FormJacobianLocal 69c4762a1bSJed Brown external MySNESConverged 70c4762a1bSJed Brown 71c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 72c4762a1bSJed Brown! Initialize program 73c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 74c4762a1bSJed Brown 75d8606c27SBarry Smith PetscCallA(PetscInitialize(ierr)) 76d8606c27SBarry Smith PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)) 77d8606c27SBarry Smith PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)) 78c4762a1bSJed Brown 79c4762a1bSJed Brown! Initialize problem parameters 80c4762a1bSJed Brown 81c4762a1bSJed Brown i1 = 1 82c4762a1bSJed Brown i4 = 4 83c4762a1bSJed Brown lambda_max = 6.81 84c4762a1bSJed Brown lambda_min = 0.0 85c4762a1bSJed Brown lambda = 6.0 86d8606c27SBarry Smith PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)) 87c4762a1bSJed Brown! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check' 88c4762a1bSJed Brown if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then 89c4762a1bSJed Brown ierr = PETSC_ERR_ARG_OUTOFRANGE; SETERRA(PETSC_COMM_WORLD,ierr,'Lambda') 90c4762a1bSJed Brown endif 91c4762a1bSJed Brown 92c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 93c4762a1bSJed Brown! Create nonlinear solver context 94c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 95c4762a1bSJed Brown 96d8606c27SBarry Smith PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr)) 97c4762a1bSJed Brown 98c4762a1bSJed Brown! Set convergence test routine if desired 99c4762a1bSJed Brown 100d8606c27SBarry Smith PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)) 101c4762a1bSJed Brown if (flg) then 102d8606c27SBarry Smith PetscCallA(SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)) 103c4762a1bSJed Brown endif 104c4762a1bSJed Brown 105c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 106c4762a1bSJed Brown! Create vector data structures; set function evaluation routine 107c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 108c4762a1bSJed Brown 109c4762a1bSJed Brown! Create distributed array (DMDA) to manage parallel grid and vectors 110c4762a1bSJed Brown 11160cf0239SBarry Smith! This really needs only the star-type stencil, but we use the box stencil temporarily. 11260cf0239SBarry Smith 11360cf0239SBarry Smith#if defined(PETSC_HAVE_FORTRAN_FREE_LINE_LENGTH_NONE) 114d8606c27SBarry 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)) 11560cf0239SBarry Smith#else 11660cf0239SBarry Smith call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1, & 11760cf0239SBarry Smith PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr) 11860cf0239SBarry Smith#endif 119d8606c27SBarry Smith PetscCallA(DMSetFromOptions(da,ierr)) 120d8606c27SBarry Smith PetscCallA(DMSetUp(da,ierr)) 121c4762a1bSJed Brown 122c4762a1bSJed Brown! Extract global and local vectors from DMDA; then duplicate for remaining 123c4762a1bSJed Brown! vectors that are the same types 124c4762a1bSJed Brown 125d8606c27SBarry Smith PetscCallA(DMCreateGlobalVector(da,x,ierr)) 126d8606c27SBarry Smith PetscCallA(VecDuplicate(x,r,ierr)) 127c4762a1bSJed Brown 128c4762a1bSJed Brown! Get local grid boundaries (for 2-dimensional DMDA) 129c4762a1bSJed Brown 13060cf0239SBarry Smith#if defined(PETSC_HAVE_FORTRAN_FREE_LINE_LENGTH_NONE) 131d8606c27SBarry 