C++ PrecalcShapeset::set_quad_order方法代码示例

static void old_projection(Element* e, int order, double2* proj, double* old[2])
{
  int mo2 = quad2d.get_max_order();
  int np = quad2d.get_num_points(mo2);

  for (unsigned int k = 0; k < e->nvert; k++) // loop over vertices
  {
    // vertex basis functions in all integration points
    double* vd;
    int index_v = ref_map_shapeset.get_vertex_index(k);
    ref_map_pss.set_active_shape(index_v);
    ref_map_pss.set_quad_order(mo2);
    vd = ref_map_pss.get_fn_values();

    for (int m = 0; m < 2; m++)   // part 0 or 1
      for (int j = 0; j < np; j++)
        old[m][j] += proj[k][m] * vd[j];

    for (int ii = 0; ii < order - 1; ii++)
    {
      // edge basis functions in all integration points
      double* ed;
      int index_e = ref_map_shapeset.get_edge_index(k,0,ii+2);
      ref_map_pss.set_active_shape(index_e);
      ref_map_pss.set_quad_order(mo2);
      ed = ref_map_pss.get_fn_values();

      for (int m = 0; m < 2; m++)  //part 0 or 1
        for (int j = 0; j < np; j++)
          old[m][j] += proj[e->nvert + k * (order-1) + ii][m] * ed[j];
    }
  }
}

void test_edge_rotation()
{
  info("Testing edge rotation...");
  int mode = shapeset.get_mode();
  int ne = mode ? 4 : 3;
  
  for (int ori = 0; ori <= 1; ori++)
  {
    for (int order = 0; order <= shapeset.get_max_order(); order++)
    {
      double *e01, *e02, *ee1, *ee2;
      precalc.set_active_shape(shapeset.get_edge_index(0, ori, order));
      precalc.set_quad_order(quad.get_edge_points(0));
      e01 = precalc.get_fn_values(0);
      if (nc > 1) e02 = precalc.get_fn_values(1);
      
      for (int e = 1; e < ne; e++)
      {
        precalc.set_active_shape(shapeset.get_edge_index(e, ori, order));
        precalc.set_quad_order(quad.get_edge_points(e));
        ee1 = precalc.get_fn_values(0);
        if (nc > 1) ee2 = precalc.get_fn_values(1);
        
        int np = quad.get_num_points(quad.get_edge_points(0));
        if (nc == 1)
        {
          for (int i = 0; i < np; i++)
            if (!eq(e01[i], ee1[i]))
            {
              info("order=%d, ori=%d, edge=%d -- not equal to edge 0", order, ori, e);
            }  
        }
        else
        {
          for (int i = 0; i < np; i++)
          {
            double x = rot[mode][e][0][0] * ee1[i] + rot[mode][e][0][1] * ee2[i];
            double y = rot[mode][e][1][0] * ee1[i] + rot[mode][e][1][1] * ee2[i];
            if (!eq(e01[i], x) || !eq(e02[i], y))
            {
              info("order=%d, ori=%d, edge=%d -- not equal to edge 0", order, ori, e);
              printf("x comp: 0-ta %g, %d-ta %g\n", e01[i], e, x);
              printf("y comp: 0-ta %g, %d-ta %g\n\n", e02[i], e, y);
            }  
          }
        }          
      }
    }
  }
}

void RefMap::calc_second_ref_map(int order)
{
  assert(quad_2d != NULL);
  int i, j, np = quad_2d->get_num_points(order);

  AUTOLA_OR(double3x2, k, np);
  memset(k, 0, k.size);
  ref_map_pss.force_transform(sub_idx, ctm);
  for (i = 0; i < nc; i++)
  {
    double *dxy, *dxx, *dyy;
    ref_map_pss.set_active_shape(indices[i]);
    ref_map_pss.set_quad_order(order, H2D_FN_ALL);
    dxx = ref_map_pss.get_dxx_values();
    dyy = ref_map_pss.get_dyy_values();
    dxy = ref_map_pss.get_dxy_values();
    for (j = 0; j < np; j++)
    {
      k[j][0][0] += coeffs[i][0] * dxx[j];
      k[j][0][1] += coeffs[i][1] * dxx[j];
      k[j][1][0] += coeffs[i][0] * dxy[j];
      k[j][1][1] += coeffs[i][1] * dxy[j];
      k[j][2][0] += coeffs[i][0] * dyy[j];
      k[j][2][1] += coeffs[i][1] * dyy[j];
    }
  }

  double3x2* mm = cur_node->second_ref_map[order] = new double3x2[np];
  double2x2* m = get_inv_ref_map(order);
  for (j = 0; j < np; j++)
  {
    double a, b;
    // coefficients in second derivative with respect to xx
    a = sqr(m[j][0][0])*k[j][0][0] + 2*m[j][0][0]*m[j][0][1]*k[j][1][0] + sqr(m[j][0][1])*k[j][2][0];
    b = sqr(m[j][0][0])*k[j][0][1] + 2*m[j][0][0]*m[j][0][1]*k[j][1][1] + sqr(m[j][0][1])*k[j][2][1];
    mm[j][0][0] = -(a * m[j][0][0] + b * m[j][1][0]); // du/dx
    mm[j][0][1] = -(a * m[j][0][1] + b * m[j][1][1]); // du/dy

