/*
 *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 *
 *<LicenseText>
 *
 * CitcomS by Louis Moresi, Shijie Zhong, Lijie Han, Eh Tan,
 * Clint Conrad, Michael Gurnis, and Eun-seo Choi.
 * Copyright (C) 1994-2005, California Institute of Technology.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 *</LicenseText>
 *
 *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 */
#include <math.h>

#include "global_defs.h"
#include "parallel_related.h"

/* Setup global mesh parameters */
void regional_global_derived_values(E)
     struct All_variables *E;

{
    int d,i,nox,noz,noy;
    void parallel_process_termination();


   E->mesh.levmax = E->mesh.levels-1;
   nox = (E->mesh.mgunitx * (int) pow(2.0,((double)E->mesh.levmax)))*E->parallel.nprocx + 1;
   noy = (E->mesh.mgunity * (int) pow(2.0,((double)E->mesh.levmax)))*E->parallel.nprocy + 1;

   if (E->control.NMULTIGRID||E->control.EMULTIGRID)  {
      E->mesh.levmax = E->mesh.levels-1;
      E->mesh.gridmax = E->mesh.levmax;
      E->mesh.nox = (E->mesh.mgunitx * (int) pow(2.0,((double)E->mesh.levmax)))*E->parallel.nprocx + 1;
      E->mesh.noy = (E->mesh.mgunity * (int) pow(2.0,((double)E->mesh.levmax)))*E->parallel.nprocy + 1;
      E->mesh.noz = (E->mesh.mgunitz * (int) pow(2.0,((double)E->mesh.levmax)))*E->parallel.nprocz + 1;
      }
   else   {
      if (nox!=E->mesh.nox || noy!=E->mesh.noy) {
         if (E->parallel.me==0)
            fprintf(stderr,"inconsistent mesh for interpolation, quit the run\n");
         parallel_process_termination();
         }
      E->mesh.gridmax = E->mesh.levmax;
      E->mesh.gridmin = E->mesh.levmax;
     }

   if(E->mesh.nsd != 3)
      E->mesh.noy = 1;

   E->mesh.nnx[1] = E->mesh.nox;
   E->mesh.nnx[2] = E->mesh.noy;
   E->mesh.nnx[3] = E->mesh.noz;
   E->mesh.elx = E->mesh.nox-1;
   E->mesh.ely = E->mesh.noy-1;
   E->mesh.elz = E->mesh.noz-1;

   E->mesh.nno = E->sphere.caps;
   for(d=1;d<=E->mesh.nsd;d++)
      E->mesh.nno *= E->mesh.nnx[d];

/*
   E->mesh.nel = E->sphere.caps*E->mesh.elx*E->mesh.elz*E->mesh.ely;
*/
   E->mesh.nel = E->mesh.elx*E->mesh.elz*E->mesh.ely;

   E->mesh.nnov = E->mesh.nno;

   E->mesh.neq = E->mesh.nnov*E->mesh.nsd;

   E->mesh.npno = E->mesh.nel;
   E->mesh.nsf = E->mesh.nox*E->mesh.noy;

   for(i=E->mesh.levmax;i>=E->mesh.levmin;i--) {
      if (E->control.NMULTIGRID||E->control.EMULTIGRID)
	{ nox = (E->mesh.mgunitx * (int) pow(2.0,(double)i))*E->parallel.nprocx + 1;
	  noy = (E->mesh.mgunity * (int) pow(2.0,(double)i))*E->parallel.nprocy + 1;
	  noz = (E->mesh.mgunitz * (int) pow(2.0,(double)i))*E->parallel.nprocz + 1;
	}
      else
	{ noz = E->mesh.noz;
	  nox = (E->mesh.mgunitx * (int) pow(2.0,(double)i))*E->parallel.nprocx + 1;
	  noy = (E->mesh.mgunity * (int) pow(2.0,(double)i))*E->parallel.nprocy + 1;
          if (i<E->mesh.levmax) noz=2;
	}

      E->mesh.ELX[i] = nox-1;
      E->mesh.ELY[i] = noy-1;
      E->mesh.ELZ[i] = noz-1;
      E->mesh.NNO[i] = nox * noz * noy;
      E->mesh.NEL[i] = (nox-1) * (noz-1) * (noy-1);
      E->mesh.NPNO[i] = E->mesh.NEL[i] ;
      E->mesh.NOX[i] = nox;
      E->mesh.NOZ[i] = noz;
      E->mesh.NOY[i] = noy;

      E->mesh.NNOV[i] = E->mesh.NNO[i];
      E->mesh.NEQ[i] = E->mesh.nsd * E->mesh.NNOV[i] ;

