xref: /petsc/src/ts/tutorials/power_grid/ex6.c (revision 4e8208cbcbc709572b8abe32f33c78b69c819375)

static char help[] = "Time-dependent PDE in 2d for calculating joint PDF. \n";
/*
   p_t = -x_t*p_x -y_t*p_y + f(t)*p_yy
   xmin < x < xmax, ymin < y < ymax;
   x_t = (y - ws)  y_t = (ws/2H)*(Pm - Pmax*sin(x))

   Boundary conditions: -bc_type 0 => Zero dirichlet boundary
                        -bc_type 1 => Steady state boundary condition
   Steady state boundary condition found by setting p_t = 0
*/

#include <petscdm.h>
#include <petscdmda.h>
#include <petscts.h>

/*
   User-defined data structures and routines
*/
typedef struct {
  PetscScalar ws;         /* Synchronous speed */
  PetscScalar H;          /* Inertia constant */
  PetscScalar D;          /* Damping constant */
  PetscScalar Pmax;       /* Maximum power output of generator */
  PetscScalar PM_min;     /* Mean mechanical power input */
  PetscScalar lambda;     /* correlation time */
  PetscScalar q;          /* noise strength */
  PetscScalar mux;        /* Initial average angle */
  PetscScalar sigmax;     /* Standard deviation of initial angle */
  PetscScalar muy;        /* Average speed */
  PetscScalar sigmay;     /* standard deviation of initial speed */
  PetscScalar rho;        /* Cross-correlation coefficient */
  PetscScalar t0;         /* Initial time */
  PetscScalar tmax;       /* Final time */
  PetscScalar xmin;       /* left boundary of angle */
  PetscScalar xmax;       /* right boundary of angle */
  PetscScalar ymin;       /* bottom boundary of speed */
  PetscScalar ymax;       /* top boundary of speed */
  PetscScalar dx;         /* x step size */
  PetscScalar dy;         /* y step size */
  PetscInt    bc;         /* Boundary conditions */
  PetscScalar disper_coe; /* Dispersion coefficient */
  DM          da;
} AppCtx;

PetscErrorCode Parameter_settings(AppCtx *);
PetscErrorCode ini_bou(Vec, AppCtx *);
PetscErrorCode IFunction(TS, PetscReal, Vec, Vec, Vec, void *);
PetscErrorCode IJacobian(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *);
PetscErrorCode PostStep(TS);

int main(int argc, char **argv)
{
  Vec         x;    /* Solution vector */
  TS          ts;   /* Time-stepping context */
  AppCtx      user; /* Application context */
  Mat         J;
  PetscViewer viewer;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, "petscopt_ex6", help));
  /* Get physics and time parameters */
  PetscCall(Parameter_settings(&user));
  /* Create a 2D DA with dof = 1 */
  PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &user.da));
  PetscCall(DMSetFromOptions(user.da));
  PetscCall(DMSetUp(user.da));
  /* Set x and y coordinates */
  PetscCall(DMDASetUniformCoordinates(user.da, user.xmin, user.xmax, user.ymin, user.ymax, 0.0, 1.0));

  /* Get global vector x from DM  */
  PetscCall(DMCreateGlobalVector(user.da, &x));

  PetscCall(ini_bou(x, &user));
  PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "ini_x", FILE_MODE_WRITE, &viewer));
  PetscCall(VecView(x, viewer));
  PetscCall(PetscViewerDestroy(&viewer));

  /* Get Jacobian matrix nonzero structure from the da */
  PetscCall(DMSetMatType(user.da, MATAIJ));
  PetscCall(DMCreateMatrix(user.da, &J));

  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
  PetscCall(TSSetIFunction(ts, NULL, IFunction, &user));
  PetscCall(TSSetIJacobian(ts, J, J, IJacobian, &user));
  PetscCall(TSSetApplicationContext(ts, &user));
  PetscCall(TSSetMaxTime(ts, user.tmax));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
  PetscCall(TSSetTime(ts, user.t0));
  PetscCall(TSSetTimeStep(ts, .005));
  PetscCall(TSSetFromOptions(ts));
  PetscCall(TSSetPostStep(ts, PostStep));
  PetscCall(TSSolve(ts, x));

  PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "fin_x", FILE_MODE_WRITE, &viewer));
  PetscCall(VecView(x, viewer));
  PetscCall(PetscViewerDestroy(&viewer));

  PetscCall(VecDestroy(&x));
  PetscCall(MatDestroy(&J));
  PetscCall(DMDestroy(&user.da));
  PetscCall(TSDestroy(&ts));
  PetscCall(PetscFinalize());
  return 0;
}