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)) 13260cf0239SBarry Smith#else 13360cf0239SBarry Smith call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, & 13460cf0239SBarry Smith PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, & 13560cf0239SBarry Smith PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr) 13660cf0239SBarry Smith#endif 137d8606c27SBarry Smith PetscCallA(DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)) 138d8606c27SBarry Smith PetscCallA(DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)) 139c4762a1bSJed Brown 140c4762a1bSJed Brown! Here we shift the starting indices up by one so that we can easily 141c4762a1bSJed Brown! use the Fortran convention of 1-based indices (rather 0-based indices). 142c4762a1bSJed Brown 143c4762a1bSJed Brown xs = xs+1 144c4762a1bSJed Brown ys = ys+1 145c4762a1bSJed Brown gxs = gxs+1 146c4762a1bSJed Brown gys = gys+1 147c4762a1bSJed Brown 148c4762a1bSJed Brown ye = ys+ym-1 149c4762a1bSJed Brown xe = xs+xm-1 150c4762a1bSJed Brown gye = gys+gym-1 151c4762a1bSJed Brown gxe = gxs+gxm-1 152c4762a1bSJed Brown 153c4762a1bSJed Brown! Set function evaluation routine and vector 154c4762a1bSJed Brown 155d8606c27SBarry Smith PetscCallA(DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)) 156d8606c27SBarry Smith PetscCallA(DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)) 157d8606c27SBarry Smith PetscCallA(SNESSetDM(snes,da,ierr)) 158c4762a1bSJed Brown 159c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 160c4762a1bSJed Brown! Customize nonlinear solver; set runtime options 161c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 162c4762a1bSJed Brown 163c4762a1bSJed Brown! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>) 164c4762a1bSJed Brown 165d8606c27SBarry Smith PetscCallA(SNESSetFromOptions(snes,ierr)) 166c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 167c4762a1bSJed Brown! Evaluate initial guess; then solve nonlinear system. 168c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 169c4762a1bSJed Brown 170c4762a1bSJed Brown! Note: The user should initialize the vector, x, with the initial guess 171c4762a1bSJed Brown! for the nonlinear solver prior to calling SNESSolve(). In particular, 172c4762a1bSJed Brown! to employ an initial guess of zero, the user should explicitly set 173c4762a1bSJed Brown! this vector to zero by calling VecSet(). 174c4762a1bSJed Brown 175d8606c27SBarry Smith PetscCallA(FormInitialGuess(x,ierr)) 176d8606c27SBarry Smith PetscCallA(SNESSolve(snes,PETSC_NULL_VEC,x,ierr)) 177d8606c27SBarry Smith PetscCallA(SNESGetIterationNumber(snes,its,ierr)) 178c4762a1bSJed Brown if (rank .eq. 0) then 179c4762a1bSJed Brown write(6,100) its 180c4762a1bSJed Brown endif 181c4762a1bSJed Brown 100 format('Number of SNES iterations = ',i5) 182c4762a1bSJed Brown 183c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 184c4762a1bSJed Brown! Free work space. All PETSc objects should be destroyed when they 185c4762a1bSJed Brown! are no longer needed. 