<a name="general"></a>
<h3>General</h3>
<ol>
+
+ <li> New: 2nd derivatives are implemented for polynomials_BDM in 3D.
+ <br>
+ (Alistair Bentley, 2015/10/27)
+ </li>
+
<li> New: Preliminary support for parallel, adaptive, geometric multigrid is
now in place with changes to MGConstrainedDoFs (many new functions), MGTransfer,
MGTools::extract_inner_interface_dofs, MGTransferPrebuilt,
(Alistair Bentley, 2015/10/24)
</li>
- <li> New: Triangulation::set_all_manifold_ids_on_boundary(boundary_id, manifold_id)
+ <li> New: Triangulation::set_all_manifold_ids_on_boundary(boundary_id, manifold_id)
which sets the manifold_id for all parts of the boundary with a given boundary_id.
<br>
(Alberto Sartori, 2015/10/22)
*</dl>
*
*
- * @todo Second derivatives in 3D are missing.
*
* @ingroup Polynomials
* @author Guido Kanschat
}
if (grad_grads.size() != 0)
{
- Assert(false,ExcNotImplemented());
+ grad_grads[start][0][0][0] = 0.;
+ grad_grads[start][0][0][1] = monovali[1][2]*monovalk[2][0];
+ grad_grads[start][0][0][2] = monovali[1][1]*monovalk[2][1];
+ grad_grads[start][0][1][0] = monovali[1][2]*monovalk[2][0];
+ grad_grads[start][0][1][1] = unit_point(0)*monovali[1][3]*monovalk[2][0];
+ grad_grads[start][0][1][2] = unit_point(0)*monovali[1][2]*monovalk[2][1];
+ grad_grads[start][0][2][0] = monovali[1][1]*monovalk[2][1];
+ grad_grads[start][0][2][1] = unit_point(0)*monovali[1][2]*monovalk[2][1];
+ grad_grads[start][0][2][2] = unit_point(0)*monovali[1][1]*monovalk[2][2];
+ grad_grads[start][1][0][0] = 0.;
+ grad_grads[start][1][0][1] = 0.;
+ grad_grads[start][1][0][2] = 0.;
+ grad_grads[start][1][1][0] = 0.;
+ grad_grads[start][1][1][1] = -monovali[1][2]*monovalk[2][0];
+ grad_grads[start][1][1][2] = -monovali[1][1]*monovalk[2][1];
+ grad_grads[start][1][2][0] = 0.;
+ grad_grads[start][1][2][1] = -monovali[1][1]*monovalk[2][1];
+ grad_grads[start][1][2][2] = -monovali[1][0]*monovalk[2][2];
+ grad_grads[start][2][0][0] = 0.;
+ grad_grads[start][2][0][1] = 0.;
+ grad_grads[start][2][0][2] = 0.;
+ grad_grads[start][2][1][0] = 0.;
+ grad_grads[start][2][1][1] = 0.;
+ grad_grads[start][2][1][2] = 0.;
+ grad_grads[start][2][2][0] = 0.;
+ grad_grads[start][2][2][1] = 0.;
+ grad_grads[start][2][2][2] = 0.;
+
+ grad_grads[start+1][0][0][0] = 0.;
+ grad_grads[start+1][0][0][1] = 0.;
+ grad_grads[start+1][0][0][2] = 0.;
+ grad_grads[start+1][0][1][0] = 0.;
+ grad_grads[start+1][0][1][1] = 0.;
+ grad_grads[start+1][0][1][2] = 0.;
+ grad_grads[start+1][0][2][0] = 0.;
+ grad_grads[start+1][0][2][1] = 0.;
+ grad_grads[start+1][0][2][2] = 0.;
+ grad_grads[start+1][1][0][0] = unit_point(1)*monovali[2][1]*monovalk[0][2];
+ grad_grads[start+1][1][0][1] = monovali[2][1]*monovalk[0][1];
+ grad_grads[start+1][1][0][2] = unit_point(1)*monovali[2][2]*monovalk[0][1];
+ grad_grads[start+1][1][1][0] = monovalk[0][1]*monovali[2][1];
+ grad_grads[start+1][1][1][1] = 0.;
+ grad_grads[start+1][1][1][2] = monovalk[0][0]*monovali[2][2];
+ grad_grads[start+1][1][2][0] = unit_point(1)*monovalk[0][1]*monovali[2][2];
+ grad_grads[start+1][1][2][1] = monovalk[0][0]*monovali[2][2];
+ grad_grads[start+1][1][2][2] = unit_point(1)*monovalk[0][0]*monovali[2][3];
+ grad_grads[start+1][2][0][0] = -monovalk[0][2]*monovali[2][0];
+ grad_grads[start+1][2][0][1] = 0.;
