path: root/src/Cartoon2DBC.c

/*@@
   @file      Cartoon2DBC.c
   @date      Thu Nov  4 13:35:00 MET 1999
   @author    Sai Iyer
   @desc 
              Apply Cartoon2D boundary conditions
              An implementation of Steve Brandt's idea for doing
              axisymmetry with 3d stencils.
              Cactus 4 version of Bernd Bruegmann's code.             
   @enddesc
 @@*/

#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
#include <ctype.h>
#include <stdarg.h>
#include <string.h>
#include <math.h>

#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_FortranString.h"

#include "Cartoon2D_tensors.h"

static const char *rcsid = "$Id$";

CCTK_FILEVERSION(Development_Cartoon2D_Cartoon2DBC_c)

CCTK_INT BndCartoon2DVN(cGH *GH, CCTK_INT tensortype, const char *var);
CCTK_INT BndCartoon2DVI(cGH *GH, CCTK_INT tensortype, CCTK_INT vi);
CCTK_REAL Cartoon2DInterp(cGH *GH, CCTK_REAL *f, CCTK_INT i, CCTK_INT di,
                             CCTK_INT ijk, CCTK_REAL x);
CCTK_REAL interpolate_local(CCTK_INT order, CCTK_REAL x0, CCTK_REAL dx, 
			 CCTK_REAL y[], CCTK_REAL x);
void CCTK_FCALL CCTK_FNAME(BndCartoon2DVI)(CCTK_INT *retval, cGH *GH, 
                CCTK_INT *tensortype, CCTK_INT *vi);
void CCTK_FCALL CCTK_FNAME(BndCartoon2DVN)(CCTK_INT *retval, cGH *GH,
                CCTK_INT *tensortype, ONE_FORTSTRING_ARG);


/* set boundaries of a grid tensor assuming axisymmetry 
   - handles lower boundary in x
   - does not touch other boundaries
   - coordinates and rotation coefficients are independent of z and should
     be precomputed
   - this is also true for the constants in interpolator, but this may 
     be too messy
   - minimizes conceptual warpage, not computationally optimized
*/
/* uses rotation matrix and its inverse as linear transformation on
   arbitrary tensor indices -- I consider this a good compromise
   between doing index loops versus using explicit formulas in
   cos(phi) etc with messy signs 
*/

CCTK_INT BndCartoon2DVI(cGH *GH, CCTK_INT tensortype, CCTK_INT vi)

{
  DECLARE_CCTK_PARAMETERS

  static int xindx=-1;

  CCTK_INT i, j, k, di, dj, ijk;
  CCTK_INT jj, n, s;
  CCTK_INT lnx, lny, lnz, ny;
  CCTK_INT n_tensortype;
  CCTK_INT timelevel;
  CCTK_REAL *xp;
  CCTK_REAL x, y, rho;
  CCTK_REAL lx0, dx0, dy0;
  CCTK_REAL rxx, rxy, ryx, ryy;
  CCTK_REAL sxx, sxy, syx, syy;
  CCTK_REAL f[6], fx, fy, fz, fxx, fxy, fxz, fyy, fyz, fzz;
  CCTK_REAL *t, *tx, *ty, *tz, *txx, *txy, *txz, *tyy, *tyz, *tzz;


  switch (tensortype) {
  case TENSORTYPE_SCALAR:
    n_tensortype = N_TENSORTYPE_SCALAR;
    break;
  case TENSORTYPE_U:
    n_tensortype = N_TENSORTYPE_U;
    break;
  case TENSORTYPE_DDSYM:
    n_tensortype = N_TENSORTYPE_DDSYM;
    break;
  default:
    CCTK_WARN(0,"Tensor type not recognized by Cartoon2D.");
  }
    
  s = GH->cctk_nghostzones[0];
  lnx = GH->cctk_lsh[0];
  lny = GH->cctk_lsh[1];
  lnz = GH->cctk_lsh[2];
  ny  = GH->cctk_gsh[1];

  xindx = (xindx<0)?CCTK_CoordIndex(-1,"x","cart3d"):xindx;
  xp    = GH->data[xindx][0];

/*  xp  = GH->data[CCTK_CoordIndex(-1,"x","cart3d")][0];*/
  lx0 = xp[0];
  dx0 = GH->cctk_delta_space[0]/GH->cctk_levfac[0];
  dy0 = GH->cctk_delta_space[1]/GH->cctk_levfac[1];

  timelevel = 0; 

  /* Cactus loop in C:  grid points with y = 0 */
  /* compare thorn_BAM_Elliptic */
  /* strides used in stencils, should be provided by cactus */
  di = 1;
  dj = lnx;