186c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 187c4762a1bSJed Brown 188d8606c27SBarry Smith PetscCallA(VecDestroy(x,ierr)) 189d8606c27SBarry Smith PetscCallA(VecDestroy(r,ierr)) 190d8606c27SBarry Smith PetscCallA(SNESDestroy(snes,ierr)) 191d8606c27SBarry Smith PetscCallA(DMDestroy(da,ierr)) 192d8606c27SBarry Smith PetscCallA(PetscFinalize(ierr)) 193c4762a1bSJed Brown end 194c4762a1bSJed Brown 195c4762a1bSJed Brown! --------------------------------------------------------------------- 196c4762a1bSJed Brown! 197c4762a1bSJed Brown! FormInitialGuess - Forms initial approximation. 198c4762a1bSJed Brown! 199c4762a1bSJed Brown! Input Parameters: 200c4762a1bSJed Brown! X - vector 201c4762a1bSJed Brown! 202c4762a1bSJed Brown! Output Parameter: 203c4762a1bSJed Brown! X - vector 204c4762a1bSJed Brown! 205c4762a1bSJed Brown! Notes: 206c4762a1bSJed Brown! This routine serves as a wrapper for the lower-level routine 207c4762a1bSJed Brown! "ApplicationInitialGuess", where the actual computations are 208c4762a1bSJed Brown! done using the standard Fortran style of treating the local 209c4762a1bSJed Brown! vector data as a multidimensional array over the local mesh. 210c4762a1bSJed Brown! This routine merely handles ghost point scatters and accesses 211c4762a1bSJed Brown! the local vector data via VecGetArray() and VecRestoreArray(). 212c4762a1bSJed Brown! 213c4762a1bSJed Brown subroutine FormInitialGuess(X,ierr) 214*dfbbaf82SBarry Smith use ex5fmodule 215c4762a1bSJed Brown implicit none 216c4762a1bSJed Brown 217c4762a1bSJed Brown! Input/output variables: 218c4762a1bSJed Brown Vec X 219c4762a1bSJed Brown PetscErrorCode ierr 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) 263*dfbbaf82SBarry Smith use ex5fmodule 264c4762a1bSJed Brown implicit none 265c4762a1bSJed Brown 266c4762a1bSJed Brown! Input/output variables: 267c4762a1bSJed Brown PetscScalar x(xs:xe,ys:ye) 268c4762a1bSJed Brown PetscErrorCode ierr 269c4762a1bSJed Brown 270c4762a1bSJed Brown! Local variables: 271c4762a1bSJed Brown PetscInt i,j 272c4762a1bSJed Brown PetscReal temp1,temp,one,hx,hy 273c4762a1bSJed Brown 274c4762a1bSJed Brown! Set parameters 275c4762a1bSJed Brown 276c4762a1bSJed Brown ierr = 0 277c4762a1bSJed Brown one = 1.0 278c4762a1bSJed Brown hx = one/((mx-1)) 279c4762a1bSJed Brown hy = one/((my-1)) 280c4762a1bSJed Brown temp1 = lambda/(lambda + one) 281c4762a1bSJed Brown 282c4762a1bSJed Brown do 20 j=ys,ye 283c4762a1bSJed Brown temp = (min(j-1,my-j))*hy 284c4762a1bSJed Brown do 10 i=xs,xe 285c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 286c4762a1bSJed Brown x(i,j) = 0.0 287c4762a1bSJed Brown else 288c4762a1bSJed Brown x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp))) 289c4762a1bSJed Brown endif 290c4762a1bSJed Brown 10 continue 291c4762a1bSJed Brown 20 continue 292c4762a1bSJed Brown 293c4762a1bSJed Brown return 294c4762a1bSJed Brown end 295c4762a1bSJed Brown 296c4762a1bSJed Brown! --------------------------------------------------------------------- 297c4762a1bSJed Brown! 298c4762a1bSJed Brown! FormFunctionLocal - Computes nonlinear function, called by 299c4762a1bSJed Brown! the higher level routine FormFunction(). 300c4762a1bSJed Brown! 301c4762a1bSJed Brown! Input Parameter: 302c4762a1bSJed Brown! x - local vector data 303c4762a1bSJed Brown! 304c4762a1bSJed Brown! Output Parameters: 305c4762a1bSJed Brown! f - local vector data, f(x) 306c4762a1bSJed Brown! ierr - error code 307c4762a1bSJed Brown! 308c4762a1bSJed Brown! Notes: 309c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 310c4762a1bSJed Brown! 