1c4762a1bSJed Brown! 2c4762a1bSJed Brown! Description: This example solves a nonlinear system on 1 processor with SNES. 3c4762a1bSJed Brown! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular 4c4762a1bSJed Brown! domain. The command line options include: 5c4762a1bSJed Brown! -par <parameter>, where <parameter> indicates the nonlinearity of the problem 6c4762a1bSJed Brown! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81) 7c4762a1bSJed Brown! -mx <xg>, where <xg> = number of grid points in the x-direction 8c4762a1bSJed Brown! -my <yg>, where <yg> = number of grid points in the y-direction 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! The parallel version of this code is snes/tutorials/ex5f.F 28c4762a1bSJed Brown! 29c4762a1bSJed Brown! -------------------------------------------------------------------------- 30c4762a1bSJed Brown subroutine postcheck(snes,x,y,w,changed_y,changed_w,ctx,ierr) 31c4762a1bSJed Brown#include <petsc/finclude/petscsnes.h> 32c4762a1bSJed Brown use petscsnes 33c4762a1bSJed Brown implicit none 34c4762a1bSJed Brown SNES snes 35c4762a1bSJed Brown PetscReal norm 36c4762a1bSJed Brown Vec tmp,x,y,w 37c4762a1bSJed Brown PetscBool changed_w,changed_y 38c4762a1bSJed Brown PetscErrorCode ierr 39c4762a1bSJed Brown PetscInt ctx 40c4762a1bSJed Brown PetscScalar mone 4124fb275aSStefano Zampini MPI_Comm comm 42c4762a1bSJed Brown 4324fb275aSStefano Zampini character(len=PETSC_MAX_PATH_LEN) :: outputString 4424fb275aSStefano Zampini 4524fb275aSStefano Zampini PetscCallA(PetscObjectGetComm(snes,comm,ierr)) 46d8606c27SBarry Smith PetscCallA(VecDuplicate(x,tmp,ierr)) 47c4762a1bSJed Brown mone = -1.0 48d8606c27SBarry Smith PetscCallA(VecWAXPY(tmp,mone,x,w,ierr)) 49d8606c27SBarry Smith PetscCallA(VecNorm(tmp,NORM_2,norm,ierr)) 50d8606c27SBarry Smith PetscCallA(VecDestroy(tmp,ierr)) 5124fb275aSStefano Zampini write(outputString,*) norm 5224fb275aSStefano Zampini PetscCallA(PetscPrintf(comm,'Norm of search step '//trim(outputString)//'\n',ierr)) 53c4762a1bSJed Brown end 54c4762a1bSJed Brown 55c4762a1bSJed Brown program main 56c4762a1bSJed Brown#include <petsc/finclude/petscdraw.h> 57c4762a1bSJed Brown use petscsnes 58c4762a1bSJed Brown implicit none 5917a42bb7SSatish Balay interface SNESSetJacobian 6017a42bb7SSatish Balay subroutine SNESSetJacobian1(a,b,c,d,e,z) 6117a42bb7SSatish Balay use petscsnes 6217a42bb7SSatish Balay SNES a 6317a42bb7SSatish Balay Mat b 6417a42bb7SSatish Balay Mat c 6517a42bb7SSatish Balay external d 6617a42bb7SSatish Balay MatFDColoring e 6717a42bb7SSatish Balay PetscErrorCode z 6817a42bb7SSatish Balay end subroutine 6917a42bb7SSatish Balay subroutine SNESSetJacobian2(a,b,c,d,e,z) 7017a42bb7SSatish Balay use petscsnes 7117a42bb7SSatish Balay SNES a 7217a42bb7SSatish Balay Mat b 7317a42bb7SSatish Balay Mat c 7417a42bb7SSatish Balay external d 7517a42bb7SSatish Balay integer e 7617a42bb7SSatish Balay PetscErrorCode z 7717a42bb7SSatish Balay end subroutine 7817a42bb7SSatish Balay end interface 79c4762a1bSJed Brown! 80c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 81c4762a1bSJed Brown! Variable declarations 82c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 83c4762a1bSJed Brown! 84c4762a1bSJed Brown! Variables: 85c4762a1bSJed Brown! snes - nonlinear solver 86c4762a1bSJed Brown! x, r - solution, residual vectors 87c4762a1bSJed Brown! J - Jacobian matrix 88c4762a1bSJed Brown! its - iterations for convergence 89c4762a1bSJed Brown! matrix_free - flag - 1 indicates matrix-free version 90c4762a1bSJed Brown! lambda - nonlinearity parameter 91c4762a1bSJed Brown! draw - drawing context 92c4762a1bSJed Brown! 