static char help[] = "Solves the time dependent Allen-Cahn equation with IMEX methods";

/*
 * allen_cahn.c
 *
 *  Created on: Jun 8, 2012
 *      Author: Hong Zhang
 */

#include <petscts.h>

/*
 * application context
 */
typedef struct {
  PetscReal param;         /* parameter */
  PetscReal xleft, xright; /* range in x-direction */
  PetscInt  mx;            /* Discretization in x-direction */
} AppCtx;

static PetscErrorCode RHSFunction(TS, PetscReal, Vec, Vec, void *);
static PetscErrorCode FormIFunction(TS, PetscReal, Vec, Vec, Vec, void *);
static PetscErrorCode FormIJacobian(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *ctx);
static PetscErrorCode FormInitialSolution(TS, Vec, void *);

int main(int argc, char **argv)
{
  TS        ts;
  Vec       x; /* solution vector */
  Mat       A; /* Jacobian */
  PetscInt  steps, mx;
  PetscReal ftime;
  AppCtx    user; /* user-defined work context */

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));

  /* Initialize user application context */
  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Allen-Cahn equation", "");
  user.param  = 9e-4;
  user.xleft  = -1.;
  user.xright = 2.;
  user.mx     = 400;
  PetscCall(PetscOptionsReal("-eps", "parameter", "", user.param, &user.param, NULL));
  PetscOptionsEnd();

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  /*
   * PetscCall(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL));
   */
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Create necessary matrix and vectors, solve same ODE on every process
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, user.mx, user.mx));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatSetUp(A));
  PetscCall(MatCreateVecs(A, &x, NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Create time stepping solver context
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetType(ts, TSEIMEX));
  PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user));
  PetscCall(TSSetIFunction(ts, NULL, FormIFunction, &user));
  PetscCall(TSSetIJacobian(ts, A, A, FormIJacobian, &user));
  ftime = 22;
  PetscCall(TSSetMaxTime(ts, ftime));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(FormInitialSolution(ts, x, &user));
  PetscCall(TSSetSolution(ts, x));
  PetscCall(VecGetSize(x, &mx));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetFromOptions(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Solve nonlinear system
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSolve(ts, x));
  PetscCall(TSGetTime(ts, &ftime));
  PetscCall(TSGetStepNumber(ts, &steps));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "eps %g, steps %" PetscInt_FMT ", ftime %g\n", (double)user.param, steps, (double)ftime));
  /*   PetscCall(VecView(x,PETSC_VIEWER_STDOUT_WORLD));*/

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Free work space.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatDestroy(&A));
  PetscCall(VecDestroy(&x));
  PetscCall(TSDestroy(&ts));
  PetscCall(PetscFinalize());
  return 0;
}

static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec X, Vec F, void *ptr)
{
  AppCtx            *user = (AppCtx *)ptr;
  PetscScalar       *f;
  const PetscScalar *x;
  PetscInt           i, mx;
  PetscReal          hx, eps;

  PetscFunctionBegin;
  mx  = user->mx;
  eps = user->param;
  hx  = (user->xright - user->xleft) / (mx - 1);
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(VecGetArray(F, &f));
  f[0] = 2. * eps * (x[1] - x[0]) / (hx * hx); /*boundary*/
  for (i = 1; i < mx - 1; i++) f[i] = eps * (x[i + 1] - 2. * x[i] + x[i - 1]) / (hx * hx);
  f[mx - 1] = 2. * eps * (x[mx - 2] - x[mx - 1]) / (hx * hx); /*boundary*/
  PetscCall(VecRestoreArrayRead(X, &x));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode FormIFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ptr)
{
  AppCtx            *user = (AppCtx *)ptr;
  PetscScalar       *f;
  const PetscScalar *x, *xdot;
  PetscInt           i, mx;

  PetscFunctionBegin;
  mx = user->mx;
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(VecGetArrayRead(Xdot, &xdot));
  PetscCall(VecGetArray(F, &f));

  for (i = 0; i < mx; i++) f[i] = xdot[i] - x[i] * (1. - x[i] * x[i]);

  PetscCall(VecRestoreArrayRead(X, &x));
  PetscCall(VecRestoreArrayRead(Xdot, &xdot));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode FormIJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat J, Mat Jpre, void *ctx)
{
  AppCtx            *user = (AppCtx *)ctx;
  PetscScalar        v;
  const PetscScalar *x;
  PetscInt           i, col;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(U, &x));
  for (i = 0; i < user->mx; i++) {
    v   = a - 1. + 3. * x[i] * x[i];
    col = i;
    PetscCall(MatSetValues(J, 1, &i, 1, &col, &v, INSERT_VALUES));
  }
  PetscCall(VecRestoreArrayRead(U, &x));

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

static PetscErrorCode FormInitialSolution(TS ts, Vec U, void *ctx)
{
  AppCtx      *user = (AppCtx *)ctx;
  PetscInt     i;
  PetscScalar *x;
  PetscReal    hx, x_map;

  PetscFunctionBegin;
  hx = (user->xright - user->xleft) / (PetscReal)(user->mx - 1);
  PetscCall(VecGetArray(U, &x));
  for (i = 0; i < user->mx; i++) {
    x_map = user->xleft + i * hx;
    if (x_map >= 0.7065) {
      x[i] = PetscTanhReal((x_map - 0.8) / (2. * PetscSqrtReal(user->param)));
    } else if (x_map >= 0.4865) {
      x[i] = PetscTanhReal((0.613 - x_map) / (2. * PetscSqrtReal(user->param)));
    } else if (x_map >= 0.28) {
      x[i] = PetscTanhReal((x_map - 0.36) / (2. * PetscSqrtReal(user->param)));
    } else if (x_map >= -0.7) {
      x[i] = PetscTanhReal((0.2 - x_map) / (2. * PetscSqrtReal(user->param)));
    } else if (x_map >= -1) {
      x[i] = PetscTanhReal((x_map + 0.9) / (2. * PetscSqrtReal(user->param)));
    }
  }
  PetscCall(VecRestoreArray(U, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

     test:
       args: -ts_rtol 1e-04 -ts_time_step 0.025 -pc_type lu -ksp_error_if_not_converged TRUE -ts_type eimex -ts_adapt_type none -ts_eimex_order_adapt -ts_eimex_max_rows 7 -ts_monitor_draw_solution
       requires: x
       timeoutfactor: 3

TEST*/