+ grad_grads[start+1][2][0][2] = -monovalk[0][1]*monovali[2][1];
+ grad_grads[start+1][2][1][0] = 0.;
+ grad_grads[start+1][2][1][1] = 0.;
+ grad_grads[start+1][2][1][2] = 0.;
+ grad_grads[start+1][2][2][0] = -monovalk[0][1]*monovali[2][1];
+ grad_grads[start+1][2][2][1] = 0.;
+ grad_grads[start+1][2][2][2] = -monovalk[0][0]*monovali[2][2];
+
+ grad_grads[start+2][0][0][0] = -monovali[0][2]*monovalk[1][0];
+ grad_grads[start+2][0][0][1] = -monovali[0][1]*monovalk[1][1];
+ grad_grads[start+2][0][0][2] = 0.;
+ grad_grads[start+2][0][1][0] = -monovali[0][1]*monovalk[1][1];
+ grad_grads[start+2][0][1][1] = -monovali[0][0]*monovalk[1][2];
+ grad_grads[start+2][0][1][2] = 0.;
+ grad_grads[start+2][0][2][0] = 0.;
+ grad_grads[start+2][0][2][1] = 0.;
+ grad_grads[start+2][0][2][2] = 0.;
+ grad_grads[start+2][1][0][0] = 0.;
+ grad_grads[start+2][1][0][1] = 0.;
+ grad_grads[start+2][1][0][2] = 0.;
+ grad_grads[start+2][1][1][0] = 0.;
+ grad_grads[start+2][1][1][1] = 0.;
+ grad_grads[start+2][1][1][2] = 0.;
+ grad_grads[start+2][1][2][0] = 0.;
+ grad_grads[start+2][1][2][1] = 0.;
+ grad_grads[start+2][1][2][2] = 0.;
+ grad_grads[start+2][2][0][0] = unit_point(2)*monovali[0][3]*monovalk[1][0];
+ grad_grads[start+2][2][0][1] = unit_point(2)*monovali[0][2]*monovalk[1][1];
+ grad_grads[start+2][2][0][2] = monovali[0][2]*monovalk[1][0];
+ grad_grads[start+2][2][1][0] = unit_point(2)*monovali[0][2]*monovalk[1][1];
+ grad_grads[start+2][2][1][1] = unit_point(2)*monovali[0][1]*monovalk[1][2];
+ grad_grads[start+2][2][1][2] = monovali[0][1]*monovalk[1][1];
+ grad_grads[start+2][2][2][0] = monovali[0][2]*monovalk[1][0];
+ grad_grads[start+2][2][2][1] = monovali[0][1]*monovalk[1][1];
+ grad_grads[start+2][2][2][2] = 0.;
+
}
}
Assert(start == n_pols, ExcInternalError());
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2010 - 2014 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+// Tests 3D polynomials_BDM grad grad at a collection of points on the unit square
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/job_identifier.h>
+#include <deal.II/base/tensor.h>
+#include <deal.II/base/polynomials_bdm.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <vector>
+#include <iomanip>
+#include <fstream>
+
+using namespace std;
+
+template <int dim>
+void plot(const PolynomialsBDM<dim> &poly)
+{
+
+ const PolynomialSpace<dim> legendre_poly_space = Polynomials::Legendre::generate_complete_basis(poly.degree());
+
+ const Point<3> p0(0,0,0);
+ const Point<3> p1(0.25,0.5,0.75);
+ const Point<3> p2(0.75,0.5,0.25);
+ const Point<3> p3(0.75,0.25,0.5);
+ const Point<3> p4(1.0,1.0,1.0);
+
+ std::vector<Point<3> > points;
+ points.push_back(p0);
+ points.push_back(p1);
+ points.push_back(p2);
+ points.push_back(p3);
+ points.push_back(p4);
+
+ std::vector<Tensor<1,dim> > values;
+ std::vector<Tensor<2,dim> > grads;
+ std::vector<Tensor<3,dim> > grads2(poly.n());
+ std::vector<Tensor<4,dim> > thirds;
+ std::vector<Tensor<5,dim> > fourths;
+
+ const unsigned int n_sub = legendre_poly_space.n();
+
+ for (unsigned int k=0; k<points.size(); ++k)
+ {
+ if (k%(poly.degree()+4) == 0)
+ deallog << "BDM" << poly.degree() << '<' << dim << '>' << std::endl;
+
+ unsigned int start = dim*n_sub;
+
+ deallog << "BDM" << poly.degree() << '<' << dim << '>'
+ << points[k] << std::endl;
