xref: /petsc/src/ts/impls/explicit/rk/rk.c (revision 8cc058d9cd56c1ccb3be12a47760ddfc446aaffc)

/*
 * Code for Timestepping with Runge Kutta
 *
 * Written by
 * Asbjorn Hoiland Aarrestad
 * asbjorn@aarrestad.com
 * http://asbjorn.aarrestad.com/
 *
 */
#include <petsc-private/tsimpl.h>                /*I   "petscts.h"   I*/
#include <time.h>

typedef struct {
  Vec         y1,y2;        /* work wectors for the two rk permuations */
  PetscInt    nok,nnok;     /* counters for ok and not ok steps */
  PetscReal   maxerror;     /* variable to tell the maxerror allowed */
  PetscReal   ferror;       /* variable to tell (global maxerror)/(total time) */
  PetscReal   tolerance;    /* initial value set for maxerror by user */
  Vec         tmp,tmp_y,*k; /* two temp vectors and the k vectors for rk */
  PetscScalar a[7][6];      /* rk scalars */
  PetscScalar b1[7],b2[7];  /* rk scalars */
  PetscReal   c[7];         /* rk scalars */
  PetscInt    p,s;          /* variables to tell the size of the runge-kutta solver */
} TS_RK;

#undef __FUNCT__
#define __FUNCT__ "TSRKSetTolerance_RK"
PetscErrorCode  TSRKSetTolerance_RK(TS ts,PetscReal aabs)
{
  TS_RK *rk = (TS_RK*)ts->data;

  PetscFunctionBegin;
  rk->tolerance = aabs;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSRKSetTolerance"
/*@
   TSRKSetTolerance - Sets the total error the RK explicit time integrators
                      will allow over the given time interval.

   Logically Collective on TS

   Input parameters:
+    ts  - the time-step context
-    aabs - the absolute tolerance

   Level: intermediate

.keywords: RK, tolerance

.seealso: TSSundialsSetTolerance()

@*/
PetscErrorCode  TSRKSetTolerance(TS ts,PetscReal aabs)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidLogicalCollectiveReal(ts,aabs,2);
  ierr = PetscTryMethod(ts,"TSRKSetTolerance_C",(TS,PetscReal),(ts,aabs));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "TSSetUp_RK"
static PetscErrorCode TSSetUp_RK(TS ts)
{
  TS_RK          *rk = (TS_RK*)ts->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  rk->nok      = 0;
  rk->nnok     = 0;
  rk->maxerror = rk->tolerance;

  /* fixing maxerror: global vs local */
  rk->ferror = rk->maxerror / (ts->max_time - ts->ptime);

  /* 34.0/45.0 gives double precision division */
  /* defining variables needed for Runge-Kutta computing */
  /* when changing below, please remember to change a, b1, b2 and c above! */
  /* Found in table on page 171: Dormand-Prince 5(4) */

  /* are these right? */
  rk->p=6;
  rk->s=7;

  rk->a[1][0]=1.0/5.0;
  rk->a[2][0]=3.0/40.0;
  rk->a[2][1]=9.0/40.0;
  rk->a[3][0]=44.0/45.0;
  rk->a[3][1]=-56.0/15.0;
  rk->a[3][2]=32.0/9.0;
  rk->a[4][0]=19372.0/6561.0;
  rk->a[4][1]=-25360.0/2187.0;
  rk->a[4][2]=64448.0/6561.0;
  rk->a[4][3]=-212.0/729.0;
  rk->a[5][0]=9017.0/3168.0;
  rk->a[5][1]=-355.0/33.0;
  rk->a[5][2]=46732.0/5247.0;
  rk->a[5][3]=49.0/176.0;
  rk->a[5][4]=-5103.0/18656.0;
  rk->a[6][0]=35.0/384.0;
  rk->a[6][1]=0.0;
  rk->a[6][2]=500.0/1113.0;
  rk->a[6][3]=125.0/192.0;
  rk->a[6][4]=-2187.0/6784.0;
  rk->a[6][5]=11.0/84.0;


  rk->c[0]=0.0;
  rk->c[1]=1.0/5.0;
  rk->c[2]=3.0/10.0;
  rk->c[3]=4.0/5.0;
  rk->c[4]=8.0/9.0;
  rk->c[5]=1.0;
  rk->c[6]=1.0;

  rk->b1[0]=35.0/384.0;
  rk->b1[1]=0.0;
  rk->b1[2]=500.0/1113.0;
  rk->b1[3]=125.0/192.0;
  rk->b1[4]=-2187.0/6784.0;
  rk->b1[5]=11.0/84.0;
  rk->b1[6]=0.0;

  rk->b2[0]=5179.0/57600.0;
  rk->b2[1]=0.0;
  rk->b2[2]=7571.0/16695.0;
  rk->b2[3]=393.0/640.0;
  rk->b2[4]=-92097.0/339200.0;
  rk->b2[5]=187.0/2100.0;
  rk->b2[6]=1.0/40.0;