      }

/* Scaling from dimensionless units to Millions of years for input velocity
   and time, timdir is the direction of time for advection. CPC 6/25/00 */

    /* Myr */
    E->data.scalet = (E->data.radius_km*1e3*E->data.radius_km*1e3/E->data.therm_diff)/(1.e6*365.25*24*3600);
    /* cm/yr */
    E->data.scalev = (E->data.radius_km*1e3/E->data.therm_diff)/(100*365.25*24*3600);
    E->data.timedir = E->control.Atemp / fabs(E->control.Atemp);


    if(E->control.print_convergence && E->parallel.me==0)
	fprintf(stderr,"Problem has %d x %d x %d nodes\n",E->mesh.nox,E->mesh.noz,E->mesh.noy);

   return;
}



/* =================================================
   Standard node positions including mesh refinement

   =================================================  */

void regional_node_locations(E)
  struct All_variables *E;
{
  int i,j,k,lev;
  double ro,dr,*rr,*RR,fo;
  float tt1;
  int nox,noy,noz,step;
  int nn;
  char output_file[255];
  char a[100];
  FILE *fp1;

  void regional_coord_of_cap();
  void rotate_mesh ();
  void compute_angle_surf_area ();
  void parallel_process_termination();

  rr = (double *)  malloc((E->mesh.noz+1)*sizeof(double));
  RR = (double *)  malloc((E->mesh.noz+1)*sizeof(double));
  nox=E->mesh.nox;
  noy=E->mesh.noy;
  noz=E->mesh.noz;


  if(E->control.coor==1)    {
      sprintf(output_file,"%s",E->control.coor_file);
      fp1=fopen(output_file,"r");
	if (fp1 == NULL) {
          fprintf(E->fp,"(Nodal_mesh.c #1) Cannot open %s\n",output_file);
          exit(8);
	}

      fscanf(fp1,"%s %d",a,&i);
      for(i=1;i<=nox;i++)
      fscanf(fp1,"%d %f",&nn,&tt1);

      fscanf(fp1,"%s %d",a,&i);
      for(i=1;i<=noy;i++)
      fscanf(fp1,"%d %f",&nn,&tt1);

      fscanf(fp1,"%s %d",a,&i);
      for (k=1;k<=E->mesh.noz;k++)  {
      fscanf(fp1,"%d %f",&nn,&tt1);
      rr[k]=tt1;
      }
      E->sphere.ri = rr[1];
      E->sphere.ro = rr[E->mesh.noz];

      fclose(fp1);

   }

    else {
      dr = (E->sphere.ro-E->sphere.ri)/(E->mesh.noz-1);
      for (k=1;k<=E->mesh.noz;k++)  {
      rr[k] = E->sphere.ri + (k-1)*dr;
      }

    }



  for (i=1;i<=E->lmesh.noz;i++)  {
      k = E->lmesh.nzs+i-1;
      RR[i] = rr[k];
      }

  for (lev=E->mesh.levmin;lev<=E->mesh.levmax;lev++) {

    if (E->control.NMULTIGRID||E->control.EMULTIGRID)
        step = (int) pow(2.0,(double)(E->mesh.levmax-lev));
    else
        step = 1;

      for (i=1;i<=E->lmesh.NOZ[lev];i++)
         E->sphere.R[lev][i] = RR[(i-1)*step+1];

    }          /* lev   */


/*    do not need to rotate for the mesh grid for one regional problem   */


  ro = -0.5*(M_PI/4.0)/E->lmesh.elx;
  fo = 0.0;

  E->sphere.dircos[1][1] = cos(ro)*cos(fo);
  E->sphere.dircos[1][2] = cos(ro)*sin(fo);
  E->sphere.dircos[1][3] = -sin(ro);
  E->sphere.dircos[2][1] = -sin(fo);
  E->sphere.dircos[2][2] = cos(fo);
  E->sphere.dircos[2][3] = 0.0;
  E->sphere.dircos[3][1] = sin(ro)*cos(fo);
  E->sphere.dircos[3][2] = sin(ro)*sin(fo);
  E->sphere.dircos[3][3] = cos(ro);

  for (j=1;j<=E->sphere.caps_per_proc;j++)   {
     regional_coord_of_cap(E,j,0);
     }