93c4762a1bSJed Brown SNES snes 94c4762a1bSJed Brown MatColoring mc 95c4762a1bSJed Brown Vec x,r 96c4762a1bSJed Brown PetscDraw draw 97c4762a1bSJed Brown Mat J 98c4762a1bSJed Brown PetscBool matrix_free,flg,fd_coloring 99c4762a1bSJed Brown PetscErrorCode ierr 100c4762a1bSJed Brown PetscInt its,N, mx,my,i5 101c4762a1bSJed Brown PetscMPIInt size,rank 102c4762a1bSJed Brown PetscReal lambda_max,lambda_min,lambda 103c4762a1bSJed Brown MatFDColoring fdcoloring 104c4762a1bSJed Brown ISColoring iscoloring 105c4762a1bSJed Brown PetscBool pc 106c4762a1bSJed Brown external postcheck 107c4762a1bSJed Brown 10824fb275aSStefano Zampini character(len=PETSC_MAX_PATH_LEN) :: outputString 10924fb275aSStefano Zampini 11042ce371bSBarry Smith PetscScalar,pointer :: lx_v(:) 111c4762a1bSJed Brown 112c4762a1bSJed Brown! Store parameters in common block 113c4762a1bSJed Brown 114c4762a1bSJed Brown common /params/ lambda,mx,my,fd_coloring 115c4762a1bSJed Brown 116c4762a1bSJed Brown! Note: Any user-defined Fortran routines (such as FormJacobian) 117c4762a1bSJed Brown! MUST be declared as external. 118c4762a1bSJed Brown 119c4762a1bSJed Brown external FormFunction,FormInitialGuess,FormJacobian 120c4762a1bSJed Brown 121c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 122c4762a1bSJed Brown! Initialize program 123c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 124c4762a1bSJed Brown 125d8606c27SBarry Smith PetscCallA(PetscInitialize(ierr)) 126d8606c27SBarry Smith PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)) 127d8606c27SBarry Smith PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)) 128c4762a1bSJed Brown 129dcb3e689SBarry Smith PetscCheckA(size .eq. 1,PETSC_COMM_SELF,PETSC_ERR_WRONG_MPI_SIZE,'This is a uniprocessor example only') 130c4762a1bSJed Brown 131c4762a1bSJed Brown! Initialize problem parameters 132c4762a1bSJed Brown i5 = 5 133c4762a1bSJed Brown lambda_max = 6.81 134c4762a1bSJed Brown lambda_min = 0.0 135c4762a1bSJed Brown lambda = 6.0 136c4762a1bSJed Brown mx = 4 137c4762a1bSJed Brown my = 4 138d8606c27SBarry Smith PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-mx',mx,flg,ierr)) 139d8606c27SBarry Smith PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my',my,flg,ierr)) 140d8606c27SBarry Smith PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,flg,ierr)) 141dcb3e689SBarry Smith PetscCheckA(lambda .lt. lambda_max .and. lambda .gt. lambda_min,PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda out of range ') 142c4762a1bSJed Brown N = mx*my 143c4762a1bSJed Brown pc = PETSC_FALSE 144d8606c27SBarry Smith PetscCallA(PetscOptionsGetBool(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-pc',pc,PETSC_NULL_BOOL,ierr)) 145c4762a1bSJed Brown 146c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 147c4762a1bSJed Brown! Create nonlinear solver context 148c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 149c4762a1bSJed Brown 150d8606c27SBarry Smith PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr)) 151c4762a1bSJed Brown 152c4762a1bSJed Brown if (pc .eqv. PETSC_TRUE) then 153d8606c27SBarry Smith PetscCallA(SNESSetType(snes,SNESNEWTONTR,ierr)) 154d8606c27SBarry Smith PetscCallA(SNESNewtonTRSetPostCheck(snes, postcheck,snes,ierr)) 155c4762a1bSJed Brown endif 156c4762a1bSJed Brown 157c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 158c4762a1bSJed Brown! Create vector data structures; set function evaluation routine 159c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 160c4762a1bSJed Brown 161d8606c27SBarry Smith PetscCallA(VecCreate(PETSC_COMM_WORLD,x,ierr)) 162d8606c27SBarry Smith PetscCallA(VecSetSizes(x,PETSC_DECIDE,N,ierr)) 163d8606c27SBarry Smith PetscCallA(VecSetFromOptions(x,ierr)) 164d8606c27SBarry Smith PetscCallA(VecDuplicate(x,r,ierr)) 165c4762a1bSJed Brown 166c4762a1bSJed Brown! Set function evaluation routine and vector. Whenever the nonlinear 167c4762a1bSJed Brown! solver needs to evaluate the nonlinear function, it will call this 168c4762a1bSJed Brown! routine. 169c4762a1bSJed Brown! - Note that the final routine argument is the user-defined 170c4762a1bSJed Brown! context that provides application-specific data for the 171c4762a1bSJed Brown! function evaluation routine. 172c4762a1bSJed Brown 173d8606c27SBarry Smith PetscCallA(SNESSetFunction(snes,r,FormFunction,fdcoloring,ierr)) 174c4762a1bSJed Brown 175c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 176c4762a1bSJed Brown! Create matrix data structure; set Jacobian evaluation routine 177c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 178c4762a1bSJed Brown 179c4762a1bSJed Brown! Create matrix. Here we only approximately preallocate storage space 180c4762a1bSJed Brown! for the Jacobian. See the users manual for a discussion of better 181c4762a1bSJed Brown! techniques for preallocating matrix memory. 