PetscErrorCode PostStep(TS ts)
{
  Vec         X;
  AppCtx     *user;
  PetscScalar sum;
  PetscReal   t;

  PetscFunctionBegin;
  PetscCall(TSGetApplicationContext(ts, &user));
  PetscCall(TSGetTime(ts, &t));
  PetscCall(TSGetSolution(ts, &X));
  PetscCall(VecSum(X, &sum));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "sum(p)*dw*dtheta at t = %3.2f = %3.6f\n", (double)t, (double)(sum * user->dx * user->dy)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode ini_bou(Vec X, AppCtx *user)
{
  DM            cda;
  DMDACoor2d  **coors;
  PetscScalar **p;
  Vec           gc;
  PetscInt      i, j;
  PetscInt      xs, ys, xm, ym, M, N;
  PetscScalar   xi, yi;
  PetscScalar   sigmax = user->sigmax, sigmay = user->sigmay;
  PetscScalar   rho = user->rho;
  PetscScalar   mux = user->mux, muy = user->muy;
  PetscMPIInt   rank;

  PetscFunctionBeginUser;
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
  PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
  user->dx = (user->xmax - user->xmin) / (M - 1);
  user->dy = (user->ymax - user->ymin) / (N - 1);
  PetscCall(DMGetCoordinateDM(user->da, &cda));
  PetscCall(DMGetCoordinates(user->da, &gc));
  PetscCall(DMDAVecGetArray(cda, gc, &coors));
  PetscCall(DMDAVecGetArray(user->da, X, &p));
  PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0));
  for (i = xs; i < xs + xm; i++) {
    for (j = ys; j < ys + ym; j++) {
      xi = coors[j][i].x;
      yi = coors[j][i].y;
      if (i == 0 || j == 0 || i == M - 1 || j == N - 1) p[j][i] = 0.0;
      else
        p[j][i] = (0.5 / (PETSC_PI * sigmax * sigmay * PetscSqrtScalar(1.0 - rho * rho))) * PetscExpScalar(-0.5 / (1 - rho * rho) * (PetscPowScalar((xi - mux) / sigmax, 2) + PetscPowScalar((yi - muy) / sigmay, 2) - 2 * rho * (xi - mux) * (yi - muy) / (sigmax * sigmay)));
    }
  }
  /*  p[N/2+N%2][M/2+M%2] = 1/(user->dx*user->dy); */

  PetscCall(DMDAVecRestoreArray(cda, gc, &coors));
  PetscCall(DMDAVecRestoreArray(user->da, X, &p));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* First advection term */
PetscErrorCode adv1(PetscScalar **p, PetscScalar y, PetscInt i, PetscInt j, PetscInt M, PetscScalar *p1, AppCtx *user)
{
  PetscScalar f; /* v1,v2,v3,v4,v5,s1,s2,s3; */

  PetscFunctionBegin;
  /*  if (i > 2 && i < M-2) {
    v1 = (y-user->ws)*(p[j][i-2] - p[j][i-3])/user->dx;
    v2 = (y-user->ws)*(p[j][i-1] - p[j][i-2])/user->dx;
    v3 = (y-user->ws)*(p[j][i] - p[j][i-1])/user->dx;
    v4 = (y-user->ws)*(p[j][i+1] - p[j][i])/user->dx;
    v5 = (y-user->ws)*(p[j][i+1] - p[j][i+2])/user->dx;

    s1 = v1/3.0 - (7.0/6.0)*v2 + (11.0/6.0)*v3;
    s2 =-v2/6.0 + (5.0/6.0)*v3 + (1.0/3.0)*v4;
    s3 = v3/3.0 + (5.0/6.0)*v4 - (1.0/6.0)*v5;

    *p1 = 0.1*s1 + 0.6*s2 + 0.3*s3;
    } else *p1 = 0.0; */
  f   = (y - user->ws);
  *p1 = f * (p[j][i + 1] - p[j][i - 1]) / (2 * user->dx);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Second advection term */
PetscErrorCode adv2(PetscScalar **p, PetscScalar x, PetscInt i, PetscInt j, PetscInt N, PetscScalar *p2, AppCtx *user)
{
  PetscScalar f; /* v1,v2,v3,v4,v5,s1,s2,s3; */