  if (E->control.verbose) {
  for (lev=E->mesh.levmin;lev<=E->mesh.levmax;lev++) {
    fprintf(E->fp_out,"output_coordinates before rotation %d \n",lev);
    for (j=1;j<=E->sphere.caps_per_proc;j++)  {
      fprintf(E->fp_out,"output_coordinates for cap %d %d\n",j,E->lmesh.NNO[lev]);
      for (i=1;i<=E->lmesh.NNO[lev];i++)
        if(i%E->lmesh.NOZ[lev]==1)
             fprintf(E->fp_out,"%d %d %g %g %g\n",j,i,E->SX[lev][j][1][i],E->SX[lev][j][2][i],E->SX[lev][j][3][i]);
      }
    }
    fflush(E->fp_out);
  }
                   /* rotate the mesh to avoid two poles on mesh points */
/*
  for (j=1;j<=E->sphere.caps_per_proc;j++)   {
     rotate_mesh(E,j,0);
     }
*/

  compute_angle_surf_area (E);   /* used for interpolation */


  for (lev=E->mesh.levmin;lev<=E->mesh.levmax;lev++)
    for (j=1;j<=E->sphere.caps_per_proc;j++)
      for (i=1;i<=E->lmesh.NNO[lev];i++)  {
        E->SinCos[lev][j][0][i] = sin(E->SX[lev][j][1][i]);
        E->SinCos[lev][j][1][i] = sin(E->SX[lev][j][2][i]);
        E->SinCos[lev][j][2][i] = cos(E->SX[lev][j][1][i]);
        E->SinCos[lev][j][3][i] = cos(E->SX[lev][j][2][i]);
        }

/*
  if (E->parallel.me_loc[3]==E->parallel.nprocz-1)  {
    sprintf(output_file,"coord.%d",E->parallel.me);
    fp=fopen(output_file,"w");
	if (fp == NULL) {
          fprintf(E->fp,"(Nodal_mesh.c #2) Cannot open %s\n",output_file);
          exit(8);
	}
    for(m=1;m<=E->sphere.caps_per_proc;m++)  {
      for(i=1;i<=E->lmesh.noy;i++) {
        for(j=1;j<=E->lmesh.nox;j++)  {
           node=1+(j-1)*E->lmesh.noz+(i-1)*E->lmesh.nox*E->lmesh.noz;
           t1 = 90.0-E->sx[m][1][node]/M_PI*180.0;
           f1 = E->sx[m][2][node]/M_PI*180.0;
           fprintf(fp,"%f %f\n",t1,f1);
           }
        fprintf(fp,">\n");
        }
      for(j=1;j<=E->lmesh.nox;j++)  {
        for(i=1;i<=E->lmesh.noy;i++) {
           node=1+(j-1)*E->lmesh.noz+(i-1)*E->lmesh.nox*E->lmesh.noz;
           t1 = 90.0-E->sx[m][1][node]/M_PI*180.0;
           f1 = E->sx[m][2][node]/M_PI*180.0;
           fprintf(fp,"%f %f\n",t1,f1);
           }
        fprintf(fp,">\n");
        }
      }
     fclose(fp);
     }
*/


  if (E->control.verbose) {
  for (lev=E->mesh.levmin;lev<=E->mesh.levmax;lev++)   {
    fprintf(E->fp_out,"output_coordinates after rotation %d \n",lev);
    for (j=1;j<=E->sphere.caps_per_proc;j++)
      for (i=1;i<=E->lmesh.NNO[lev];i++)
        if(i%E->lmesh.NOZ[lev]==1)
             fprintf(E->fp_out,"%d %d %g %g %g\n",j,i,E->SX[lev][j][1][i],E->SX[lev][j][2][i],E->SX[lev][j][3][i]);
      }
    fflush(E->fp_out);
  }
   free((void *)rr);
   free((void *)RR);

   return;
}



void regional_construct_tic_from_input(struct All_variables *E)
{
  double modified_plgndr_a(int, int, double);
  void temperatures_conform_bcs();

  int i, j ,k , kk, m, p, node, nodet;
  int nox, noy, noz, gnoz;
  double r1, f1, t1;
  int mm, ll;
  double con, temp;

  double tlen = M_PI / (E->control.theta_max - E->control.theta_min);
  double flen = M_PI / (E->control.fi_max - E->control.fi_min);

  noy=E->lmesh.noy;
  nox=E->lmesh.nox;
  noz=E->lmesh.noz;
  gnoz=E->mesh.noz;

  if (E->convection.tic_method == 0) {


    /* set up a linear temperature profile first */
    for(m=1;m<=E->sphere.caps_per_proc;m++)
      for(i=1;i<=noy;i++)
	for(j=1;j<=nox;j++)
	  for(k=1;k<=noz;k++) {
	    node=k+(j-1)*noz+(i-1)*nox*noz;
	    r1=E->sx[m][3][node];
	    E->T[m][node] = E->control.TBCbotval - (E->control.TBCtopval + E->control.TBCbotval)*(r1 - E->sphere.ri)/(E->sphere.ro - E->sphere.ri);
	  }

