Date: 2025-03-29T05:58:41+00:00

Actual source code: ex42.c

      1: static char help[] = "Newton's method to solve a two-variable system that comes from the Rosenbrock function.\n\n";

      3: /*
      4:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
      5:    file automatically includes:
      6:      petscsys.h       - base PETSc routines   petscvec.h - vectors
      7:      petscmat.h - matrices
      8:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
      9:      petscviewer.h - viewers               petscpc.h  - preconditioners
     10:      petscksp.h   - linear solvers
     11: */
     12: #include <petscsnes.h>

     14: extern PetscErrorCode FormJacobian1(SNES, Vec, Mat, Mat, void *);
     15: extern PetscErrorCode FormFunction1(SNES, Vec, Vec, void *);

     17: int main(int argc, char **argv)
     18: {
     19:   SNES                snes; /* nonlinear solver context */
     20:   Vec                 x;    /* solution vector */
     21:   Mat                 J;    /* Jacobian matrix */
     22:   PetscInt            its;
     23:   PetscScalar        *xx;
     24:   SNESConvergedReason reason;
     25:   PetscBool           test_ghost = PETSC_FALSE;

     27:   PetscFunctionBeginUser;
     28:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     29:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_ghost", &test_ghost, NULL));

     31:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     32:      Create nonlinear solver context
     33:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     34:   PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));

     36:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     37:      Create matrix and vector data structures; set corresponding routines
     38:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     39:   /*
     40:      Create vectors for solution and nonlinear function
     41:   */
     42:   if (test_ghost) {
     43:     PetscInt gIdx[] = {0, 1};
     44:     PetscInt nghost = 2;

     46:     PetscCall(PetscOptionsGetInt(NULL, NULL, "-nghost", &nghost, NULL));
     47:     PetscCall(VecCreateGhost(PETSC_COMM_WORLD, 2, PETSC_DECIDE, PetscMin(nghost, 2), gIdx, &x));
     48:   } else {
     49:     PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
     50:     PetscCall(VecSetSizes(x, 2, PETSC_DECIDE));
     51:     PetscCall(VecSetFromOptions(x));
     52:   }

     54:   /*
     55:      Create Jacobian matrix data structure
     56:   */
     57:   PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
     58:   PetscCall(MatSetSizes(J, 2, 2, PETSC_DECIDE, PETSC_DECIDE));
     59:   PetscCall(MatSetFromOptions(J));
     60:   PetscCall(MatSetUp(J));

     62:   /*
     63:      Set function evaluation routine and vector.
     64:   */
     65:   PetscCall(SNESSetFunction(snes, NULL, FormFunction1, &test_ghost));

     67:   /*
     68:      Set Jacobian matrix data structure and Jacobian evaluation routine
     69:   */
     70:   PetscCall(SNESSetJacobian(snes, J, J, FormJacobian1, &test_ghost));

     72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     73:      Customize nonlinear solver; set runtime options
     74:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     75:   PetscCall(SNESSetFromOptions(snes));

     77:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     78:      Evaluate initial guess; then solve nonlinear system
     79:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     80:   PetscCall(VecGetArray(x, &xx));
     81:   xx[0] = -1.2;
     82:   xx[1] = 1.0;
     83:   PetscCall(VecRestoreArray(x, &xx));

     85:   /*
     86:      Note: The user should initialize the vector, x, with the initial guess
     87:      for the nonlinear solver prior to calling SNESSolve().  In particular,
     88:      to employ an initial guess of zero, the user should explicitly set
     89:      this vector to zero by calling VecSet().
     90:   */

     92:   PetscCall(SNESSolve(snes, NULL, x));
     93:   PetscCall(VecViewFromOptions(x, NULL, "-sol_view"));
     94:   PetscCall(SNESGetIterationNumber(snes, &its));
     95:   PetscCall(SNESGetConvergedReason(snes, &reason));
     96:   /*
     97:      Some systems computes a residual that is identically zero, thus converging
     98:      due to FNORM_ABS, others converge due to FNORM_RELATIVE.  Here, we only
     99:      report the reason if the iteration did not converge so that the tests are
    100:      reproducible.
    101:   */
    102:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%s number of SNES iterations = %" PetscInt_FMT "\n", reason > 0 ? "CONVERGED" : SNESConvergedReasons[reason], its));

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:      Free work space.  All PETSc objects should be destroyed when they
    106:      are no longer needed.
    107:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    109:   PetscCall(VecDestroy(&x));
    110:   PetscCall(MatDestroy(&J));
    111:   PetscCall(SNESDestroy(&snes));
    112:   PetscCall(PetscFinalize());
    113:   return 0;
    114: }