  /* y = 0 */
  j = ny/2;

  /* z-direction: include lower and upper boundary */
  for (k = 0; k < lnz; k++)

  /* y-direction: as many zombies as the evolution stencil needs */
  for (jj = 1, dj = jj*lnx; jj <= ny/2; jj++, dj = jj*lnx) 

  /* x-direction: zombie for x < 0, including upper boundary for extrapol */
  for (i = -s; i < lnx; i++) {

    /* index into linear memory */
    ijk = CCTK_GFINDEX3D(GH,i,j,k);
   
    /* what a neat way to hack in the zombie for x < 0, y = 0 */
    if (i < 0) {i += s; ijk += s; dj = 0;}

    /* compute coordinates (could also use Cactus grid function) */
    x = lx0 + dx0 * i;
    y = (dj) ? dy0 * jj : 0;
    rho = sqrt(x*x + y*y);

    /* compute rotation matrix
       note that this also works for x <= 0 (at lower boundary in x)
       note that rho is nonzero by definition if cactus checks dy ... 
    */
    rxx = x/rho;
    ryx = y/rho;
    rxy = -ryx;
    ryy = rxx;

    /* inverse rotation matrix, assuming detr = 1 */
    sxx = ryy;
    syx = -ryx;
    sxy = -rxy;
    syy = rxx;

    /* interpolate grid functions */
    for (n = 0; n < n_tensortype; n++)
      f[n] = Cartoon2DInterp(GH, GH->data[vi+n][timelevel], i, di, ijk, rho); 

    /* rotate grid tensor by matrix multiplication */
    if (tensortype == TENSORTYPE_SCALAR) {
      t = GH->data[vi][timelevel];
      t[ijk+dj] = f[0];
      t[ijk-dj] = f[0];
    }
    else if (tensortype == TENSORTYPE_U) {
      tx = GH->data[vi][timelevel];
      ty = GH->data[vi+1][timelevel];
      tz = GH->data[vi+2][timelevel];
      fx = f[0];
      fy = f[1];
      fz = f[2];

      tx[ijk+dj] = rxx * fx + rxy * fy;
      ty[ijk+dj] = ryx * fx + ryy * fy;
      tz[ijk+dj] = fz;

      tx[ijk-dj] = sxx * fx + sxy * fy;
      ty[ijk-dj] = syx * fx + syy * fy;
      tz[ijk-dj] = fz;
    }
    else if (tensortype == TENSORTYPE_DDSYM) {
      txx = GH->data[vi][timelevel];
      txy = GH->data[vi+1][timelevel];
      txz = GH->data[vi+2][timelevel];
      tyy = GH->data[vi+3][timelevel];
      tyz = GH->data[vi+4][timelevel];
      tzz = GH->data[vi+5][timelevel];
      fxx = f[0];
      fxy = f[1];
      fxz = f[2];
      fyy = f[3];
      fyz = f[4];
      fzz = f[5];
      
      txx[ijk+dj] = fxx*sxx*sxx + 2*fxy*sxx*syx + fyy*syx*syx;
      tyy[ijk+dj] = fxx*sxy*sxy + 2*fxy*sxy*syy + fyy*syy*syy;
      txy[ijk+dj] = fxx*sxx*sxy + fxy*(sxy*syx+sxx*syy) + fyy*syx*syy;
      txz[ijk+dj] = fxz*sxx + fyz*syx;
      tyz[ijk+dj] = fxz*sxy + fyz*syy;
      tzz[ijk+dj] = fzz;

      txx[ijk-dj] = fxx*rxx*rxx + 2*fxy*rxx*ryx + fyy*ryx*ryx;
      tyy[ijk-dj] = fxx*rxy*rxy + 2*fxy*rxy*ryy + fyy*ryy*ryy;
      txy[ijk-dj] = fxx*rxx*rxy + fxy*(rxy*ryx+rxx*ryy) + fyy*ryx*ryy;
      txz[ijk-dj] = fxz*rxx + fyz*ryx;
      tyz[ijk-dj] = fxz*rxy + fyz*ryy;
      tzz[ijk-dj] = fzz;
    } 
    else {
      return(-1);
    }

    /* what a neat way to hack out the zombies for x < 0, y = 0 */
    if (dj == 0) {i -= s; ijk -= s; dj = jj*lnx;}
  }