    /* This part put a temperature anomaly at depth where the global
       node number is equal to load_depth. The horizontal pattern of
       the anomaly is given by spherical harmonic ll & mm. */

    for (p=0; p<E->convection.number_of_perturbations; p++) {
      mm = E->convection.perturb_mm[p];
      ll = E->convection.perturb_ll[p];
      con = E->convection.perturb_mag[p];
      kk = E->convection.load_depth[p];

      if ( (kk < 1) || (kk >= gnoz) ) continue;

      k = kk - E->lmesh.nzs + 1;
      if ( (k < 1) || (k >= noz) ) continue; /* if layer k is not inside this proc. */
      if (E->parallel.me_loc[1] == 0 && E->parallel.me_loc[2] == 0)

      for(m=1;m<=E->sphere.caps_per_proc;m++)
	for(i=1;i<=noy;i++)
	  for(j=1;j<=nox;j++) {
	    node=k+(j-1)*noz+(i-1)*nox*noz;
	    t1 = (E->sx[m][1][node] - E->control.theta_min) * tlen;
	    f1 = (E->sx[m][2][node] - E->control.fi_min) * flen;

	    E->T[m][node] += con*cos(ll*t1)*cos(mm*f1);

	    /*
	      t1=E->sx[m][1][node];
	      f1=E->sx[m][2][node];
	      E->T[m][node] += con*modified_plgndr_a(ll,mm,t1)*cos(mm*f1);
	    */
	  }
    }

  }
  else if (E->convection.tic_method == 1) {
      /* set up a top thermal boundary layer */
      for(m=1;m<=E->sphere.caps_per_proc;m++)
          for(i=1;i<=noy;i++)
              for(j=1;j<=nox;j++)
                  for(k=1;k<=noz;k++) {
                      node=k+(j-1)*noz+(i-1)*nox*noz;
                      r1=E->sx[m][3][node];
                      temp = 0.2*(E->sphere.ro-r1) * 0.5/sqrt(E->convection.half_space_age/E->data.scalet);
                      E->T[m][node] = E->control.TBCbotval*erf(temp);
                  }

  }
  else if (E->convection.tic_method == 2) {
    double temp;
    double theta_center = E->convection.blob_center[0];
    double fi_center = E->convection.blob_center[1];
    double r_center = E->convection.blob_center[2];
    double radius = E->convection.blob_radius;
    double amp = E->convection.blob_dT;
	double x_center,y_center,z_center;
	double theta,fi,r,x,y,z,distance;

	fprintf(stderr,"center=%e %e %e radius=%e dT=%e\n",theta_center,fi_center,r_center,radius,amp);
	/* set up a thermal boundary layer first */
    for(m=1;m<=E->sphere.caps_per_proc;m++)
      for(i=1;i<=noy;i++)
        for(j=1;j<=nox;j++)
          for(k=1;k<=noz;k++) {
            node=k+(j-1)*noz+(i-1)*nox*noz;
            r1=E->sx[m][3][node];
            temp = 0.2*(E->sphere.ro-r1) * 0.5/sqrt(E->convection.half_space_age/E->data.scalet);
            E->T[m][node] = E->control.TBCbotval*erf(temp);
          }

    x_center = r_center * sin(fi_center) * cos(theta_center);
    y_center = r_center * sin(fi_center) * sin(theta_center);
    z_center = r_center * cos(fi_center);

    /* compute temperature field according to nodal coordinate */
    for(m=1;m<=E->sphere.caps_per_proc;m++)
        for(k=1;k<=E->lmesh.noy;k++)
            for(j=1;j<=E->lmesh.nox;j++)
                for(i=1;i<=E->lmesh.noz;i++)  {
                    node = i + (j-1)*E->lmesh.noz
                             + (k-1)*E->lmesh.noz*E->lmesh.nox;

                    theta = E->sx[m][1][node];
                    fi = E->sx[m][2][node];
                    r = E->sx[m][3][node];

                    distance = sqrt((theta - theta_center)*(theta - theta_center) +
                                    (fi - fi_center)*(fi - fi_center) +
                                    (r - r_center)*(r - r_center));

                    if (distance < radius)
                      E->T[m][node] += amp * exp(-1.0*distance/radius);
                }
  }
  else if (E->convection.tic_method == 3) {
    /* set up a linear temperature profile first */
    for(m=1;m<=E->sphere.caps_per_proc;m++)
      for(i=1;i<=noy;i++)
	for(j=1;j<=nox;j++)
	  for(k=1;k<=noz;k++) {
	    node=k+(j-1)*noz+(i-1)*nox*noz;
	    r1=E->sx[m][3][node];
	    E->T[m][node] = E->control.TBCbotval - (E->control.TBCtopval + E->control.TBCbotval)*(r1 - E->sphere.ri)/(E->sphere.ro - E->sphere.ri);
	  }