    116: PetscErrorCode VecCheckGhosted(Vec X, PetscBool test_rev)
    117: {
    118:   PetscFunctionBeginUser;
    119:   PetscCall(VecGhostUpdateBegin(X, INSERT_VALUES, SCATTER_FORWARD));
    120:   PetscCall(VecGhostUpdateEnd(X, INSERT_VALUES, SCATTER_FORWARD));
    121:   if (test_rev) {
    122:     PetscCall(VecGhostUpdateBegin(X, INSERT_VALUES, SCATTER_REVERSE));
    123:     PetscCall(VecGhostUpdateEnd(X, INSERT_VALUES, SCATTER_REVERSE));
    124:   }
    125:   PetscFunctionReturn(PETSC_SUCCESS);
    126: }

    128: PetscErrorCode FormFunction1(SNES snes, Vec x, Vec f, void *ctx)
    129: {
    130:   PetscScalar       *ff;
    131:   const PetscScalar *xx;

    133:   PetscFunctionBeginUser;
    134:   if (*(PetscBool *)ctx) {
    135:     PetscCall(VecCheckGhosted(x, PETSC_FALSE));
    136:     PetscCall(VecCheckGhosted(f, PETSC_TRUE));
    137:   }

    139:   /*
    140:     Get pointers to vector data.
    141:     - For default PETSc vectors, VecGetArray() returns a pointer to
    142:     the data array.  Otherwise, the routine is implementation dependent.
    143:     - You MUST call VecRestoreArray() when you no longer need access to
    144:     the array.
    145:   */
    146:   PetscCall(VecGetArrayRead(x, &xx));
    147:   PetscCall(VecGetArray(f, &ff));

    149:   /* Compute function */
    150:   ff[0] = -2.0 + 2.0 * xx[0] + 400.0 * xx[0] * xx[0] * xx[0] - 400.0 * xx[0] * xx[1];
    151:   ff[1] = -200.0 * xx[0] * xx[0] + 200.0 * xx[1];

    153:   /* Restore vectors */
    154:   PetscCall(VecRestoreArrayRead(x, &xx));
    155:   PetscCall(VecRestoreArray(f, &ff));
    156:   PetscFunctionReturn(PETSC_SUCCESS);
    157: }

    159: PetscErrorCode FormJacobian1(SNES snes, Vec x, Mat jac, Mat B, void *ctx)
    160: {
    161:   const PetscScalar *xx;
    162:   PetscScalar        A[4];
    163:   PetscInt           idx[2];
    164:   PetscMPIInt        rank;

    166:   PetscFunctionBeginUser;
    167:   if (*(PetscBool *)ctx) { PetscCall(VecCheckGhosted(x, PETSC_FALSE)); }
    168:   /*
    169:      Get pointer to vector data
    170:   */
    171:   PetscCall(VecGetArrayRead(x, &xx));

    173:   /*
    174:      Compute Jacobian entries and insert into matrix.
    175:       - Since this is such a small problem, we set all entries for
    176:         the matrix at once.
    177:   */
    178:   A[0] = 2.0 + 1200.0 * xx[0] * xx[0] - 400.0 * xx[1];
    179:   A[1] = -400.0 * xx[0];
    180:   A[2] = -400.0 * xx[0];
    181:   A[3] = 200;

    183:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)x), &rank));
    184:   idx[0] = 2 * rank;
    185:   idx[1] = 2 * rank + 1;

    187:   PetscCall(MatSetValues(B, 2, idx, 2, idx, A, INSERT_VALUES));

    189:   /*
    190:      Restore vector
    191:   */
    192:   PetscCall(VecRestoreArrayRead(x, &xx));

    194:   /*
    195:      Assemble matrix
    196:   */
    197:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    198:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    199:   if (jac != B) {
    200:     PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
    201:     PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
    202:   }
    203:   PetscFunctionReturn(PETSC_SUCCESS);
    204: }

    206: /*TEST

    208:    test:
    209:       suffix: 1
    210:       args: -snes_monitor_short -snes_max_it 1000 -sol_view
    211:       requires: !single

    213:    test:
    214:       suffix: 2
    215:       args: -snes_monitor_short -snes_max_it 1000 -snes_type newtontrdc -snes_trdc_use_cauchy false -sol_view
    216:       requires: !single

    218:    test:
    219:       suffix: ghosts
    220:       nsize: {{1 2}}
    221:       args: -snes_max_it 4 -snes_type {{newtontr newtonls}} -nghost {{0 1 2}} -test_ghost
    222:       requires: !single

    224: TEST*/