  PetscFunctionBegin;
  /*  if (j > 2 && j < N-2) {
    v1 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j-2][i] - p[j-3][i])/user->dy;
    v2 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j-1][i] - p[j-2][i])/user->dy;
    v3 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j][i] - p[j-1][i])/user->dy;
    v4 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j+1][i] - p[j][i])/user->dy;
    v5 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j+2][i] - p[j+1][i])/user->dy;

    s1 = v1/3.0 - (7.0/6.0)*v2 + (11.0/6.0)*v3;
    s2 =-v2/6.0 + (5.0/6.0)*v3 + (1.0/3.0)*v4;
    s3 = v3/3.0 + (5.0/6.0)*v4 - (1.0/6.0)*v5;

    *p2 = 0.1*s1 + 0.6*s2 + 0.3*s3;
    } else *p2 = 0.0; */
  f   = (user->ws / (2 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(x));
  *p2 = f * (p[j + 1][i] - p[j - 1][i]) / (2 * user->dy);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Diffusion term */
PetscErrorCode diffuse(PetscScalar **p, PetscInt i, PetscInt j, PetscReal t, PetscScalar *p_diff, AppCtx *user)
{
  PetscFunctionBeginUser;
  *p_diff = user->disper_coe * ((p[j - 1][i] - 2 * p[j][i] + p[j + 1][i]) / (user->dy * user->dy));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode BoundaryConditions(PetscScalar **p, DMDACoor2d **coors, PetscInt i, PetscInt j, PetscInt M, PetscInt N, PetscScalar **f, AppCtx *user)
{
  PetscScalar fwc, fthetac;
  PetscScalar w = coors[j][i].y, theta = coors[j][i].x;

  PetscFunctionBeginUser;
  if (user->bc == 0) { /* Natural boundary condition */
    f[j][i] = p[j][i];
  } else { /* Steady state boundary condition */
    fthetac = user->ws / (2 * user->H) * (user->PM_min - user->Pmax * PetscSinScalar(theta));
    fwc     = (w * w / 2.0 - user->ws * w);
    if (i == 0 && j == 0) { /* left bottom corner */
      f[j][i] = fwc * (p[j][i + 1] - p[j][i]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j][i]) / user->dy;
    } else if (i == 0 && j == N - 1) { /* right bottom corner */
      f[j][i] = fwc * (p[j][i + 1] - p[j][i]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j][i] - p[j - 1][i]) / user->dy;
    } else if (i == M - 1 && j == 0) { /* left top corner */
      f[j][i] = fwc * (p[j][i] - p[j][i - 1]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j][i]) / user->dy;
    } else if (i == M - 1 && j == N - 1) { /* right top corner */
      f[j][i] = fwc * (p[j][i] - p[j][i - 1]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j][i] - p[j - 1][i]) / user->dy;
    } else if (i == 0) { /* Bottom edge */
      f[j][i] = fwc * (p[j][i + 1] - p[j][i]) / (user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j - 1][i]) / (2 * user->dy);
    } else if (i == M - 1) { /* Top edge */
      f[j][i] = fwc * (p[j][i] - p[j][i - 1]) / (user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j - 1][i]) / (2 * user->dy);
    } else if (j == 0) { /* Left edge */
      f[j][i] = fwc * (p[j][i + 1] - p[j][i - 1]) / (2 * user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j][i]) / (user->dy);
    } else if (j == N - 1) { /* Right edge */
      f[j][i] = fwc * (p[j][i + 1] - p[j][i - 1]) / (2 * user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j][i] - p[j - 1][i]) / (user->dy);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, PetscCtx ctx)
{
  AppCtx       *user = (AppCtx *)ctx;
  DM            cda;
  DMDACoor2d  **coors;
  PetscScalar **p, **f, **pdot;
  PetscInt      i, j;
  PetscInt      xs, ys, xm, ym, M, N;
  Vec           localX, gc, localXdot;
  PetscScalar   p_adv1, p_adv2, p_diff;

  PetscFunctionBeginUser;
  PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
  PetscCall(DMGetCoordinateDM(user->da, &cda));
  PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0));

  PetscCall(DMGetLocalVector(user->da, &localX));
  PetscCall(DMGetLocalVector(user->da, &localXdot));

  PetscCall(DMGlobalToLocalBegin(user->da, X, INSERT_VALUES, localX));
  PetscCall(DMGlobalToLocalEnd(user->da, X, INSERT_VALUES, localX));
  PetscCall(DMGlobalToLocalBegin(user->da, Xdot, INSERT_VALUES, localXdot));
  PetscCall(DMGlobalToLocalEnd(user->da, Xdot, INSERT_VALUES, localXdot));

