smfl.c

The Free Finite Element Package is a library which contains numerical methods required when working

/*--------------------------------------------------------------------------

Free Finite Element Package                             
Copyright (c) 2002-2006 by Joerg Frochte
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:

1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
----------------------------------------------------------------------------*/

#include "smfl.h"

/** 
 * \file 
 * \brief Functions to create and modify a mesh/grid  
 * \author Joerg Frochte 
 *
 * , based on vecl 
 *
*/

static inline int smfl_pair_equal (MEML_INT * a, MEML_INT * b)
{
  if ((a[0] == b[0]) || (a[0] == b[1]))
    {
      if ((a[1] == b[0]) || (a[1] == b[1]))
	return (MEML_TRUE);
      else
	return (MEML_FALSE);
    }
  else
    return (MEML_FALSE);
}


static inline MEML_INT smfl_in_liste (MEML_INT a, MEML_INT b,
				      MEML_INT ** edges,
				      MEML_INT number_of_edges,
				      MEML_INT * inout)
{
  MEML_INT i;

  for (i = 0; i < number_of_edges; i++)
    {
      if (edges[i][0] == -1)
	{
	  (*inout) = 1;
	  return (i);
	}
      else if (edges[i][0] == a)
	{
	  if (edges[i][1] == b)
	    {
	      (*inout) = 0;
	      return (i);
	    }
	}
    }

  return (-1);
}

static inline MEML_INT smfl_in_liste_fast (MEML_INT a, MEML_INT b,
					   MEML_INT ** edges, 
					   MEML_INT number_of_edges)
{
    MEML_INT suchpunkt = number_of_edges/2;
    MEML_INT schrittweite = number_of_edges/4;

    if (schrittweite<1)
	schrittweite = 1;
    
    while (1)
    {
	if (edges[suchpunkt][0] == a)
	{
	    if (suchpunkt != 0)
	    {
		while (edges[suchpunkt-1][0] == a)
		{
		    suchpunkt--;
		    if (suchpunkt==0)
			break;
		}
	    }
	    
	    while (edges[suchpunkt][1] != b)
		suchpunkt++;
	    
	    return(suchpunkt);
	}
	else if (edges[suchpunkt][0] < a)
	{
	    suchpunkt = suchpunkt + schrittweite;
	    schrittweite = schrittweite/2;
	    if (schrittweite<1)
		schrittweite = 1;
	}
	else
	{
	    suchpunkt = suchpunkt - schrittweite;
	    schrittweite = schrittweite/2;
	    if (schrittweite<1)
		schrittweite = 1;
	}
    }
}


TRIANGLE smfl_get_triangle (MEML_INT w_triangle, MEML_INT * triangle)
{

  TRIANGLE temp;

  /* Zugriff klar machen 
     in Triangles stehen die Punkte die ein Dreieck ausmachen 
     also z.B. triangle= [ 1 17 5]
     Um nun den Punkt 17 zu kriegen muss man bei 2*17 und 2*17+1
     nachschlagen. */

  temp.p[0] = triangle[3 * w_triangle];
  temp.p[1] = triangle[3 * w_triangle + 1];
  temp.p[2] = triangle[3 * w_triangle + 2];

  return (temp);
}

inline T_POINTS smfl_get_t_points (TRIANGLE triangle, MEML_FLOAT * points)
{

  T_POINTS temp;

  temp.a1[0] = points[2 * (triangle.p[0] - 1)];
  temp.a1[1] = points[2 * (triangle.p[0] - 1) + 1];

  temp.a2[0] = points[2 * (triangle.p[1] - 1)];
  temp.a2[1] = points[2 * (triangle.p[1] - 1) + 1];

  temp.a3[0] = points[2 * (triangle.p[2] - 1)];
  temp.a3[1] = points[2 * (triangle.p[2] - 1) + 1];

  return (temp);


}

static void triangles2edges (MESH * new_mesh)
{
  MEML_INT kanten[3][2], i, j, temp, position, l;
  TRIANGLE dreieck;
  INDEXARRAY *wohin;
  INDEXARRAY *e2dreieck;
  INDEXARRAY *kanten_punkt1;
  INDEXARRAY *kanten_punkt2;
  INDEXARRAY *kanten_punkt2_temp;
  INDEXARRAY *e2dreieck_temp;
  MEML_INT anzahl_kanten=0;