+ poly.compute(points[k], values, grads, grads2, thirds, fourths);
+
+ for (unsigned int i=0; i<poly.degree()+1; ++i,start+=dim)
+ for (unsigned int j=0; j < dim; ++j)
+ {
+ for (unsigned int d1=0; d1<dim; ++d1)
+ for (unsigned int d2=0; d2<dim; ++d2)
+ for (unsigned int d3=0; d3<dim; ++d3)
+ deallog << '\t' << grads2[start+j][d1][d2][d3];
+ }
+ deallog << std::endl;
+ }
+}
+
+int main()
+{
+ const std::string logname = "output";
+ std::ofstream logfile(logname.c_str());
+ deallog << std::setprecision(3);
+ deallog.attach(logfile);
+ deallog.depth_console(0);
+ deallog.threshold_double(1.e-10);
+
+
+ PolynomialsBDM<3> p31(1);
+ PolynomialsBDM<3> p32(2);
+ PolynomialsBDM<3> p33(3);
+
+ plot(p31);
+ plot(p32);
+ plot(p33);
+}
--- /dev/null
+
+DEAL::BDM1<3>
+DEAL::BDM1<3>0.00 0.00 0.00
+DEAL:: 0 0 1.00 0 0 0 1.00 0 0 0 0 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 0 0 0 0 0 -1.00 0 0 0 -1.00 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 0 0 2.00 0 0
+DEAL::BDM1<3>0.250 0.500 0.750
+DEAL:: 0 0 1.00 0 0 0 1.00 0 0 0 0 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 0 0 0 0 0 -1.00 0 0 0 -1.00 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 0 0 2.00 0 0
+DEAL::BDM1<3>0.750 0.500 0.250
+DEAL:: 0 0 1.00 0 0 0 1.00 0 0 0 0 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 0 0 0 0 0 -1.00 0 0 0 -1.00 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 0 0 2.00 0 0
+DEAL::BDM1<3>0.750 0.250 0.500
+DEAL:: 0 0 1.00 0 0 0 1.00 0 0 0 0 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 0 0 0 0 0 -1.00 0 0 0 -1.00 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 0 0 2.00 0 0
+DEAL::BDM1<3>1.00 1.00 1.00
+DEAL:: 0 0 1.00 0 0 0 1.00 0 0 0 0 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 0 0 0 0 0 -1.00 0 0 0 -1.00 0 0 0 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0 1.00 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 2.00 0 0 0 0 0 0 0 0 0 -2.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 0 0 0 2.00 0 0
+DEAL::BDM2<3>
+DEAL::BDM2<3>0.00 0.00 0.00
+DEAL:: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+DEAL::BDM2<3>0.250 0.500 0.750
+DEAL:: 0 0 1.50 0 0 0 1.50 0 0.500 0 0 0 0 0 -1.50 0 -1.50 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0.500 0 0.500 0 0 0 0 0 -1.50 0 -0.500 0 0 0 -0.500 0 0 0 -1.00 0 -1.00 -0.500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.50 1.00 0 1.00 0 0 1.50 1.00 1.50 0 0.500 1.00 0.500 0 0 0 0 0 -1.50 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.50 1.00 1.50 0 0.500 1.00 0.500 0 0 0 -1.50 0 0 0 -1.50 0 -0.500 -1.00 -0.500 0 -0.500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.50 1.00 1.50 0 0.500 1.00 0.500 0 0 3.00 0 3.00 1.50 0 0 0 0 0 0 0 0 -3.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.50 0 4.50 3.00 0 0 0 0 0 0 0 0 -4.50 -1.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.50 0 1.50 0 0 0 1.50 0 0
+DEAL::BDM2<3>0.750 0.500 0.250
+DEAL:: 0 0 0.500 0 0 0 0.500 0 1.50 0 0 0 0 0 -0.500 0 -0.500 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 1.50 0 1.50 0 0 0 0 0 -0.500 0 -1.50 0 0 0 -1.50 0 0 0 -1.00 0 -1.00 -1.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 1.00 0 1.00 0 0 0.500 1.00 0.500 0 1.50 1.00 1.50 0 0 0 0 0 -0.500 -1.00 0 -1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 1.00 0.500 0 1.50 1.00 1.50 0 0 0 -0.500 0 0 0 -0.500 0 -1.50 -1.00 -1.50 0 -1.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 1.00 0.500 0 1.50 1.00 1.50 0 0 3.00 0 3.00 4.50 0 0 0 0 0 0 0 0 -3.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.50 0 1.50 3.00 0 0 0 0 0 0 0 0 -1.50 -4.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.50 0 4.50 0 0 0 4.50 0 0