  PetscCall(DMGetCoordinatesLocal(user->da, &gc));

  PetscCall(DMDAVecGetArrayRead(cda, gc, &coors));
  PetscCall(DMDAVecGetArrayRead(user->da, localX, &p));
  PetscCall(DMDAVecGetArrayRead(user->da, localXdot, &pdot));
  PetscCall(DMDAVecGetArray(user->da, F, &f));

  user->disper_coe = PetscPowScalar((user->lambda * user->ws) / (2 * user->H), 2) * user->q * (1.0 - PetscExpScalar(-t / user->lambda));
  for (i = xs; i < xs + xm; i++) {
    for (j = ys; j < ys + ym; j++) {
      if (i == 0 || j == 0 || i == M - 1 || j == N - 1) {
        PetscCall(BoundaryConditions(p, coors, i, j, M, N, f, user));
      } else {
        PetscCall(adv1(p, coors[j][i].y, i, j, M, &p_adv1, user));
        PetscCall(adv2(p, coors[j][i].x, i, j, N, &p_adv2, user));
        PetscCall(diffuse(p, i, j, t, &p_diff, user));
        f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
      }
    }
  }
  PetscCall(DMDAVecRestoreArrayRead(user->da, localX, &p));
  PetscCall(DMDAVecRestoreArrayRead(user->da, localX, &pdot));
  PetscCall(DMRestoreLocalVector(user->da, &localX));
  PetscCall(DMRestoreLocalVector(user->da, &localXdot));
  PetscCall(DMDAVecRestoreArray(user->da, F, &f));
  PetscCall(DMDAVecRestoreArrayRead(cda, gc, &coors));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat J, Mat Jpre, PetscCtx ctx)
{
  AppCtx      *user = (AppCtx *)ctx;
  DM           cda;
  DMDACoor2d **coors;
  PetscInt     i, j;
  PetscInt     xs, ys, xm, ym, M, N;
  Vec          gc;
  PetscScalar  val[5], xi, yi;
  MatStencil   row, col[5];
  PetscScalar  c1, c3, c5;

  PetscFunctionBeginUser;
  PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
  PetscCall(DMGetCoordinateDM(user->da, &cda));
  PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0));