311c4762a1bSJed Brown! 312c4762a1bSJed Brown subroutine FormFunctionLocal(info,x,f,da,ierr) 313*dfbbaf82SBarry Smith use ex5fmodule 314c4762a1bSJed Brown implicit none 315c4762a1bSJed Brown 316c4762a1bSJed Brown DM da 317c4762a1bSJed Brown 318c4762a1bSJed Brown! Input/output variables: 319c4762a1bSJed Brown DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE) 320c4762a1bSJed Brown PetscScalar x(gxs:gxe,gys:gye) 321c4762a1bSJed Brown PetscScalar f(xs:xe,ys:ye) 322c4762a1bSJed Brown PetscErrorCode ierr 323c4762a1bSJed Brown 324c4762a1bSJed Brown! Local variables: 325c4762a1bSJed Brown PetscScalar two,one,hx,hy 326c4762a1bSJed Brown PetscScalar hxdhy,hydhx,sc 327c4762a1bSJed Brown PetscScalar u,uxx,uyy 328c4762a1bSJed Brown PetscInt i,j 329c4762a1bSJed Brown 330c4762a1bSJed Brown xs = info(DMDA_LOCAL_INFO_XS)+1 331c4762a1bSJed Brown xe = xs+info(DMDA_LOCAL_INFO_XM)-1 332c4762a1bSJed Brown ys = info(DMDA_LOCAL_INFO_YS)+1 333c4762a1bSJed Brown ye = ys+info(DMDA_LOCAL_INFO_YM)-1 334c4762a1bSJed Brown mx = info(DMDA_LOCAL_INFO_MX) 335c4762a1bSJed Brown my = info(DMDA_LOCAL_INFO_MY) 336c4762a1bSJed Brown 337c4762a1bSJed Brown one = 1.0 338c4762a1bSJed Brown two = 2.0 339c4762a1bSJed Brown hx = one/(mx-1) 340c4762a1bSJed Brown hy = one/(my-1) 341c4762a1bSJed Brown sc = hx*hy*lambda 342c4762a1bSJed Brown hxdhy = hx/hy 343c4762a1bSJed Brown hydhx = hy/hx 344c4762a1bSJed Brown 345c4762a1bSJed Brown! Compute function over the locally owned part of the grid 346c4762a1bSJed Brown 347c4762a1bSJed Brown do 20 j=ys,ye 348c4762a1bSJed Brown do 10 i=xs,xe 349c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 350c4762a1bSJed Brown f(i,j) = x(i,j) 351c4762a1bSJed Brown else 352c4762a1bSJed Brown u = x(i,j) 353c4762a1bSJed Brown uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j)) 354c4762a1bSJed Brown uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1)) 355c4762a1bSJed Brown f(i,j) = uxx + uyy - sc*exp(u) 356c4762a1bSJed Brown endif 357c4762a1bSJed Brown 10 continue 358c4762a1bSJed Brown 20 continue 359c4762a1bSJed Brown 360d8606c27SBarry Smith PetscCall(PetscLogFlops(11.0d0*ym*xm,ierr)) 361c4762a1bSJed Brown 362c4762a1bSJed Brown return 363c4762a1bSJed Brown end 364c4762a1bSJed Brown 365c4762a1bSJed Brown! --------------------------------------------------------------------- 366c4762a1bSJed Brown! 367c4762a1bSJed Brown! FormJacobianLocal - Computes Jacobian matrix, called by 368c4762a1bSJed Brown! the higher level routine FormJacobian(). 369c4762a1bSJed Brown! 370c4762a1bSJed Brown! Input Parameters: 371c4762a1bSJed Brown! x - local vector data 372c4762a1bSJed Brown! 373c4762a1bSJed Brown! Output Parameters: 374c4762a1bSJed Brown! jac - Jacobian matrix 375c4762a1bSJed Brown! jac_prec - optionally different preconditioning matrix (not used here) 376c4762a1bSJed Brown! ierr - error code 377c4762a1bSJed Brown! 378c4762a1bSJed Brown! Notes: 379c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 380c4762a1bSJed Brown! 381c4762a1bSJed Brown! Notes: 382c4762a1bSJed Brown! Due to grid point reordering with DMDAs, we must always work 383c4762a1bSJed Brown! with the local grid points, and then transform them to the new 384c4762a1bSJed Brown! global numbering with the "ltog" mapping 385c4762a1bSJed Brown! We cannot work directly with the global numbers for the original 386c4762a1bSJed Brown! uniprocessor grid! 387c4762a1bSJed Brown! 