182c4762a1bSJed Brown 183d8606c27SBarry Smith PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr)) 184c4762a1bSJed Brown if (.not. matrix_free) then 185*5d83a8b1SBarry Smith PetscCallA(MatCreateSeqAIJ(PETSC_COMM_WORLD,N,N,i5,PETSC_NULL_INTEGER_ARRAY,J,ierr)) 186c4762a1bSJed Brown endif 187c4762a1bSJed Brown 188c4762a1bSJed Brown! 189c4762a1bSJed Brown! This option will cause the Jacobian to be computed via finite differences 190c4762a1bSJed Brown! efficiently using a coloring of the columns of the matrix. 191c4762a1bSJed Brown! 192c4762a1bSJed Brown fd_coloring = .false. 193d8606c27SBarry Smith PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_fd_coloring',fd_coloring,ierr)) 194c4762a1bSJed Brown if (fd_coloring) then 195c4762a1bSJed Brown 196c4762a1bSJed Brown! 197c4762a1bSJed Brown! This initializes the nonzero structure of the Jacobian. This is artificial 198c4762a1bSJed Brown! because clearly if we had a routine to compute the Jacobian we won't need 199c4762a1bSJed Brown! to use finite differences. 200c4762a1bSJed Brown! 201d8606c27SBarry Smith PetscCallA(FormJacobian(snes,x,J,J,0,ierr)) 202c4762a1bSJed Brown! 203c4762a1bSJed Brown! Color the matrix, i.e. determine groups of columns that share no common 204a5b23f4aSJose E. Roman! rows. These columns in the Jacobian can all be computed simultaneously. 205c4762a1bSJed Brown! 206d8606c27SBarry Smith PetscCallA(MatColoringCreate(J,mc,ierr)) 207d8606c27SBarry Smith PetscCallA(MatColoringSetType(mc,MATCOLORINGNATURAL,ierr)) 208d8606c27SBarry Smith PetscCallA(MatColoringSetFromOptions(mc,ierr)) 209d8606c27SBarry Smith PetscCallA(MatColoringApply(mc,iscoloring,ierr)) 210d8606c27SBarry Smith PetscCallA(MatColoringDestroy(mc,ierr)) 211c4762a1bSJed Brown! 212c4762a1bSJed Brown! Create the data structure that SNESComputeJacobianDefaultColor() uses 213c4762a1bSJed Brown! to compute the actual Jacobians via finite differences. 214c4762a1bSJed Brown! 215d8606c27SBarry Smith PetscCallA(MatFDColoringCreate(J,iscoloring,fdcoloring,ierr)) 216d8606c27SBarry Smith PetscCallA(MatFDColoringSetFunction(fdcoloring,FormFunction,fdcoloring,ierr)) 217d8606c27SBarry Smith PetscCallA(MatFDColoringSetFromOptions(fdcoloring,ierr)) 218d8606c27SBarry Smith PetscCallA(MatFDColoringSetUp(J,iscoloring,fdcoloring,ierr)) 219c4762a1bSJed Brown! 220c4762a1bSJed Brown! Tell SNES to use the routine SNESComputeJacobianDefaultColor() 221c4762a1bSJed Brown! to compute Jacobians. 222c4762a1bSJed Brown! 223d8606c27SBarry Smith PetscCallA(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,fdcoloring,ierr)) 224d8606c27SBarry Smith PetscCallA(ISColoringDestroy(iscoloring,ierr)) 225c4762a1bSJed Brown 226c4762a1bSJed Brown else if (.not. matrix_free) then 227c4762a1bSJed Brown 228c4762a1bSJed Brown! Set Jacobian matrix data structure and default Jacobian evaluation 229c4762a1bSJed Brown! routine. Whenever the nonlinear solver needs to compute the 230c4762a1bSJed Brown! Jacobian matrix, it will call this routine. 231c4762a1bSJed Brown! - Note that the final routine argument is the user-defined 232c4762a1bSJed Brown! context that provides application-specific data for the 233c4762a1bSJed Brown! Jacobian evaluation routine. 234c4762a1bSJed Brown! - The user can override with: 235c4762a1bSJed Brown! -snes_fd : default finite differencing approximation of Jacobian 236c4762a1bSJed Brown! -snes_mf : matrix-free Newton-Krylov method with no preconditioning 237c4762a1bSJed Brown! (unless user explicitly sets preconditioner) 238c4762a1bSJed Brown! -snes_mf_operator : form preconditioning matrix as set by the user, 239c4762a1bSJed Brown! but use matrix-free approx for Jacobian-vector 240c4762a1bSJed Brown! products within Newton-Krylov method 241c4762a1bSJed Brown! 