+DEAL::BDM2<3>0.750 0.250 0.500
+DEAL:: 0 0 1.00 0 0 0 1.00 0 1.50 0 0 0 0 0 -1.00 0 -1.00 -0.500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 1.50 0 1.50 0 0 0 0 0 -1.00 0 -1.50 0 0 0 -1.50 0 0 0 -0.500 0 -0.500 -1.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0.500 0 0.500 0 0 1.00 0.500 1.00 0 1.50 0.500 1.50 0 0 0 0 0 -1.00 -0.500 0 -0.500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0.500 1.00 0 1.50 0.500 1.50 0 0 0 -1.00 0 0 0 -1.00 0 -1.50 -0.500 -1.50 0 -1.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.00 0.500 1.00 0 1.50 0.500 1.50 0 0 1.50 0 1.50 4.50 0 0 0 0 0 0 0 0 -1.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.00 0 3.00 1.50 0 0 0 0 0 0 0 0 -3.00 -4.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.00 0 4.50 0 0 0 4.50 0 0
+DEAL::BDM2<3>1.00 1.00 1.00
+DEAL:: 0 0 2.00 0 0 0 2.00 0 2.00 0 0 0 0 0 -2.00 0 -2.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 2.00 0 2.00 0 0 0 0 0 -2.00 0 -2.00 0 0 0 -2.00 0 0 0 -2.00 0 -2.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 2.00 0 2.00 0 0 2.00 2.00 2.00 0 2.00 2.00 2.00 0 0 0 0 0 -2.00 -2.00 0 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 2.00 2.00 0 2.00 2.00 2.00 0 0 0 -2.00 0 0 0 -2.00 0 -2.00 -2.00 -2.00 0 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.00 2.00 2.00 0 2.00 2.00 2.00 0 0 6.00 0 6.00 6.00 0 0 0 0 0 0 0 0 -6.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.00 0 6.00 6.00 0 0 0 0 0 0 0 0 -6.00 -6.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.00 0 6.00 0 0 0 6.00 0 0
+DEAL::BDM3<3>
+DEAL::BDM3<3>0.00 0.00 0.00
+DEAL:: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+DEAL::BDM3<3>0.250 0.500 0.750
+DEAL:: 0 0 1.69 0 0 0 1.69 0 1.12 0 0 0 0 0 -1.69 0 -1.69 -2.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.750 0.188 0 0.188 0 0 0 0 0 -1.12 0 -0.188 0 0 0 -0.188 0 0 0 -0.750 0 -0.750 -0.750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.25 0.750 0 0.750 0 0 1.12 1.50 1.12 0 0.750 1.50 0.750 0.500 0 0 0 0 -1.12 -1.50 0 -1.50 -0.500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.50 0.750 0.500 0.750 0 0.125 0.500 0.125 0 -1.12 0 -0.750 0 0 0 -0.750 0 -0.125 -0.500 -0.500 0 -0.500 -0.125 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.50 0.500 1.50 0.750 0.500 0.500 0.500 0 0 2.25 0.750 2.25 1.12 0.750 0.750 0.750 0 0 0 0 0 -2.25 -0.750 0 -0.750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.69 2.25 1.69 0 1.12 2.25 1.12 0.750 0 0 -1.69 0 0 0 -1.69 0 -1.12 -0.750 -0.188 0 -0.188 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.25 1.12 0.750 1.12 0 0.188 0.750 0.188 0 0 3.00 0 3.00 3.00 0 0 0 0 0 0 0 0 -3.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.75 0 6.75 9.00 0 0 0 0 0 0 0 0 -6.75 -0.750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.50 0 0.750 0 0 0 0.750 0 0
+DEAL::BDM3<3>0.750 0.500 0.250
