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_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;
}
}
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];
}
}