242d8606c27SBarry Smith PetscCallA(SNESSetJacobian(snes,J,J,FormJacobian,0,ierr)) 243c4762a1bSJed Brown endif 244c4762a1bSJed Brown 245c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 246c4762a1bSJed Brown! Customize nonlinear solver; set runtime options 247c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 248c4762a1bSJed Brown 249c4762a1bSJed Brown! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>) 250c4762a1bSJed Brown 251d8606c27SBarry Smith PetscCallA(SNESSetFromOptions(snes,ierr)) 252c4762a1bSJed Brown 253c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 254c4762a1bSJed Brown! Evaluate initial guess; then solve nonlinear system. 255c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 256c4762a1bSJed Brown 257c4762a1bSJed Brown! Note: The user should initialize the vector, x, with the initial guess 258c4762a1bSJed Brown! for the nonlinear solver prior to calling SNESSolve(). In particular, 259c4762a1bSJed Brown! to employ an initial guess of zero, the user should explicitly set 260c4762a1bSJed Brown! this vector to zero by calling VecSet(). 261c4762a1bSJed Brown 262d8606c27SBarry Smith PetscCallA(FormInitialGuess(x,ierr)) 263d8606c27SBarry Smith PetscCallA(SNESSolve(snes,PETSC_NULL_VEC,x,ierr)) 264d8606c27SBarry Smith PetscCallA(SNESGetIterationNumber(snes,its,ierr)) 26524fb275aSStefano Zampini write(outputString,*) its 26624fb275aSStefano Zampini PetscCallA(PetscPrintf(PETSC_COMM_WORLD,'Number of SNES iterations = '//trim(outputString)//'\n',ierr)) 267c4762a1bSJed Brown 268c4762a1bSJed Brown! PetscDraw contour plot of solution 269c4762a1bSJed Brown 270d8606c27SBarry Smith PetscCallA(PetscDrawCreate(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,'Solution',300,0,300,300,draw,ierr)) 271d8606c27SBarry Smith PetscCallA(PetscDrawSetFromOptions(draw,ierr)) 272c4762a1bSJed Brown 27342ce371bSBarry Smith PetscCallA(VecGetArrayReadF90(x,lx_v,ierr)) 27442ce371bSBarry Smith PetscCallA(PetscDrawTensorContour(draw,mx,my,PETSC_NULL_REAL,PETSC_NULL_REAL,lx_v,ierr)) 27542ce371bSBarry Smith PetscCallA(VecRestoreArrayReadF90(x,lx_v,ierr)) 276c4762a1bSJed Brown 277c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 278c4762a1bSJed Brown! Free work space. All PETSc objects should be destroyed when they 279c4762a1bSJed Brown! are no longer needed. 280c4762a1bSJed Brown! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 281c4762a1bSJed Brown 282d8606c27SBarry Smith if (.not. matrix_free) PetscCallA(MatDestroy(J,ierr)) 283d8606c27SBarry Smith if (fd_coloring) PetscCallA(MatFDColoringDestroy(fdcoloring,ierr)) 284c4762a1bSJed Brown 285d8606c27SBarry Smith PetscCallA(VecDestroy(x,ierr)) 286d8606c27SBarry Smith PetscCallA(VecDestroy(r,ierr)) 287d8606c27SBarry Smith PetscCallA(SNESDestroy(snes,ierr)) 288d8606c27SBarry Smith PetscCallA(PetscDrawDestroy(draw,ierr)) 289d8606c27SBarry Smith PetscCallA(PetscFinalize(ierr)) 290c4762a1bSJed Brown end 291c4762a1bSJed Brown 292c4762a1bSJed Brown! --------------------------------------------------------------------- 293c4762a1bSJed Brown! 294c4762a1bSJed Brown! FormInitialGuess - Forms initial approximation. 295c4762a1bSJed Brown! 296c4762a1bSJed Brown! Input Parameter: 297c4762a1bSJed Brown! X - vector 298c4762a1bSJed Brown! 299c4762a1bSJed Brown! Output Parameters: 300c4762a1bSJed Brown! X - vector 301c4762a1bSJed Brown! ierr - error code 302c4762a1bSJed Brown! 303c4762a1bSJed Brown! Notes: 304c4762a1bSJed Brown! This routine serves as a wrapper for the lower-level routine 305c4762a1bSJed Brown! "ApplicationInitialGuess", where the actual computations are 306c4762a1bSJed Brown! done using the standard Fortran style of treating the local 307c4762a1bSJed Brown! vector data as a multidimensional array over the local mesh. 308c4762a1bSJed Brown! This routine merely accesses the local vector data via 30942ce371bSBarry Smith! VecGetArrayF90() and VecRestoreArrayF90(). 310c4762a1bSJed Brown! 