  /* syncs needed after interpolation (actually only for x direction) */
    CCTK_SyncGroup(GH, CCTK_GroupNameFromVarI(vi)); 

  return(0);
}

void CCTK_FCALL CCTK_FNAME(BndCartoon2DVI)(CCTK_INT *retval, cGH *GH, CCTK_INT *tensortype, CCTK_INT *vi) {
  *retval = BndCartoon2DVI(GH, *tensortype, *vi);
}

CCTK_INT BndCartoon2DVN(cGH *GH, CCTK_INT tensortype, const char *impvarname)
{
  DECLARE_CCTK_PARAMETERS

  CCTK_INT vi;

  if (verbose) printf("cartoon2D called for %s\n", impvarname);
  vi = CCTK_VarIndex(impvarname);

  return(BndCartoon2DVI(GH, tensortype, vi));
}

void CCTK_FCALL CCTK_FNAME(BndCartoon2DVN)(CCTK_INT *retval, cGH *GH, CCTK_INT *tensortype, ONE_FORTSTRING_ARG) {
  ONE_FORTSTRING_CREATE(impvarname)
  *retval = BndCartoon2DVN(GH, *tensortype, impvarname);
  free(impvarname);
}

CCTK_INT BndCartoon2DGN(cGH *GH, CCTK_INT tensortype, const char *group)
{
  DECLARE_CCTK_PARAMETERS

  CCTK_INT n_tensortype;

  if (verbose) printf("cartoon2D called for %s\n", group);

  switch (tensortype) {
  case TENSORTYPE_SCALAR:
    n_tensortype = N_TENSORTYPE_SCALAR;
    break;
  case TENSORTYPE_U:
    n_tensortype = N_TENSORTYPE_U;
    break;
  case TENSORTYPE_DDSYM:
    n_tensortype = N_TENSORTYPE_DDSYM;
    break;
  default:
    CCTK_WARN(0,"Tensor type not recognized by Cartoon2D.");
  }

  if(CCTK_NumVarsInGroup(group) != n_tensortype){
    char *msg;
    msg = malloc(1024*sizeof(char));
    sprintf(msg, "%s should have only %d component(s).\n", 
	    group, n_tensortype);
    CCTK_WARN(0,msg);
    free(msg);
  }
  
  return(BndCartoon2DVI(GH, tensortype, CCTK_FirstVarIndex(group)));
}
void CCTK_FCALL CCTK_FNAME(BndCartoon2DGN)(CCTK_INT *retval, cGH *GH, CCTK_INT *tensortype, ONE_FORTSTRING_ARG) {
  ONE_FORTSTRING_CREATE(group)
  *retval = BndCartoon2DGN(GH, *tensortype, group);
  free(group);
}

/* interpolation on x-axis */
CCTK_REAL Cartoon2DInterp(cGH *GH, CCTK_REAL *f, CCTK_INT i, CCTK_INT di, 
              CCTK_INT ijk, CCTK_REAL x)
{
  DECLARE_CCTK_PARAMETERS

  static int xindx=-1;

  CCTK_REAL x0;
  CCTK_REAL lx0, dx0;
  CCTK_REAL y[6], r;
  CCTK_REAL *xp;
  CCTK_INT lnx;
  CCTK_INT n, offset;

  lnx = GH->cctk_lsh[0];

  xindx = (xindx<0)?CCTK_CoordIndex(-1,"x","cart3d"):xindx;
  xp    = GH->data[xindx][0];


/*  xp = GH->data[CCTK_CoordIndex(-1,"x","cart3d")][0];*/
  lx0 = xp[0];
  dx0 = GH->cctk_delta_space[0]/GH->cctk_levfac[0];

  /* find i such that x(i) < x <= x(i+1)
     for rotation on entry always x > x(i), but sometimes also x > x(i+1) */
  while (x > lx0 + dx0 * (i+1)) {i++; ijk++;}

  /* first attempt to interface to JT's interpolator */

  /* offset of stencil, note that rotation leads to x close to x0 
       for large x */
  offset = order/2;
  
  /* shift stencil at boundaries */
  /* note that for simplicity we don't distinguish between true boundaries
     and decomposition boundaries: the sync fixes that! */
  if (i-offset < 0) offset = i;
  if (i-offset+order >= lnx) offset = i+order-lnx+1;
  
  /* fill in info */
  /* fills in old data near axis, but as long as stencil at axis is 
     centered, no interpolation happens anyway */
  x0 = lx0 + dx0 * (i-offset);
  for (n = 0; n <= order; n++) {
    y[n] = f[ijk-offset+n];
  }
  
  /* call interpolator */
  r = interpolate_local(order, x0, dx0, y, x);
  
  return r;
}