388c4762a1bSJed Brown! Two methods are available for imposing this transformation 389c4762a1bSJed Brown! when setting matrix entries: 390c4762a1bSJed Brown! (A) MatSetValuesLocal(), using the local ordering (including 391c4762a1bSJed Brown! ghost points!) 392c4762a1bSJed Brown! by calling MatSetValuesLocal() 393c4762a1bSJed Brown! (B) MatSetValues(), using the global ordering 394c4762a1bSJed Brown! - Use DMDAGetGlobalIndices() to extract the local-to-global map 395c4762a1bSJed Brown! - Then apply this map explicitly yourself 396c4762a1bSJed Brown! - Set matrix entries using the global ordering by calling 397c4762a1bSJed Brown! MatSetValues() 398c4762a1bSJed Brown! Option (A) seems cleaner/easier in many cases, and is the procedure 399c4762a1bSJed Brown! used in this example. 400c4762a1bSJed Brown! 401c4762a1bSJed Brown subroutine FormJacobianLocal(info,x,A,jac,da,ierr) 402*dfbbaf82SBarry Smith use ex5fmodule 403c4762a1bSJed Brown implicit none 404c4762a1bSJed Brown 405c4762a1bSJed Brown DM da 406c4762a1bSJed Brown 407c4762a1bSJed Brown! Input/output variables: 408c4762a1bSJed Brown PetscScalar x(gxs:gxe,gys:gye) 409c4762a1bSJed Brown Mat A,jac 410c4762a1bSJed Brown PetscErrorCode ierr 411c4762a1bSJed Brown DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE) 412c4762a1bSJed Brown 413c4762a1bSJed Brown! Local variables: 414c4762a1bSJed Brown PetscInt row,col(5),i,j,i1,i5 415c4762a1bSJed Brown PetscScalar two,one,hx,hy,v(5) 416c4762a1bSJed Brown PetscScalar hxdhy,hydhx,sc 417c4762a1bSJed Brown 418c4762a1bSJed Brown! Set parameters 419c4762a1bSJed Brown 420c4762a1bSJed Brown i1 = 1 421c4762a1bSJed Brown i5 = 5 422c4762a1bSJed Brown one = 1.0 423c4762a1bSJed Brown two = 2.0 424c4762a1bSJed Brown hx = one/(mx-1) 425c4762a1bSJed Brown hy = one/(my-1) 426c4762a1bSJed Brown sc = hx*hy 427c4762a1bSJed Brown hxdhy = hx/hy 428c4762a1bSJed Brown hydhx = hy/hx 429c4762a1bSJed Brown 430c4762a1bSJed Brown! Compute entries for the locally owned part of the Jacobian. 431c4762a1bSJed Brown! - Currently, all PETSc parallel matrix formats are partitioned by 432c4762a1bSJed Brown! contiguous chunks of rows across the processors. 433c4762a1bSJed Brown! - Each processor needs to insert only elements that it owns 434c4762a1bSJed Brown! locally (but any non-local elements will be sent to the 435c4762a1bSJed Brown! appropriate processor during matrix assembly). 436c4762a1bSJed Brown! - Here, we set all entries for a particular row at once. 437c4762a1bSJed Brown! - We can set matrix entries either using either 438c4762a1bSJed Brown! MatSetValuesLocal() or MatSetValues(), as discussed above. 