311c4762a1bSJed Brown subroutine FormInitialGuess(X,ierr) 312c4762a1bSJed Brown use petscsnes 313c4762a1bSJed Brown implicit none 314c4762a1bSJed Brown 315c4762a1bSJed Brown! Input/output variables: 316c4762a1bSJed Brown Vec X 317c4762a1bSJed Brown PetscErrorCode ierr 318c4762a1bSJed Brown 319c4762a1bSJed Brown! Declarations for use with local arrays: 32042ce371bSBarry Smith PetscScalar,pointer :: lx_v(:) 321c4762a1bSJed Brown 322c4762a1bSJed Brown ierr = 0 323c4762a1bSJed Brown 324c4762a1bSJed Brown! Get a pointer to vector data. 32542ce371bSBarry Smith! - VecGetArrayF90() returns a pointer to the data array. 32642ce371bSBarry Smith! - You MUST call VecRestoreArrayF90() when you no longer need access to 327c4762a1bSJed Brown! the array. 328c4762a1bSJed Brown 32942ce371bSBarry Smith PetscCallA(VecGetArrayF90(X,lx_v,ierr)) 330c4762a1bSJed Brown 331c4762a1bSJed Brown! Compute initial guess 332c4762a1bSJed Brown 33342ce371bSBarry Smith PetscCallA(ApplicationInitialGuess(lx_v,ierr)) 334c4762a1bSJed Brown 335c4762a1bSJed Brown! Restore vector 336c4762a1bSJed Brown 33742ce371bSBarry Smith PetscCallA(VecRestoreArrayF90(X,lx_v,ierr)) 338c4762a1bSJed Brown 339c4762a1bSJed Brown end 340c4762a1bSJed Brown 341c4762a1bSJed Brown! ApplicationInitialGuess - Computes initial approximation, called by 342c4762a1bSJed Brown! the higher level routine FormInitialGuess(). 343c4762a1bSJed Brown! 344c4762a1bSJed Brown! Input Parameter: 345c4762a1bSJed Brown! x - local vector data 346c4762a1bSJed Brown! 347c4762a1bSJed Brown! Output Parameters: 348c4762a1bSJed Brown! f - local vector data, f(x) 349c4762a1bSJed Brown! ierr - error code 350c4762a1bSJed Brown! 351c4762a1bSJed Brown! Notes: 352c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 353c4762a1bSJed Brown! 354c4762a1bSJed Brown subroutine ApplicationInitialGuess(x,ierr) 355c4762a1bSJed Brown use petscksp 356c4762a1bSJed Brown implicit none 357c4762a1bSJed Brown 358c4762a1bSJed Brown! Common blocks: 359c4762a1bSJed Brown PetscReal lambda 360c4762a1bSJed Brown PetscInt mx,my 361c4762a1bSJed Brown PetscBool fd_coloring 362c4762a1bSJed Brown common /params/ lambda,mx,my,fd_coloring 363c4762a1bSJed Brown 364c4762a1bSJed Brown! Input/output variables: 365c4762a1bSJed Brown PetscScalar x(mx,my) 366c4762a1bSJed Brown PetscErrorCode ierr 367c4762a1bSJed Brown 368c4762a1bSJed Brown! Local variables: 369c4762a1bSJed Brown PetscInt i,j 370c4762a1bSJed Brown PetscReal temp1,temp,hx,hy,one 371c4762a1bSJed Brown 372c4762a1bSJed Brown! Set parameters 373c4762a1bSJed Brown 374c4762a1bSJed Brown ierr = 0 375c4762a1bSJed Brown one = 1.0 376c4762a1bSJed Brown hx = one/(mx-1) 377c4762a1bSJed Brown hy = one/(my-1) 378c4762a1bSJed Brown temp1 = lambda/(lambda + one) 379c4762a1bSJed Brown 380c4762a1bSJed Brown do 20 j=1,my 381c4762a1bSJed Brown temp = min(j-1,my-j)*hy 382c4762a1bSJed Brown do 10 i=1,mx 383c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 384c4762a1bSJed Brown x(i,j) = 0.0 385c4762a1bSJed Brown else 386c4762a1bSJed Brown x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,temp)) 387c4762a1bSJed Brown endif 388c4762a1bSJed Brown 10 continue 389c4762a1bSJed Brown 20 continue 390c4762a1bSJed Brown 391c4762a1bSJed Brown end 392c4762a1bSJed Brown 393c4762a1bSJed Brown! --------------------------------------------------------------------- 394c4762a1bSJed Brown! 395c4762a1bSJed Brown! FormFunction - Evaluates nonlinear function, F(x). 396c4762a1bSJed Brown! 397c4762a1bSJed Brown! Input Parameters: 398c4762a1bSJed Brown! snes - the SNES context 399c4762a1bSJed Brown! X - input vector 400c4762a1bSJed Brown! dummy - optional user-defined context, as set by SNESSetFunction() 401c4762a1bSJed Brown! (not used here) 402c4762a1bSJed Brown! 403c4762a1bSJed Brown! Output Parameter: 404c4762a1bSJed Brown! F - vector with newly computed function 405c4762a1bSJed Brown! 406c4762a1bSJed Brown! Notes: 407c4762a1bSJed Brown! This routine serves as a wrapper for the lower-level routine 408c4762a1bSJed Brown! "ApplicationFunction", where the actual computations are 409c4762a1bSJed Brown! done using the standard Fortran style of treating the local 410c4762a1bSJed Brown! vector data as a multidimensional array over the local mesh. 411c4762a1bSJed Brown! This routine merely accesses the local vector data via 41242ce371bSBarry Smith! VecGetArrayF90() and VecRestoreArrayF90(). 