  /* speicher organisieren */
  new_mesh->edges = (MEML_INT **) calloc (new_mesh->number_of_edges,
					  sizeof (MEML_INT *));

  new_mesh->edge2triangle = (MEML_INT **) calloc (new_mesh->number_of_edges,
						  sizeof (MEML_INT *));
  new_mesh->triangle2edge =
    (MEML_INT **) calloc (new_mesh->number_of_triangles, sizeof (MEML_INT *));

  for (i = 0; i < new_mesh->number_of_edges; i++)
    {
      new_mesh->edges[i] = (MEML_INT *) calloc (2, sizeof (MEML_INT));
      /* -1 als abbruchbedingung fuer spaeter */
      new_mesh->edges[i][0] = -1;

      new_mesh->edge2triangle[i] = (MEML_INT *) calloc (2, sizeof (MEML_INT));
      new_mesh->edge2triangle[i][0] = -1;
      new_mesh->edge2triangle[i][1] = -1;
    }

  for (i = 0; i < new_mesh->number_of_triangles; i++)
    {
      new_mesh->triangle2edge[i] = (MEML_INT *) calloc (3, sizeof (MEML_INT));
      for (j = 0; j < 3; j++)
	new_mesh->triangle2edge[i][j] = -1;
    }

  kanten_punkt1 = meml_indexarray_new (new_mesh->number_of_triangles * 3);
  kanten_punkt2 = meml_indexarray_new (new_mesh->number_of_triangles * 3);
  e2dreieck = meml_indexarray_new (new_mesh->number_of_triangles * 3);
  kanten_punkt2_temp =
    meml_indexarray_new (new_mesh->number_of_triangles * 3);
  e2dreieck_temp = meml_indexarray_new (new_mesh->number_of_triangles * 3);

  /* getting the edges */
  /* numbering starts with zero */
  /* edge2triangle and triangle2edge are calculated */
  for (i = 0; i < new_mesh->number_of_triangles; i++)
    {
      dreieck = smfl_get_triangle (i, new_mesh->triangles->data);

      kanten[0][0] = dreieck.p[0];
      kanten[0][1] = dreieck.p[1];

      kanten[1][0] = dreieck.p[0];
      kanten[1][1] = dreieck.p[2];

      kanten[2][0] = dreieck.p[1];
      kanten[2][1] = dreieck.p[2];

      /* kanten so sortieren, das der kleinere knoten immer vorne steht */
      for (j = 0; j < 3; j++)
	{
	  if (kanten[j][0] > kanten[j][1])
	    {
	      temp = kanten[j][0];
	      kanten[j][0] = kanten[j][1];
	      kanten[j][1] = temp;
	    }
	}

      for (j = 0; j < 3; j++)
	{
	  kanten_punkt1->data[i * 3 + j] = kanten[j][0];
	  kanten_punkt2->data[i * 3 + j] = kanten[j][1];
	  e2dreieck->data[i * 3 + j] = i;
	}
    }

  wohin = meml_indexarray_sort (kanten_punkt1);

  for (i = 0; i < kanten_punkt2->dim; i++)
    {
      kanten_punkt2_temp->data[i] = kanten_punkt2->data[wohin->data[i]];
      e2dreieck_temp->data[i] = e2dreieck->data[wohin->data[i]];
    }

  meml_indexarray_free (wohin);
  meml_indexarray_free (kanten_punkt2);
  meml_indexarray_free (e2dreieck);

  position = 0;

  for (i = 0; i < 3 * new_mesh->number_of_triangles; i++)
    {
      if (kanten_punkt2_temp->data[i] != -1)
	{
	  /* in liste eintrage */
	  new_mesh->edges[position][0] = kanten_punkt1->data[i];
	  new_mesh->edges[position][1] = kanten_punkt2_temp->data[i];
	  anzahl_kanten++;
	  
	  new_mesh->edge2triangle[position][0] = e2dreieck_temp->data[i];

	  l = 0;
	  while (new_mesh->
		 triangle2edge[new_mesh->edge2triangle[position][0]][l] != -1)
	    l++;
	  new_mesh->triangle2edge[new_mesh->
				  edge2triangle[position][0]][l] = position;