    // coefficients in second derivative with respect to xy
    a = m[j][0][0]*m[j][1][0]*k[j][0][0] + (m[j][0][1]*m[j][1][0] + m[j][0][0]*m[j][1][1])*k[j][1][0] + m[j][0][1]*m[j][1][1]*k[j][2][0];
    b = m[j][0][0]*m[j][1][0]*k[j][0][1] + (m[j][0][1]*m[j][1][0] + m[j][0][0]*m[j][1][1])*k[j][1][1] + m[j][0][1]*m[j][1][1]*k[j][2][1];
    mm[j][1][0] = -(a * m[j][0][0] + b * m[j][1][0]); // du/dx
    mm[j][1][1] = -(a * m[j][0][1] + b * m[j][1][1]); // du/dy

    // coefficients in second derivative with respect to yy
    a = sqr(m[j][1][0])*k[j][0][0] + 2*m[j][1][0]*m[j][1][1]*k[j][1][0] + sqr(m[j][1][1])*k[j][2][0];
    b = sqr(m[j][1][0])*k[j][0][1] + 2*m[j][1][0]*m[j][1][1]*k[j][1][1] + sqr(m[j][1][1])*k[j][2][1];
    mm[j][2][0] = -(a * m[j][0][0] + b * m[j][1][0]); // du/dx
    mm[j][2][1] = -(a * m[j][0][1] + b * m[j][1][1]); // du/dy
  }
}

void RefMap::calc_phys_y(int order)
{
  // transform all y coordinates of the integration points
  int i, j, np = quad_2d->get_num_points(order);
  double* y = cur_node->phys_y[order] = new double[np];
  memset(y, 0, np * sizeof(double));
  ref_map_pss.force_transform(sub_idx, ctm);
  for (i = 0; i < nc; i++)
  {
    ref_map_pss.set_active_shape(indices[i]);
    ref_map_pss.set_quad_order(order);
    double* fn = ref_map_pss.get_fn_values();
    for (j = 0; j < np; j++)
      y[j] += coeffs[i][1] * fn[j];
  }
}

void RefMap::calc_inv_ref_map(int order)
{
  assert(quad_2d != NULL);
  int i, j, np = quad_2d->get_num_points(order);

  // construct jacobi matrices of the direct reference map for all integration points

  AUTOLA_OR(double2x2, m, np);
  memset(m, 0, m.size);
  ref_map_pss.force_transform(sub_idx, ctm);
  for (i = 0; i < nc; i++)
  {
    double *dx, *dy;
    ref_map_pss.set_active_shape(indices[i]);
    ref_map_pss.set_quad_order(order);
    ref_map_pss.get_dx_dy_values(dx, dy);
    for (j = 0; j < np; j++)
    {
      m[j][0][0] += coeffs[i][0] * dx[j];
      m[j][0][1] += coeffs[i][0] * dy[j];
      m[j][1][0] += coeffs[i][1] * dx[j];
      m[j][1][1] += coeffs[i][1] * dy[j];
    }
  }

  // calculate the jacobian and inverted matrix
  double trj = get_transform_jacobian();
  double2x2* irm = cur_node->inv_ref_map[order] = new double2x2[np];
  double* jac = cur_node->jacobian[order] = new double[np];
  for (i = 0; i < np; i++)
  {
    jac[i] = (m[i][0][0] * m[i][1][1] - m[i][0][1] * m[i][1][0]);
    double ij = 1.0 / jac[i];
    error_if(!finite(ij), "1/jac[%d] is infinity when calculating inv. ref. map for order %d (jac=%g)", i, order);
    assert_msg(ij == ij, "1/jac[%d] is NaN when calculating inv. ref. map for order %d (jac=%g)", i, order);