413c4762a1bSJed Brown! 414c4762a1bSJed Brown subroutine FormFunction(snes,X,F,fdcoloring,ierr) 415c4762a1bSJed Brown use petscsnes 416c4762a1bSJed Brown implicit none 417c4762a1bSJed Brown 418c4762a1bSJed Brown! Input/output variables: 419c4762a1bSJed Brown SNES snes 420c4762a1bSJed Brown Vec X,F 421c4762a1bSJed Brown PetscErrorCode ierr 422c4762a1bSJed Brown MatFDColoring fdcoloring 423c4762a1bSJed Brown 424c4762a1bSJed Brown! Common blocks: 425c4762a1bSJed Brown PetscReal lambda 426c4762a1bSJed Brown PetscInt mx,my 427c4762a1bSJed Brown PetscBool fd_coloring 428c4762a1bSJed Brown common /params/ lambda,mx,my,fd_coloring 429c4762a1bSJed Brown 430c4762a1bSJed Brown! Declarations for use with local arrays: 43142ce371bSBarry Smith PetscScalar,pointer :: lx_v(:), lf_v(:) 432c4762a1bSJed Brown PetscInt, pointer :: indices(:) 433c4762a1bSJed Brown 434c4762a1bSJed Brown! Get pointers to vector data. 43542ce371bSBarry Smith! - VecGetArrayF90() returns a pointer to the data array. 43642ce371bSBarry Smith! - You MUST call VecRestoreArrayF90() when you no longer need access to 437c4762a1bSJed Brown! the array. 438c4762a1bSJed Brown 43942ce371bSBarry Smith PetscCallA(VecGetArrayReadF90(X,lx_v,ierr)) 44042ce371bSBarry Smith PetscCallA(VecGetArrayF90(F,lf_v,ierr)) 441c4762a1bSJed Brown 442c4762a1bSJed Brown! Compute function 443c4762a1bSJed Brown 44442ce371bSBarry Smith PetscCallA(ApplicationFunction(lx_v,lf_v,ierr)) 445c4762a1bSJed Brown 446c4762a1bSJed Brown! Restore vectors 447c4762a1bSJed Brown 44842ce371bSBarry Smith PetscCallA(VecRestoreArrayReadF90(X,lx_v,ierr)) 44942ce371bSBarry Smith PetscCallA(VecRestoreArrayF90(F,lf_v,ierr)) 450c4762a1bSJed Brown 451d8606c27SBarry Smith PetscCallA(PetscLogFlops(11.0d0*mx*my,ierr)) 452c4762a1bSJed Brown! 453c4762a1bSJed Brown! fdcoloring is in the common block and used here ONLY to test the 454c4762a1bSJed Brown! calls to MatFDColoringGetPerturbedColumnsF90() and MatFDColoringRestorePerturbedColumnsF90() 455c4762a1bSJed Brown! 456c4762a1bSJed Brown if (fd_coloring) then 457d8606c27SBarry Smith PetscCallA(MatFDColoringGetPerturbedColumnsF90(fdcoloring,indices,ierr)) 458c4762a1bSJed Brown print*,'Indices from GetPerturbedColumnsF90' 459c4762a1bSJed Brown write(*,1000) indices 460c4762a1bSJed Brown 1000 format(50i4) 461d8606c27SBarry Smith PetscCallA(MatFDColoringRestorePerturbedColumnsF90(fdcoloring,indices,ierr)) 462c4762a1bSJed Brown endif 463c4762a1bSJed Brown end 464c4762a1bSJed Brown 465c4762a1bSJed Brown! --------------------------------------------------------------------- 466c4762a1bSJed Brown! 467c4762a1bSJed Brown! ApplicationFunction - Computes nonlinear function, called by 468c4762a1bSJed Brown! the higher level routine FormFunction(). 469c4762a1bSJed Brown! 470c4762a1bSJed Brown! Input Parameter: 471c4762a1bSJed Brown! x - local vector data 472c4762a1bSJed Brown! 473c4762a1bSJed Brown! Output Parameters: 474c4762a1bSJed Brown! f - local vector data, f(x) 475c4762a1bSJed Brown! ierr - error code 476c4762a1bSJed Brown! 477c4762a1bSJed Brown! Notes: 478c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 479c4762a1bSJed Brown! 480c4762a1bSJed Brown subroutine ApplicationFunction(x,f,ierr) 481c4762a1bSJed Brown use petscsnes 482c4762a1bSJed Brown implicit none 483c4762a1bSJed Brown 484c4762a1bSJed Brown! Common blocks: 485c4762a1bSJed Brown PetscReal lambda 486c4762a1bSJed Brown PetscInt mx,my 487c4762a1bSJed Brown PetscBool fd_coloring 488c4762a1bSJed Brown common /params/ lambda,mx,my,fd_coloring 489c4762a1bSJed Brown 490c4762a1bSJed Brown! Input/output variables: 491c4762a1bSJed Brown PetscScalar x(mx,my),f(mx,my) 492c4762a1bSJed Brown PetscErrorCode ierr 493c4762a1bSJed Brown 494c4762a1bSJed Brown! Local variables: 495c4762a1bSJed Brown PetscScalar two,one,hx,hy 496c4762a1bSJed Brown PetscScalar hxdhy,hydhx,sc 497c4762a1bSJed Brown PetscScalar u,uxx,uyy 498c4762a1bSJed Brown PetscInt i,j 499c4762a1bSJed Brown 500c4762a1bSJed Brown ierr = 0 501c4762a1bSJed Brown one = 1.0 502c4762a1bSJed Brown two = 2.0 503c4762a1bSJed Brown hx = one/(mx-1) 