	  j = i + 1;

	  if (j < kanten_punkt1->dim)
	    {
	      while (kanten_punkt1->data[i] == kanten_punkt1->data[j])
		{
		  if (kanten_punkt2_temp->data[i] ==
		      kanten_punkt2_temp->data[j])
		    {
		      new_mesh->edge2triangle[position][1] =
			e2dreieck_temp->data[j];
		      kanten_punkt2_temp->data[j] = -1;

		      l = 0;
		      while (new_mesh->
			     triangle2edge[new_mesh->
					   edge2triangle[position][1]][l]
			     != -1)
			l++;
		      new_mesh->triangle2edge[new_mesh->
					      edge2triangle[position][1]]
			[l] = position;

		      break;
		    }
		  if (j + 1 < kanten_punkt1->dim)
		    j = j + 1;
		  else
		    break;
		}
	    }
	  position = position + 1;
	}
    }

  /* ueberfluessige kanten wegschmeissen */
  
  for (i = anzahl_kanten; i < new_mesh->number_of_edges; i++)
    {
      free(new_mesh->edge2triangle[i]);
      free(new_mesh->edges[i]);
    }

  /* speicher der ueberfluessigen kanten freigeben */
  new_mesh->number_of_edges = anzahl_kanten;

  new_mesh->edges = realloc (new_mesh->edges,new_mesh->number_of_edges * sizeof (MEML_INT *));


  new_mesh->number_of_boundary_edges = 0;

  for (i = 0; i < new_mesh->number_of_edges; i++)
    {
      if (new_mesh->edge2triangle[i][1] == -1)
	new_mesh->number_of_boundary_edges++;
    }

  new_mesh->boundary_edges =
    (MEML_INT *) calloc (new_mesh->number_of_boundary_edges,
			 sizeof (MEML_INT));

  j = 0;
  for (i = 0; i < new_mesh->number_of_edges; i++)
    {
      if (new_mesh->edge2triangle[i][1] == -1)
	{
	  new_mesh->boundary_edges[j] = i;
	  j++;
	}
    }

  meml_indexarray_free (kanten_punkt1);
  meml_indexarray_free (kanten_punkt2_temp);
  meml_indexarray_free (e2dreieck_temp);
}

static void calculating_triangles_adof (MESH * new_mesh)
{
  int *used;
  MEML_INT i, kante, temp;
  MEML_FLOAT x1, y1, x2, y2;
  TRIANGLE dreieck;
  MEML_INT pair[3][2];
  MEML_INT check[2];

  if (new_mesh->degrees_of_freedom_per_triangle == 3)
    {
      new_mesh->triangles_adof = NULL;
      new_mesh->additional_degrees_of_freedom = meml_vector_new (1);
    }
  else if (new_mesh->degrees_of_freedom_per_triangle == 6)
    {
      used = (int *) calloc (new_mesh->number_of_triangles, sizeof (int));

      new_mesh->triangles_adof =
	(MEML_INT **) calloc (new_mesh->number_of_triangles + 1,
			      sizeof (MEML_INT *));

      for (i = 0; i < new_mesh->number_of_triangles; i++)
	{
	  new_mesh->triangles_adof[i] =
	    (MEML_INT *) calloc (3, sizeof (MEML_INT));
	}
      new_mesh->additional_degrees_of_freedom =
	meml_vector_new (new_mesh->number_of_edges * 2);

      for (i = 0; i < new_mesh->number_of_edges; i++)
	{
	  x1 = new_mesh->points->data[2 * (new_mesh->edges[i][0] - 1)];
	  y1 = new_mesh->points->data[2 * (new_mesh->edges[i][0] - 1) + 1];

	  x2 = new_mesh->points->data[2 * (new_mesh->edges[i][1] - 1)];
	  y2 = new_mesh->points->data[2 * (new_mesh->edges[i][1] - 1) + 1];

	  new_mesh->additional_degrees_of_freedom->data[2 * i] =
	    x1 + (x2 - x1) / 2;
	  new_mesh->additional_degrees_of_freedom->data[2 * i + 1] =
	    y1 + (y2 - y1) / 2;

