From ad4f882f8d6d33f6ee652667073dcc8ee3d87b5f Mon Sep 17 00:00:00 2001
From: Alistair Bentley <alistairbntl@gmail.com>
Date: Tue, 27 Oct 2015 11:14:07 -0400
Subject: [PATCH] Implemented BDM_grad_grad in 3D

  * Added second derivative terms to polynomials_bdm class in 3D
  * Added tests and output to verify 2nd derivatives are returning
    proper values
  * I carefully checked the output file to confirm the correct output
    is being produced
---
 doc/news/changes.h                     |  8 ++-
 include/deal.II/base/polynomials_bdm.h |  1 -
 source/base/polynomials_bdm.cc         | 85 +++++++++++++++++++++-
 tests/base/polynomials_bdm_02.cc       | 98 ++++++++++++++++++++++++++
 tests/base/polynomials_bdm_02.output   | 34 +++++++++
 5 files changed, 223 insertions(+), 3 deletions(-)
 create mode 100644 tests/base/polynomials_bdm_02.cc
 create mode 100644 tests/base/polynomials_bdm_02.output

diff --git a/doc/news/changes.h b/doc/news/changes.h
index 8e7de962b7..a36b530aea 100644
--- a/doc/news/changes.h
+++ b/doc/news/changes.h
@@ -159,6 +159,12 @@ inconvenience this causes.
 <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,
@@ -398,7 +404,7 @@ inconvenience this causes.
   (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)
diff --git a/include/deal.II/base/polynomials_bdm.h b/include/deal.II/base/polynomials_bdm.h
index ed1b51cd07..9a24aa2eb5 100644
--- a/include/deal.II/base/polynomials_bdm.h
+++ b/include/deal.II/base/polynomials_bdm.h
@@ -92,7 +92,6 @@ DEAL_II_NAMESPACE_OPEN
  *</dl>
  *
  *
- * @todo Second derivatives in 3D are missing.
  *
  * @ingroup Polynomials
  * @author Guido Kanschat
diff --git a/source/base/polynomials_bdm.cc b/source/base/polynomials_bdm.cc
index 3653da62f1..cdf32d22f0 100644
--- a/source/base/polynomials_bdm.cc
+++ b/source/base/polynomials_bdm.cc
@@ -244,7 +244,90 @@ PolynomialsBDM<dim>::compute (const Point<dim>            &unit_point,
             }
           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());
diff --git a/tests/base/polynomials_bdm_02.cc b/tests/base/polynomials_bdm_02.cc
new file mode 100644
index 0000000000..1ea87f7eda
--- /dev/null
+++ b/tests/base/polynomials_bdm_02.cc
@@ -0,0 +1,98 @@
+// ---------------------------------------------------------------------
+//
+// 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);
+}
diff --git a/tests/base/polynomials_bdm_02.output b/tests/base/polynomials_bdm_02.output
new file mode 100644
index 0000000000..a0f2788bed
--- /dev/null
+++ b/tests/base/polynomials_bdm_02.output
@@ -0,0 +1,34 @@
+
+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
-- 
2.39.5