504c4762a1bSJed Brown hy = one/(my-1) 505c4762a1bSJed Brown sc = hx*hy*lambda 506c4762a1bSJed Brown hxdhy = hx/hy 507c4762a1bSJed Brown hydhx = hy/hx 508c4762a1bSJed Brown 509c4762a1bSJed Brown! Compute function 510c4762a1bSJed Brown 511c4762a1bSJed Brown do 20 j=1,my 512c4762a1bSJed Brown do 10 i=1,mx 513c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 514c4762a1bSJed Brown f(i,j) = x(i,j) 515c4762a1bSJed Brown else 516c4762a1bSJed Brown u = x(i,j) 517c4762a1bSJed Brown uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j)) 518c4762a1bSJed Brown uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1)) 519c4762a1bSJed Brown f(i,j) = uxx + uyy - sc*exp(u) 520c4762a1bSJed Brown endif 521c4762a1bSJed Brown 10 continue 522c4762a1bSJed Brown 20 continue 523c4762a1bSJed Brown 524c4762a1bSJed Brown end 525c4762a1bSJed Brown 526c4762a1bSJed Brown! --------------------------------------------------------------------- 527c4762a1bSJed Brown! 528c4762a1bSJed Brown! FormJacobian - Evaluates Jacobian matrix. 529c4762a1bSJed Brown! 530c4762a1bSJed Brown! Input Parameters: 531c4762a1bSJed Brown! snes - the SNES context 532c4762a1bSJed Brown! x - input vector 533c4762a1bSJed Brown! dummy - optional user-defined context, as set by SNESSetJacobian() 534c4762a1bSJed Brown! (not used here) 535c4762a1bSJed Brown! 536c4762a1bSJed Brown! Output Parameters: 537c4762a1bSJed Brown! jac - Jacobian matrix 538c4762a1bSJed Brown! jac_prec - optionally different preconditioning matrix (not used here) 539c4762a1bSJed Brown! flag - flag indicating matrix structure 540c4762a1bSJed Brown! 541c4762a1bSJed Brown! Notes: 542c4762a1bSJed Brown! This routine serves as a wrapper for the lower-level routine 543c4762a1bSJed Brown! "ApplicationJacobian", where the actual computations are 544c4762a1bSJed Brown! done using the standard Fortran style of treating the local 545c4762a1bSJed Brown! vector data as a multidimensional array over the local mesh. 546c4762a1bSJed Brown! This routine merely accesses the local vector data via 54742ce371bSBarry Smith! VecGetArrayF90() and VecRestoreArrayF90(). 548c4762a1bSJed Brown! 549c4762a1bSJed Brown subroutine FormJacobian(snes,X,jac,jac_prec,dummy,ierr) 550c4762a1bSJed Brown use petscsnes 551c4762a1bSJed Brown implicit none 552c4762a1bSJed Brown 553c4762a1bSJed Brown! Input/output variables: 554c4762a1bSJed Brown SNES snes 555c4762a1bSJed Brown Vec X 556c4762a1bSJed Brown Mat jac,jac_prec 557c4762a1bSJed Brown PetscErrorCode ierr 558c4762a1bSJed Brown integer dummy 559c4762a1bSJed Brown 560c4762a1bSJed Brown! Common blocks: 561c4762a1bSJed Brown PetscReal lambda 562c4762a1bSJed Brown PetscInt mx,my 563c4762a1bSJed Brown PetscBool fd_coloring 564c4762a1bSJed Brown common /params/ lambda,mx,my,fd_coloring 565c4762a1bSJed Brown 566c4762a1bSJed Brown! Declarations for use with local array: 56742ce371bSBarry Smith PetscScalar,pointer :: lx_v(:) 568c4762a1bSJed Brown 569c4762a1bSJed Brown! Get a pointer to vector data 570c4762a1bSJed Brown 57142ce371bSBarry Smith PetscCallA(VecGetArrayReadF90(X,lx_v,ierr)) 572c4762a1bSJed Brown 573c4762a1bSJed Brown! Compute Jacobian entries 574c4762a1bSJed Brown 57542ce371bSBarry Smith PetscCallA(ApplicationJacobian(lx_v,jac,jac_prec,ierr)) 576c4762a1bSJed Brown 577c4762a1bSJed Brown! Restore vector 578c4762a1bSJed Brown 57942ce371bSBarry Smith PetscCallA(VecRestoreArrayReadF90(X,lx_v,ierr)) 580c4762a1bSJed Brown 581c4762a1bSJed Brown! Assemble matrix 582c4762a1bSJed Brown 583d8606c27SBarry Smith PetscCallA(MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)) 584d8606c27SBarry Smith PetscCallA(MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)) 585c4762a1bSJed Brown 586c4762a1bSJed Brown end 587c4762a1bSJed Brown 588c4762a1bSJed Brown! --------------------------------------------------------------------- 589c4762a1bSJed Brown! 590c4762a1bSJed Brown! ApplicationJacobian - Computes Jacobian matrix, called by 591c4762a1bSJed Brown! the higher level routine FormJacobian(). 592c4762a1bSJed Brown! 593c4762a1bSJed Brown! Input Parameters: 594c4762a1bSJed Brown! x - local vector data 595c4762a1bSJed Brown! 