    /* This part put a temperature anomaly for whole mantle. The horizontal
       pattern of the anomaly is given by spherical harmonic ll & mm. */

    for (p=0; p<E->convection.number_of_perturbations; p++) {
      mm = E->convection.perturb_mm[p];
      ll = E->convection.perturb_ll[p];
      con = E->convection.perturb_mag[p];
      kk = E->convection.load_depth[p];

      if ( (kk < 1) || (kk >= gnoz) ) continue;

      if (E->parallel.me == 0)
	fprintf(stderr,"Initial temperature perturbation:  layer=%d  mag=%g  l=%d  m=%d\n", kk, con, ll, mm);

      for(m=1;m<=E->sphere.caps_per_proc;m++)
	for(i=1;i<=noy;i++)
	  for(j=1;j<=nox;j++)
            for(k=1;k<=noz;k++) {
	      node=k+(j-1)*noz+(i-1)*nox*noz;
	      t1=E->sx[m][1][node];
	      f1=E->sx[m][2][node];
	      r1=E->sx[m][3][node];
              E->T[m][node] += con*(cos(mm*f1)+sin(mm*f1))
                  *sin(M_PI*(r1-E->sphere.ri)/(E->sphere.ro-E->sphere.ri));
	  }
    }
  }

  temperatures_conform_bcs(E);

  return;
}


/* setup boundary node and element arrays for bookkeeping */

void regional_construct_boundary( struct All_variables *E)
{
  const int dims=E->mesh.nsd;

  int m, i, j, k, d, el, count;
  int isBoundary;
  int normalFlag[4];

  /* boundary = all - interior */
  int max_size = E->lmesh.elx*E->lmesh.ely*E->lmesh.elz
    - (E->lmesh.elx-2)*(E->lmesh.ely-2)*(E->lmesh.elz-2) + 1;

  for(m=1;m<=E->sphere.caps_per_proc;m++) {
    E->boundary.element[m] = (int *)malloc(max_size*sizeof(int));

    for(d=1; d<=dims; d++)
      E->boundary.normal[m][d] = (int *)malloc(max_size*sizeof(int));

  }

  for(m=1;m<=E->sphere.caps_per_proc;m++) {
    count = 1;
    for(k=1; k<=E->lmesh.ely; k++)
      for(j=1; j<=E->lmesh.elx; j++)
	for(i=1; i<=E->lmesh.elz; i++) {

	  isBoundary = 0;
	  for(d=1; d<=dims; d++)
	    normalFlag[d] = 0;

	  if((E->parallel.me_loc[1] == 0) && (j == 1)) {
	    isBoundary = 1;
	    normalFlag[1] = -1;
	  }

	  if((E->parallel.me_loc[1] == E->parallel.nprocx - 1)
	     && (j == E->lmesh.elx)) {
	    isBoundary = 1;
	    normalFlag[1] = 1;
	  }

	  if((E->parallel.me_loc[2] == 0) && (k == 1)) {
	    isBoundary = 1;
	    normalFlag[2] = -1;
	  }

	  if((E->parallel.me_loc[2] == E->parallel.nprocy - 1)
	     && (k == E->lmesh.ely)) {
	    isBoundary = 1;
	    normalFlag[2] = 1;
	  }

	  if((E->parallel.me_loc[3] == 0) && (i == 1)) {
	    isBoundary = 1;
	    normalFlag[3] = -1;
	  }

	  if((E->parallel.me_loc[3] == E->parallel.nprocz - 1)
	     && (i == E->lmesh.elz)) {
	    isBoundary = 1;
	    normalFlag[3] = 1;
	  }

	  if(isBoundary) {
	    el = i + (j-1)*E->lmesh.elz + (k-1)*E->lmesh.elz*E->lmesh.elx;
	    E->boundary.element[m][count] = el;
	    for(d=1; d<=dims; d++)
	      E->boundary.normal[m][d][count] = normalFlag[d];

	    ++count;
	  }

	} /* end for i, j, k */

    E->boundary.nel = count - 1;
  } /* end for m */
}