    // invert and transpose the matrix
    irm[i][0][0] =  m[i][1][1] * ij;
    irm[i][0][1] = -m[i][1][0] * ij;
    irm[i][1][0] = -m[i][0][1] * ij;
    irm[i][1][1] =  m[i][0][0] * ij;

    jac[i] *= trj;
  }
}

void RefMap::calc_tangent(int edge, int eo)
{
  int i, j;
  int np = quad_2d->get_num_points(eo);
  double3* tan = cur_node->tan[edge] = new double3[np];
  int a = edge, b = element->next_vert(edge);

  if (!element->is_curved())
  {
    // straight edges: the tangent at each point is just the edge length
    tan[0][0] = element->vn[b]->x - element->vn[a]->x;
    tan[0][1] = element->vn[b]->y - element->vn[a]->y;
    tan[0][2] = sqrt(sqr(tan[0][0]) + sqr(tan[0][1]));
    double inorm = 1.0 / tan[0][2];
    tan[0][0] *= inorm;
    tan[0][1] *= inorm;
    tan[0][2] *= (edge == 0 || edge == 2) ? ctm->m[0] : ctm->m[1];

    for (i = 1; i < np; i++)
      memcpy(tan+i, tan, sizeof(double3));
  }
  else
  {
    // construct jacobi matrices of the direct reference map at integration points along the edge
    static double2x2 m[15];
    assert(np <= 15);
    memset(m, 0, np*sizeof(double2x2));
    ref_map_pss.force_transform(sub_idx, ctm);
    for (i = 0; i < nc; i++)
    {
      double *dx, *dy;
      ref_map_pss.set_active_shape(indices[i]);
      ref_map_pss.set_quad_order(eo);
      ref_map_pss.get_dx_dy_values(dx, dy);
      for (j = 0; j < np; j++)
      {
        m[j][0][0] += coeffs[i][0] * dx[j];
        m[j][0][1] += coeffs[i][0] * dy[j];
        m[j][1][0] += coeffs[i][1] * dx[j];
        m[j][1][1] += coeffs[i][1] * dy[j];
      }
    }

    // multiply them by the vector of the reference edge
    double2* v1 = ref_map_shapeset.get_ref_vertex(a);
    double2* v2 = ref_map_shapeset.get_ref_vertex(b);
    double ex = (*v2)[0] - (*v1)[0];
    double ey = (*v2)[1] - (*v1)[1];
    for (i = 0; i < np; i++)
    {
      double3& t = tan[i];
      t[0] = m[i][0][0]*ex + m[i][0][1]*ey;
      t[1] = m[i][1][0]*ex + m[i][1][1]*ey;
      t[2] = sqrt(sqr(t[0]) + sqr(t[1]));
      double inorm = 1.0 / t[2];
      t[0] *= inorm;
      t[1] *= inorm;
      t[2] *= (edge == 0 || edge == 2) ? ctm->m[0] : ctm->m[1];
    }
  }
}

static void calc_bubble_projection(Element* e, Nurbs** nurbs, int order, double2* proj)
{
  ref_map_pss.set_active_element(e);

  int i, j, k;
  int mo2 = quad2d.get_max_order();
  int np = quad2d.get_num_points(mo2);
  int qo = e->is_quad() ? make_quad_order(order, order) : order;
  int nb = ref_map_shapeset.get_num_bubbles(qo);

  AUTOLA_OR(double2, fn, np);
  memset(fn, 0, sizeof(double2) * np);

  double* rhside[2];
  double* old[2];
  for (i = 0; i < 2; i++) {
    rhside[i] = new double[nb];
    old[i] = new double[np];
    memset(rhside[i], 0, sizeof(double) * nb);
    memset(old[i], 0, sizeof(double) * np);
  }

  // compute known part of projection (vertex and edge part)
  old_projection(e, order, proj, old);

  // fn values of both components of nonpolynomial function
  double3* pt = quad2d.get_points(mo2);
  for (j = 0; j < np; j++)  // over all integration points
  {
    double2 a;
    a[0] = ctm.m[0] * pt[j][0] + ctm.t[0];
    a[1] = ctm.m[1] * pt[j][1] + ctm.t[1];
    calc_ref_map(e, nurbs, a[0], a[1], fn[j]);
  }

  double2* result = proj + e->nvert + e->nvert * (order - 1);
  for (k = 0; k < 2; k++)
  {
    for (i = 0; i < nb; i++) // loop over bubble basis functions
    {
      // bubble basis functions in all integration points
      double *bfn;
      int index_i = ref_map_shapeset.get_bubble_indices(qo)[i];
      ref_map_pss.set_active_shape(index_i);
      ref_map_pss.set_quad_order(mo2);
      bfn = ref_map_pss.get_fn_values();

      for (j = 0; j < np; j++) // over all integration points
        rhside[k][i] += pt[j][2] * (bfn[j] * (fn[j][k] - old[k][j]));
    }

    // solve
    if (e->nvert == 3)
      cholsl(bubble_proj_matrix_tri, nb, bubble_tri_p, rhside[k], rhside[k]);
    else
      cholsl(bubble_proj_matrix_quad, nb, bubble_quad_p, rhside[k], rhside[k]);

    for (i = 0; i < nb; i++)
      result[i][k] = rhside[k][i];
  }

  for (i = 0; i < 2; i++) {
    delete [] rhside[i];
    delete [] old[i];
  }
}