  /* Found in table on page 170: Fehlberg 4(5) */
  /*
  rk->p=5;
  rk->s=6;

  rk->a[1][0]=1.0/4.0;
  rk->a[2][0]=3.0/32.0;
  rk->a[2][1]=9.0/32.0;
  rk->a[3][0]=1932.0/2197.0;
  rk->a[3][1]=-7200.0/2197.0;
  rk->a[3][2]=7296.0/2197.0;
  rk->a[4][0]=439.0/216.0;
  rk->a[4][1]=-8.0;
  rk->a[4][2]=3680.0/513.0;
  rk->a[4][3]=-845.0/4104.0;
  rk->a[5][0]=-8.0/27.0;
  rk->a[5][1]=2.0;
  rk->a[5][2]=-3544.0/2565.0;
  rk->a[5][3]=1859.0/4104.0;
  rk->a[5][4]=-11.0/40.0;

  rk->c[0]=0.0;
  rk->c[1]=1.0/4.0;
  rk->c[2]=3.0/8.0;
  rk->c[3]=12.0/13.0;
  rk->c[4]=1.0;
  rk->c[5]=1.0/2.0;

  rk->b1[0]=25.0/216.0;
  rk->b1[1]=0.0;
  rk->b1[2]=1408.0/2565.0;
  rk->b1[3]=2197.0/4104.0;
  rk->b1[4]=-1.0/5.0;
  rk->b1[5]=0.0;

  rk->b2[0]=16.0/135.0;
  rk->b2[1]=0.0;
  rk->b2[2]=6656.0/12825.0;
  rk->b2[3]=28561.0/56430.0;
  rk->b2[4]=-9.0/50.0;
  rk->b2[5]=2.0/55.0;
  */
  /* Found in table on page 169: Merson 4("5") */
  /*
  rk->p=4;
  rk->s=5;
  rk->a[1][0] = 1.0/3.0;
  rk->a[2][0] = 1.0/6.0;
  rk->a[2][1] = 1.0/6.0;
  rk->a[3][0] = 1.0/8.0;
  rk->a[3][1] = 0.0;
  rk->a[3][2] = 3.0/8.0;
  rk->a[4][0] = 1.0/2.0;
  rk->a[4][1] = 0.0;
  rk->a[4][2] = -3.0/2.0;
  rk->a[4][3] = 2.0;

  rk->c[0] = 0.0;
  rk->c[1] = 1.0/3.0;
  rk->c[2] = 1.0/3.0;
  rk->c[3] = 0.5;
  rk->c[4] = 1.0;

  rk->b1[0] = 1.0/2.0;
  rk->b1[1] = 0.0;
  rk->b1[2] = -3.0/2.0;
  rk->b1[3] = 2.0;
  rk->b1[4] = 0.0;

  rk->b2[0] = 1.0/6.0;
  rk->b2[1] = 0.0;
  rk->b2[2] = 0.0;
  rk->b2[3] = 2.0/3.0;
  rk->b2[4] = 1.0/6.0;
  */

  /* making b2 -> e=b1-b2 */
  /*
    for (i=0;i<rk->s;i++) {
     rk->b2[i] = (rk->b1[i]) - (rk->b2[i]);
  }
  */
  rk->b2[0]=71.0/57600.0;
  rk->b2[1]=0.0;
  rk->b2[2]=-71.0/16695.0;
  rk->b2[3]=71.0/1920.0;
  rk->b2[4]=-17253.0/339200.0;
  rk->b2[5]=22.0/525.0;
  rk->b2[6]=-1.0/40.0;