  PetscCall(DMGetCoordinatesLocal(user->da, &gc));
  PetscCall(DMDAVecGetArrayRead(cda, gc, &coors));
  for (i = xs; i < xs + xm; i++) {
    for (j = ys; j < ys + ym; j++) {
      PetscInt nc = 0;
      xi          = coors[j][i].x;
      yi          = coors[j][i].y;
      row.i       = i;
      row.j       = j;
      if (i == 0 || j == 0 || i == M - 1 || j == N - 1) {
        if (user->bc == 0) {
          col[nc].i = i;
          col[nc].j = j;
          val[nc++] = 1.0;
        } else {
          PetscScalar fthetac, fwc;
          fthetac = user->ws / (2 * user->H) * (user->PM_min - user->Pmax * PetscSinScalar(xi));
          fwc     = (yi * yi / 2.0 - user->ws * yi);
          if (i == 0 && j == 0) {
            col[nc].i = i + 1;
            col[nc].j = j;
            val[nc++] = fwc / user->dx;
            col[nc].i = i;
            col[nc].j = j + 1;
            val[nc++] = -user->disper_coe / user->dy;
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = -fwc / user->dx + fthetac + user->disper_coe / user->dy;
          } else if (i == 0 && j == N - 1) {
            col[nc].i = i + 1;
            col[nc].j = j;
            val[nc++] = fwc / user->dx;
            col[nc].i = i;
            col[nc].j = j - 1;
            val[nc++] = user->disper_coe / user->dy;
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = -fwc / user->dx + fthetac - user->disper_coe / user->dy;
          } else if (i == M - 1 && j == 0) {
            col[nc].i = i - 1;
            col[nc].j = j;
            val[nc++] = -fwc / user->dx;
            col[nc].i = i;
            col[nc].j = j + 1;
            val[nc++] = -user->disper_coe / user->dy;
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = fwc / user->dx + fthetac + user->disper_coe / user->dy;
          } else if (i == M - 1 && j == N - 1) {
            col[nc].i = i - 1;
            col[nc].j = j;
            val[nc++] = -fwc / user->dx;
            col[nc].i = i;
            col[nc].j = j - 1;
            val[nc++] = user->disper_coe / user->dy;
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = fwc / user->dx + fthetac - user->disper_coe / user->dy;
          } else if (i == 0) {
            col[nc].i = i + 1;
            col[nc].j = j;
            val[nc++] = fwc / user->dx;
            col[nc].i = i;
            col[nc].j = j + 1;
            val[nc++] = -user->disper_coe / (2 * user->dy);
            col[nc].i = i;
            col[nc].j = j - 1;
            val[nc++] = user->disper_coe / (2 * user->dy);
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = -fwc / user->dx + fthetac;
          } else if (i == M - 1) {
            col[nc].i = i - 1;
            col[nc].j = j;
            val[nc++] = -fwc / user->dx;
            col[nc].i = i;
            col[nc].j = j + 1;
            val[nc++] = -user->disper_coe / (2 * user->dy);
            col[nc].i = i;
            col[nc].j = j - 1;
            val[nc++] = user->disper_coe / (2 * user->dy);
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = fwc / user->dx + fthetac;
          } else if (j == 0) {
            col[nc].i = i + 1;
            col[nc].j = j;
            val[nc++] = fwc / (2 * user->dx);
            col[nc].i = i - 1;
            col[nc].j = j;
            val[nc++] = -fwc / (2 * user->dx);
            col[nc].i = i;
            col[nc].j = j + 1;
            val[nc++] = -user->disper_coe / user->dy;
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = user->disper_coe / user->dy + fthetac;
          } else if (j == N - 1) {
            col[nc].i = i + 1;
            col[nc].j = j;
            val[nc++] = fwc / (2 * user->dx);
            col[nc].i = i - 1;
            col[nc].j = j;
            val[nc++] = -fwc / (2 * user->dx);
            col[nc].i = i;
            col[nc].j = j - 1;
            val[nc++] = user->disper_coe / user->dy;
            col[nc].i = i;
            col[nc].j = j;
            val[nc++] = -user->disper_coe / user->dy + fthetac;
          }
        }
      } else {
        c1        = (yi - user->ws) / (2 * user->dx);
        c3        = (user->ws / (2.0 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(xi)) / (2 * user->dy);
        c5        = (PetscPowScalar((user->lambda * user->ws) / (2 * user->H), 2) * user->q * (1.0 - PetscExpScalar(-t / user->lambda))) / (user->dy * user->dy);
        col[nc].i = i - 1;
        col[nc].j = j;
        val[nc++] = c1;
        col[nc].i = i + 1;
        col[nc].j = j;
        val[nc++] = -c1;
        col[nc].i = i;
        col[nc].j = j - 1;
        val[nc++] = c3 + c5;
        col[nc].i = i;
        col[nc].j = j + 1;
        val[nc++] = -c3 + c5;
        col[nc].i = i;
        col[nc].j = j;
        val[nc++] = -2 * c5 - a;
      }
      PetscCall(MatSetValuesStencil(Jpre, 1, &row, nc, col, val, INSERT_VALUES));
    }
  }
  PetscCall(DMDAVecRestoreArrayRead(cda, gc, &coors));

  PetscCall(MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY));
  if (J != Jpre) {
    PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode Parameter_settings(AppCtx *user)
{
  PetscBool flg;

  PetscFunctionBeginUser;
  /* Set default parameters */
  user->ws     = 1.0;
  user->H      = 5.0;
  user->Pmax   = 2.1;
  user->PM_min = 1.0;
  user->lambda = 0.1;
  user->q      = 1.0;
  user->mux    = PetscAsinScalar(user->PM_min / user->Pmax);
  user->sigmax = 0.1;
  user->sigmay = 0.1;
  user->rho    = 0.0;
  user->t0     = 0.0;
  user->tmax   = 2.0;
  user->xmin   = -1.0;
  user->xmax   = 10.0;
  user->ymin   = -1.0;
  user->ymax   = 10.0;
  user->bc     = 0;

  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ws", &user->ws, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-Inertia", &user->H, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-Pmax", &user->Pmax, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-PM_min", &user->PM_min, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-lambda", &user->lambda, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-q", &user->q, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-mux", &user->mux, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-sigmax", &user->sigmax, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-muy", &user->muy, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-sigmay", &user->sigmay, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-rho", &user->rho, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-t0", &user->t0, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-tmax", &user->tmax, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-xmin", &user->xmin, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-xmax", &user->xmax, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ymin", &user->ymin, &flg));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ymax", &user->ymax, &flg));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-bc_type", &user->bc, &flg));
  user->muy = user->ws;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

   build:
      requires: !complex

   test:
      args: -nox -ts_max_steps 2
      localrunfiles: petscopt_ex6
      timeoutfactor: 4

TEST*/