	  /* die adof werden von 0 bis new_mesh->number_of_edges-1 nummeriert.
	     wenn man sie in eine steifigkeitsmatrix einbringen will 
	     muss man also number_of_points + adof rechnen... */
	  new_mesh->triangles_adof[new_mesh->
				   edge2triangle[i][0]][used[new_mesh->
							     edge2triangle
							     [i][0]]] = i;
	  used[new_mesh->edge2triangle[i][0]]++;

	  if (new_mesh->edge2triangle[i][1] != -1)
	    {
	      new_mesh->triangles_adof[new_mesh->
				       edge2triangle[i][1]][used[new_mesh->
								 edge2triangle
								 [i][1]]] = i;
	      used[new_mesh->edge2triangle[i][1]]++;
	    }
	}

      free (used);

      /* sortiere die adof im dreieck so, 
         dass Sie zum assemblierungsprossez passen */
      for (i = 0; i < new_mesh->number_of_triangles; i++)
	{
	  dreieck = smfl_get_triangle (i, new_mesh->triangles->data);

	  pair[0][0] = dreieck.p[0];
	  pair[0][1] = dreieck.p[1];

	  pair[1][0] = dreieck.p[1];
	  pair[1][1] = dreieck.p[2];

	  pair[2][0] = dreieck.p[0];
	  pair[2][1] = dreieck.p[2];

	  kante = new_mesh->triangles_adof[i][0];
	  check[0] = new_mesh->edges[kante][0];
	  check[1] = new_mesh->edges[kante][1];

	  if (smfl_pair_equal (pair[0], check) != MEML_TRUE)
	    {
	      temp = new_mesh->triangles_adof[i][2];
	      new_mesh->triangles_adof[i][2] = new_mesh->triangles_adof[i][0];
	      new_mesh->triangles_adof[i][0] = temp;

	      kante = new_mesh->triangles_adof[i][0];
	      check[0] = new_mesh->edges[kante][0];
	      check[1] = new_mesh->edges[kante][1];

	      if (smfl_pair_equal (pair[0], check) != MEML_TRUE)
		{
		  temp = new_mesh->triangles_adof[i][1];
		  new_mesh->triangles_adof[i][1] =
		    new_mesh->triangles_adof[i][0];
		  new_mesh->triangles_adof[i][0] = temp;
		}
	    }

	  kante = new_mesh->triangles_adof[i][1];
	  check[0] = new_mesh->edges[kante][0];
	  check[1] = new_mesh->edges[kante][1];

	  if (smfl_pair_equal (pair[1], check) != MEML_TRUE)
	    {
	      temp = new_mesh->triangles_adof[i][2];
	      new_mesh->triangles_adof[i][2] = new_mesh->triangles_adof[i][1];
	      new_mesh->triangles_adof[i][1] = temp;
	    }
	}

    }

  new_mesh->number_of_adof = new_mesh->additional_degrees_of_freedom->dim / 2;
}

static void calculating_points2triangle (MESH * new_mesh)
{
  int *used;
  MEML_INT i, j;
  TRIANGLE dreieck;

  used = (int *) calloc (new_mesh->number_of_points, sizeof (int));

  for (i = 0; i < new_mesh->number_of_triangles; i++)
    {
      dreieck = smfl_get_triangle (i, new_mesh->triangles->data);
      for (j = 0; j < 3; j++)
	used[dreieck.p[j] - 1]++;
    }

  new_mesh->point2triangle =
    (INDEXARRAY **) calloc (new_mesh->number_of_points,
			    sizeof (INDEXARRAY *));

  for (i = 0; i < new_mesh->number_of_points; i++)
    new_mesh->point2triangle[i] = meml_indexarray_new (used[i]);

  free (used);

  used = (int *) calloc (new_mesh->number_of_points, sizeof (int));

  for (i = 0; i < new_mesh->number_of_triangles; i++)
    {
      dreieck = smfl_get_triangle (i, new_mesh->triangles->data);
      for (j = 0; j < 3; j++)
	{
	  new_mesh->point2triangle[dreieck.p[j] -
				   1]->data[used[dreieck.p[j] - 1]] = i;
	  used[dreieck.p[j] - 1]++;
	}
    }

  free (used);
}

static void getting_neighbours (MESH * new_mesh)