+DEAL:: 0 0 0.188 0 0 0 0.188 0 1.12 0 0 0 0 0 -0.188 0 -0.188 -0.750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.25 1.69 0 1.69 0 0 0 0 0 -1.12 0 -1.69 0 0 0 -1.69 0 0 0 -0.750 0 -0.750 -2.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.750 0.750 0 0.750 0 0 0.125 0.500 0.125 0 0.750 0.500 0.750 1.50 0 0 0 0 -0.125 -0.500 0 -0.500 -0.500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 0.750 1.50 0.750 0 1.12 1.50 1.12 0 -0.125 0 -0.750 0 0 0 -0.750 0 -1.12 -0.500 -1.50 0 -1.50 -1.12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 0.500 0.500 0.750 1.50 0.500 1.50 0 0 0.750 0.750 0.750 1.12 2.25 0.750 2.25 0 0 0 0 0 -0.750 -0.750 0 -0.750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.188 0.750 0.188 0 1.12 0.750 1.12 2.25 0 0 -0.188 0 0 0 -0.188 0 -1.12 -2.25 -1.69 0 -1.69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.750 1.12 2.25 1.12 0 1.69 2.25 1.69 0 0 3.00 0 3.00 9.00 0 0 0 0 0 0 0 0 -3.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.750 0 0.750 3.00 0 0 0 0 0 0 0 0 -0.750 -6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.50 0 6.75 0 0 0 6.75 0 0
+DEAL::BDM3<3>0.750 0.250 0.500
+DEAL:: 0 0 0.750 0 0 0 0.750 0 2.25 0 0 0 0 0 -0.750 0 -0.750 -0.750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.12 1.69 0 1.69 0 0 0 0 0 -2.25 0 -1.69 0 0 0 -1.69 0 0 0 -0.188 0 -0.188 -1.12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.750 0.188 0 0.188 0 0 0.500 0.500 0.500 0 1.50 0.500 1.50 0.750 0 0 0 0 -0.500 -0.500 0 -0.500 -0.125 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 1.50 0.750 1.50 0 1.12 0.750 1.12 0 -0.500 0 -1.50 0 0 0 -1.50 0 -1.12 -0.125 -0.750 0 -0.750 -1.12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500 0.125 0.500 1.50 0.750 0.125 0.750 0 0 0.750 0.188 0.750 2.25 1.12 0.188 1.12 0 0 0 0 0 -0.750 -0.188 0 -0.188 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.750 0.750 0.750 0 2.25 0.750 2.25 1.12 0 0 -0.750 0 0 0 -0.750 0 -2.25 -1.12 -1.69 0 -1.69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.750 2.25 1.12 2.25 0 1.69 1.12 1.69 0 0 0.750 0 0.750 4.50 0 0 0 0 0 0 0 0 -0.750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.00 0 3.00 3.00 0 0 0 0 0 0 0 0 -3.00 -6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9.00 0 6.75 0 0 0 6.75 0 0
+DEAL::BDM3<3>1.00 1.00 1.00
+DEAL:: 0 0 3.00 0 0 0 3.00 0 6.00 0 0 0 0 0 -3.00 0 -3.00 -6.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.00 3.00 0 3.00 0 0 0 0 0 -6.00 0 -3.00 0 0 0 -3.00 0 0 0 -3.00 0 -3.00 -6.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.00 3.00 0 3.00 0 0 2.00 4.00 2.00 0 4.00 4.00 4.00 4.00 0 0 0 0 -2.00 -4.00 0 -4.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.00 4.00 4.00 4.00 0 2.00 4.00 2.00 0 -2.00 0 -4.00 0 0 0 -4.00 0 -2.00 -2.00 -4.00 0 -4.00 -2.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.00 2.00 4.00 4.00 4.00 2.00 4.00 0 0 6.00 3.00 6.00 6.00 6.00 3.00 6.00 0 0 0 0 0 -6.00 -3.00 0 -3.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.00 6.00 3.00 0 6.00 6.00 6.00 6.00 0 0 -3.00 0 0 0 -3.00 0 -6.00 -6.00 -3.00 0 -3.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.00 6.00 6.00 6.00 0 3.00 6.00 3.00 0 0 12.0 0 12.0 24.0 0 0 0 0 0 0 0 0 -12.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12.0 0 12.0 24.0 0 0 0 0 0 0 0 0 -12.0 -12.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24.0 0 12.0 0 0 0 12.0 0 0