  /* initializing vectors */
  ierr = VecDuplicate(ts->vec_sol,&rk->y1);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&rk->y2);CHKERRQ(ierr);
  ierr = VecDuplicate(rk->y1,&rk->tmp);CHKERRQ(ierr);
  ierr = VecDuplicate(rk->y1,&rk->tmp_y);CHKERRQ(ierr);
  ierr = VecDuplicateVecs(rk->y1,rk->s,&rk->k);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "TSRKqs"
PetscErrorCode TSRKqs(TS ts,PetscReal t,PetscReal h)
{
  TS_RK          *rk = (TS_RK*)ts->data;
  PetscErrorCode ierr;
  PetscInt       j,l;
  PetscReal      tmp_t = t;
  PetscScalar    hh    = h;

  PetscFunctionBegin;
  /* k[0]=0  */
  ierr = VecSet(rk->k[0],0.0);CHKERRQ(ierr);

  /* k[0] = derivs(t,y1) */
  ierr = TSComputeRHSFunction(ts,t,rk->y1,rk->k[0]);CHKERRQ(ierr);
  /* looping over runge-kutta variables */
  /* building the k - array of vectors */
  for (j = 1; j < rk->s; j++) {

    /* rk->tmp = 0 */
    ierr = VecSet(rk->tmp,0.0);CHKERRQ(ierr);

    for (l=0; l<j; l++) {
      /* tmp += a(j,l)*k[l] */
      ierr = VecAXPY(rk->tmp,rk->a[j][l],rk->k[l]);CHKERRQ(ierr);
    }

    /* ierr = VecView(rk->tmp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */

    /* k[j] = derivs(t+c(j)*h,y1+h*tmp,k(j)) */
    /* I need the following helpers:
       PetscScalar  tmp_t=t+c(j)*h
       Vec          tmp_y=h*tmp+y1
    */

    tmp_t = t + rk->c[j] * h;

    /* tmp_y = h * tmp + y1 */
    ierr = VecWAXPY(rk->tmp_y,hh,rk->tmp,rk->y1);CHKERRQ(ierr);

    /* rk->k[j]=0 */
    ierr = VecSet(rk->k[j],0.0);CHKERRQ(ierr);
    ierr = TSComputeRHSFunction(ts,tmp_t,rk->tmp_y,rk->k[j]);CHKERRQ(ierr);
  }

  /* tmp=0 and tmp_y=0 */
  ierr = VecSet(rk->tmp,0.0);CHKERRQ(ierr);
  ierr = VecSet(rk->tmp_y,0.0);CHKERRQ(ierr);

  for (j = 0; j < rk->s; j++) {
    /* tmp=b1[j]*k[j]+tmp  */
    ierr = VecAXPY(rk->tmp,rk->b1[j],rk->k[j]);CHKERRQ(ierr);
    /* tmp_y=b2[j]*k[j]+tmp_y */
    ierr = VecAXPY(rk->tmp_y,rk->b2[j],rk->k[j]);CHKERRQ(ierr);
  }

  /* y2 = hh * tmp_y */
  ierr = VecSet(rk->y2,0.0);CHKERRQ(ierr);
  ierr = VecAXPY(rk->y2,hh,rk->tmp_y);CHKERRQ(ierr);
  /* y1 = hh*tmp + y1 */
  ierr = VecAXPY(rk->y1,hh,rk->tmp);CHKERRQ(ierr);
  /* Finding difference between y1 and y2 */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSSolve_RK"
static PetscErrorCode TSSolve_RK(TS ts)
{
  TS_RK          *rk = (TS_RK*)ts->data;
  PetscReal      norm=0.0,dt_fac=0.0,fac = 0.0 /*,ttmp=0.0*/;
  PetscInt       i;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr);

  /* while loop to get from start to stop */
  for (i = 0; i < ts->max_steps; i++) {
    ierr = TSPreStep(ts);CHKERRQ(ierr); /* Note that this is called once per STEP, not once per STAGE. */

    /* calling rkqs */
    /*
      -- input
      ts        - pointer to ts
      ts->ptime - current time
      ts->time_step        - try this timestep
      y1        - solution for this step

      --output
      y1        - suggested solution
      y2        - check solution (runge - kutta second permutation)
    */
    ierr = TSRKqs(ts,ts->ptime,ts->time_step);CHKERRQ(ierr);
    /* counting steps */
    ts->steps++;
    /* checking for maxerror */
    /* comparing difference to maxerror */
    ierr = VecNorm(rk->y2,NORM_2,&norm);CHKERRQ(ierr);
    /* modifying maxerror to satisfy this timestep */
    rk->maxerror = rk->ferror * ts->time_step;
    /* ierr = PetscPrintf(PETSC_COMM_WORLD,"norm err: %f maxerror: %f dt: %f",norm,rk->maxerror,ts->time_step);CHKERRQ(ierr); */