596c4762a1bSJed Brown! Output Parameters: 597c4762a1bSJed Brown! jac - Jacobian matrix 598c4762a1bSJed Brown! jac_prec - optionally different preconditioning matrix (not used here) 599c4762a1bSJed Brown! ierr - error code 600c4762a1bSJed Brown! 601c4762a1bSJed Brown! Notes: 602c4762a1bSJed Brown! This routine uses standard Fortran-style computations over a 2-dim array. 603c4762a1bSJed Brown! 604c4762a1bSJed Brown subroutine ApplicationJacobian(x,jac,jac_prec,ierr) 605c4762a1bSJed Brown use petscsnes 606c4762a1bSJed Brown implicit none 607c4762a1bSJed Brown 608c4762a1bSJed Brown! Common blocks: 609c4762a1bSJed Brown PetscReal lambda 610c4762a1bSJed Brown PetscInt mx,my 611c4762a1bSJed Brown PetscBool fd_coloring 612c4762a1bSJed Brown common /params/ lambda,mx,my,fd_coloring 613c4762a1bSJed Brown 614c4762a1bSJed Brown! Input/output variables: 615c4762a1bSJed Brown PetscScalar x(mx,my) 616c4762a1bSJed Brown Mat jac,jac_prec 617c4762a1bSJed Brown PetscErrorCode ierr 618c4762a1bSJed Brown 619c4762a1bSJed Brown! Local variables: 620c4762a1bSJed Brown PetscInt i,j,row(1),col(5),i1,i5 621c4762a1bSJed Brown PetscScalar two,one, hx,hy 622c4762a1bSJed Brown PetscScalar hxdhy,hydhx,sc,v(5) 623c4762a1bSJed Brown 624c4762a1bSJed Brown! Set parameters 625c4762a1bSJed Brown 626c4762a1bSJed Brown i1 = 1 627c4762a1bSJed Brown i5 = 5 628c4762a1bSJed Brown one = 1.0 629c4762a1bSJed Brown two = 2.0 630c4762a1bSJed Brown hx = one/(mx-1) 631c4762a1bSJed Brown hy = one/(my-1) 632c4762a1bSJed Brown sc = hx*hy 633c4762a1bSJed Brown hxdhy = hx/hy 634c4762a1bSJed Brown hydhx = hy/hx 635c4762a1bSJed Brown 636c4762a1bSJed Brown! Compute entries of the Jacobian matrix 637c4762a1bSJed Brown! - Here, we set all entries for a particular row at once. 638c4762a1bSJed Brown! - Note that MatSetValues() uses 0-based row and column numbers 639c4762a1bSJed Brown! in Fortran as well as in C. 640c4762a1bSJed Brown 641c4762a1bSJed Brown do 20 j=1,my 642c4762a1bSJed Brown row(1) = (j-1)*mx - 1 643c4762a1bSJed Brown do 10 i=1,mx 644c4762a1bSJed Brown row(1) = row(1) + 1 645c4762a1bSJed Brown! boundary points 646c4762a1bSJed Brown if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then 647*5d83a8b1SBarry Smith PetscCallA(MatSetValues(jac_prec,i1,row,i1,row,[one],INSERT_VALUES,ierr)) 648c4762a1bSJed Brown! interior grid points 649c4762a1bSJed Brown else 650c4762a1bSJed Brown v(1) = -hxdhy 651c4762a1bSJed Brown v(2) = -hydhx 652c4762a1bSJed Brown v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j)) 653c4762a1bSJed Brown v(4) = -hydhx 654c4762a1bSJed Brown v(5) = -hxdhy 655c4762a1bSJed Brown col(1) = row(1) - mx 656c4762a1bSJed Brown col(2) = row(1) - 1 657c4762a1bSJed Brown col(3) = row(1) 658c4762a1bSJed Brown col(4) = row(1) + 1 659c4762a1bSJed Brown col(5) = row(1) + mx 660d8606c27SBarry Smith PetscCallA(MatSetValues(jac_prec,i1,row,i5,col,v,INSERT_VALUES,ierr)) 661c4762a1bSJed Brown endif 662c4762a1bSJed Brown 10 continue 663c4762a1bSJed Brown 20 continue 664c4762a1bSJed Brown 665c4762a1bSJed Brown end 666c4762a1bSJed Brown 667c4762a1bSJed Brown! 668c4762a1bSJed Brown!/*TEST 669c4762a1bSJed Brown! 670c4762a1bSJed Brown! build: 671c4762a1bSJed Brown! requires: !single 672c4762a1bSJed Brown! 673c4762a1bSJed Brown! test: 674c4762a1bSJed Brown! args: -snes_monitor_short -nox -snes_type newtontr -ksp_gmres_cgs_refinement_type refine_always 675c4762a1bSJed Brown! 676c4762a1bSJed Brown! test: 677c4762a1bSJed Brown! suffix: 2 678c4762a1bSJed Brown! args: -snes_monitor_short -nox -snes_fd -ksp_gmres_cgs_refinement_type refine_always 679c4762a1bSJed Brown! 680c4762a1bSJed Brown! test: 681c4762a1bSJed Brown! suffix: 3 682c4762a1bSJed Brown! args: -snes_monitor_short -nox -snes_fd_coloring -mat_coloring_type sl -ksp_gmres_cgs_refinement_type refine_always 683c4762a1bSJed Brown! filter: sort -b 684c4762a1bSJed Brown! filter_output: sort -b 685c4762a1bSJed Brown! 686c4762a1bSJed Brown! test: 687c4762a1bSJed Brown! suffix: 4 688c4762a1bSJed Brown! args: -pc -par 6.807 -nox 689c4762a1bSJed Brown! 690c4762a1bSJed Brown!TEST*/ 691