439c4762a1bSJed Brown! - Note that MatSetValues() uses 0-based row and column numbers 440c4762a1bSJed Brown! in Fortran as well as in C. 441c4762a1bSJed Brown 442c4762a1bSJed Brown do 20 j=ys,ye 443c4762a1bSJed Brown row = (j - gys)*gxm + xs - gxs - 1 444c4762a1bSJed Brown do 10 i=xs,xe 445c4762a1bSJed Brown row = row + 1 446c4762a1bSJed Brown! boundary points 447c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 448c4762a1bSJed Brown! Some f90 compilers need 4th arg to be of same type in both calls 449c4762a1bSJed Brown col(1) = row 450c4762a1bSJed Brown v(1) = one 451d8606c27SBarry Smith PetscCall(MatSetValuesLocal(jac,i1,row,i1,col,v,INSERT_VALUES,ierr)) 452c4762a1bSJed Brown! interior grid points 453c4762a1bSJed Brown else 454c4762a1bSJed Brown v(1) = -hxdhy 455c4762a1bSJed Brown v(2) = -hydhx 456c4762a1bSJed Brown v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j)) 457c4762a1bSJed Brown v(4) = -hydhx 458c4762a1bSJed Brown v(5) = -hxdhy 459c4762a1bSJed Brown col(1) = row - gxm 460c4762a1bSJed Brown col(2) = row - 1 461c4762a1bSJed Brown col(3) = row 462c4762a1bSJed Brown col(4) = row + 1 463c4762a1bSJed Brown col(5) = row + gxm 464d8606c27SBarry Smith PetscCall(MatSetValuesLocal(jac,i1,row,i5,col,v, INSERT_VALUES,ierr)) 465c4762a1bSJed Brown endif 466c4762a1bSJed Brown 10 continue 467c4762a1bSJed Brown 20 continue 468d8606c27SBarry Smith PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)) 469d8606c27SBarry Smith PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)) 470c4762a1bSJed Brown if (A .ne. jac) then 471d8606c27SBarry Smith PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)) 472d8606c27SBarry Smith PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)) 473c4762a1bSJed Brown endif 474c4762a1bSJed Brown return 475c4762a1bSJed Brown end 476c4762a1bSJed Brown 477c4762a1bSJed Brown! 478c4762a1bSJed Brown! Simple convergence test based on the infinity norm of the residual being small 479c4762a1bSJed Brown! 480c4762a1bSJed Brown subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr) 481*dfbbaf82SBarry Smith use ex5fmodule 482c4762a1bSJed Brown implicit none 483c4762a1bSJed Brown 484c4762a1bSJed Brown SNES snes 485c4762a1bSJed Brown PetscInt it,dummy 486c4762a1bSJed Brown PetscReal xnorm,snorm,fnorm,nrm 487c4762a1bSJed Brown SNESConvergedReason reason 488c4762a1bSJed Brown Vec f 489c4762a1bSJed Brown PetscErrorCode ierr 490c4762a1bSJed Brown 491d8606c27SBarry Smith PetscCall(SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)) 492d8606c27SBarry Smith PetscCall(VecNorm(f,NORM_INFINITY,nrm,ierr)) 493c4762a1bSJed Brown if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS 494c4762a1bSJed Brown 495c4762a1bSJed Brown end 496c4762a1bSJed Brown 497c4762a1bSJed Brown!/*TEST 498c4762a1bSJed Brown! 499c4762a1bSJed Brown! build: 500c4762a1bSJed Brown! requires: !complex !single 501c4762a1bSJed Brown! 502c4762a1bSJed Brown! test: 503c4762a1bSJed Brown! nsize: 4 5048f8b3c79SStefano Zampini! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short \ 5058f8b3c79SStefano Zampini! -ksp_gmres_cgs_refinement_type refine_always 506c4762a1bSJed Brown! 507c4762a1bSJed Brown! test: 508c4762a1bSJed Brown! suffix: 2 509c4762a1bSJed Brown! nsize: 4 510c4762a1bSJed Brown! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 511c4762a1bSJed Brown! 512c4762a1bSJed Brown! test: 513c4762a1bSJed Brown! suffix: 3 514c4762a1bSJed Brown! nsize: 3 515c4762a1bSJed Brown! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 516c4762a1bSJed Brown! 517c4762a1bSJed Brown! test: 518c4762a1bSJed Brown! suffix: 6 519c4762a1bSJed Brown! nsize: 1 520c4762a1bSJed Brown! args: -snes_monitor_short -my_snes_convergence 521c4762a1bSJed Brown! 522c4762a1bSJed Brown!TEST*/ 523