    /* handling ok and not ok */
    if (norm < rk->maxerror) {
      /* if ok: */
      ierr       = VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr); /* saves the suggested solution to current solution */
      ts->ptime += ts->time_step;   /* storing the new current time */
      rk->nok++;
      fac=5.0;
      /* trying to save the vector */
      ierr = TSPostStep(ts);CHKERRQ(ierr);
      ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
      if (ts->ptime >= ts->max_time) break;
    } else {
      /* if not OK */
      rk->nnok++;
      fac =1.0;
      ierr=VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr);    /* restores old solution */
    }

    /*Computing next stepsize. See page 167 in Solving ODE 1
     *
     * h_new = h * min(facmax , max(facmin , fac * (tol/err)^(1/(p+1))))
     * facmax set above
     * facmin
     */
    dt_fac = exp(log((rk->maxerror) / norm) / ((rk->p) + 1)) * 0.9;

    if (dt_fac > fac) dt_fac = fac;


    /* computing new ts->time_step */
    ts->time_step = ts->time_step * dt_fac;

    if (ts->ptime+ts->time_step > ts->max_time) ts->time_step = ts->max_time - ts->ptime;

    if (ts->time_step < 1e-14) {
      ierr          = PetscPrintf(PETSC_COMM_WORLD,"Very small steps: %f\n",ts->time_step);CHKERRQ(ierr);
      ts->time_step = 1e-14;
    }

    /* trying to purify h */
    /* (did not give any visible result) */
    /* ttmp = ts->ptime + ts->time_step;
       ts->time_step = ttmp - ts->ptime; */

  }

  ierr=VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "TSReset_RK"
static PetscErrorCode TSReset_RK(TS ts)
{
  TS_RK          *rk = (TS_RK*)ts->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecDestroy(&rk->y1);CHKERRQ(ierr);
  ierr = VecDestroy(&rk->y2);CHKERRQ(ierr);
  ierr = VecDestroy(&rk->tmp);CHKERRQ(ierr);
  ierr = VecDestroy(&rk->tmp_y);CHKERRQ(ierr);
  if (rk->k) {ierr = VecDestroyVecs(rk->s,&rk->k);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSDestroy_RK"
static PetscErrorCode TSDestroy_RK(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = TSReset_RK(ts);CHKERRQ(ierr);
  ierr = PetscFree(ts->data);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetTolerance_C","",NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/*------------------------------------------------------------*/

#undef __FUNCT__
#define __FUNCT__ "TSSetFromOptions_RK"
static PetscErrorCode TSSetFromOptions_RK(TS ts)
{
  TS_RK          *rk = (TS_RK*)ts->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscOptionsHead("RK ODE solver options");CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_rk_tol","Tolerance for convergence","TSRKSetTolerance",rk->tolerance,&rk->tolerance,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSView_RK"
static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer)
{
  TS_RK          *rk = (TS_RK*)ts->data;
  PetscBool      iascii;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  if (iascii) {
    ierr = PetscViewerASCIIPrintf(viewer,"number of ok steps: %D\n",rk->nok);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"number of rejected steps: %D\n",rk->nnok);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------ */
/*MC
      TSRK - ODE solver using the explicit Runge-Kutta methods

   Options Database:
.  -ts_rk_tol <tol> Tolerance for convergence

  Contributed by: Asbjorn Hoiland Aarrestad, asbjorn@aarrestad.com, http://asbjorn.aarrestad.com/

  Level: beginner

.seealso:  TSCreate(), TS, TSSetType(), TSEULER, TSRKSetTolerance()

M*/

#undef __FUNCT__
#define __FUNCT__ "TSCreate_RK"
PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
{
  TS_RK          *rk;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ts->ops->setup          = TSSetUp_RK;
  ts->ops->solve          = TSSolve_RK;
  ts->ops->destroy        = TSDestroy_RK;
  ts->ops->setfromoptions = TSSetFromOptions_RK;
  ts->ops->view           = TSView_RK;

  ierr = PetscNewLog(ts,TS_RK,&rk);CHKERRQ(ierr);
  ts->data = (void*)rk;

  ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetTolerance_C","TSRKSetTolerance_RK",TSRKSetTolerance_RK);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}