From deaa5ee4e54485b894f7061ba26ca81b72706eb5 Mon Sep 17 00:00:00 2001
From: Timo Heister <timo.heister@gmail.com>
Date: Sat, 26 Mar 2016 06:58:29 +0100
Subject: [PATCH] implement TensorProductManifold

---
 .../deal.II/grid/tensor_product_manifold.h    | 244 ++++++++++++++++
 tests/manifold/tensor_product_manifold_01.cc  |  88 ++++++
 .../tensor_product_manifold_01.output         |  11 +
 tests/manifold/tensor_product_manifold_02.cc  |  82 ++++++
 .../tensor_product_manifold_02.output         | 261 ++++++++++++++++++
 5 files changed, 686 insertions(+)
 create mode 100644 include/deal.II/grid/tensor_product_manifold.h
 create mode 100644 tests/manifold/tensor_product_manifold_01.cc
 create mode 100644 tests/manifold/tensor_product_manifold_01.output
 create mode 100644 tests/manifold/tensor_product_manifold_02.cc
 create mode 100644 tests/manifold/tensor_product_manifold_02.output

diff --git a/include/deal.II/grid/tensor_product_manifold.h b/include/deal.II/grid/tensor_product_manifold.h
new file mode 100644
index 0000000000..152c0929fe
--- /dev/null
+++ b/include/deal.II/grid/tensor_product_manifold.h
@@ -0,0 +1,244 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 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.
+//
+// ---------------------------------------------------------------------
+
+#ifndef dealii__tensor_product_manifold_h
+#define dealii__tensor_product_manifold_h
+
+#include <deal.II/base/config.h>
+#include <deal.II/base/subscriptor.h>
+#include <deal.II/base/point.h>
+#include <deal.II/grid/manifold.h>
+
+DEAL_II_NAMESPACE_OPEN
+
+
+
+/**
+  * @brief Tensor product manifold of two ChartManifolds.
+  *
+  * This manifold will combine the ChartManifolds @p A and @p B given in the
+  * constructor to form a new ChartManifold by building the tensor product
+  * $A\cross B$. The first @p spacedim_A
+  * dimensions in the real space and the first @p chartdim_A dimensions
+  * of the chart will be given by manifold @p A, while the remaining
+  * coordinates are given by @p B. The manifold is to be used by a
+  * <tt>Triangulation@<dim, space_dim_A+space_dim_B@></tt>.
+  *
+  * An example usage would be the combination of a SphericalManifold with
+  * space dimension 2 and a FlatManifold with space dimension 1 to form
+  * a cylindrical manifold.
+  *
+  * pull_back(), push_forward(), and push_forward_gradient() are implemented
+  * by splitting the input argument into inputs for @p A and @p B according
+  * to the given dimensions and applying the corresponding operations before
+  * concatenating the result.
+  *
+  * @note The dimension arguments @p dim_A and @p dim_B are not used.
+  *
+  * @tparam dim Dimension of cells (needs to match first template argument of
+  * the Triangulation to be attached to.
+  * @tparam dim_A Dimension of ChartManifold A.
+  * @tparam spacedim_A Spacial dimension of ChartManifold A.
+  * @tparam chartdim_A Chart dimension of ChartManifold A.
+  * @tparam dim_B Dimension of ChartManifold B.
+  * @tparam spacedim_B Spacial dimension of ChartManifold B.
+  * @tparam chartdim_B Chart dimension of ChartManifold B.
+  *
+  * @author Luca Heltai, Timo Heister, 2016
+  */
+template <int dim,
+          int dim_A, int spacedim_A, int chartdim_A,
+          int dim_B, int spacedim_B, int chartdim_B>
+class TensorProductManifold :
+  public ChartManifold<dim,spacedim_A+spacedim_B,chartdim_A+chartdim_B>
+{
+public:
+  /**
+   * The chart dimension is the sum of the chart dimensions of the manifolds
+   * @p A and @p B.
+   */
+  static const unsigned int chartdim = chartdim_A+chartdim_B;
+  /**
+   * The space dimension is the sum of the space dimensions of the manifolds
+   * @p A and @p B.
+   */
+  static const unsigned int spacedim = spacedim_A+spacedim_B;
+
+  /**
+   * Constructor.
+   */
+  TensorProductManifold (
+    const ChartManifold<dim_A, spacedim_A, chartdim_A> &manifold_A,
+    const ChartManifold<dim_B, spacedim_B, chartdim_B> &manifold_B);
+
+  /**
+   * Pull back operation.
+   */
+  virtual
+  Point<chartdim>
+  pull_back(const Point<spacedim> &space_point) const;
+
+  /**
+   * Push forward operation.
+   */
+  virtual
+  Point<spacedim>
+  push_forward(const Point<chartdim> &chart_point) const;
+
+  /**
+   * Gradient.
+   */
+  virtual
+  DerivativeForm<1,chartdim,spacedim>
+  push_forward_gradient(const Point<chartdim> &chart_point) const;
+
+private:
+  SmartPointer<const ChartManifold<dim_A, spacedim_A, chartdim_A>,
+               TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B> > manifold_A;
+
+  SmartPointer<const ChartManifold<dim_B, spacedim_B, chartdim_B>,
+               TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B> > manifold_B;
+};
+
+
+
+/*------------------Template Implementations------------------------*/
+
+
+
+namespace internal
+{
+  namespace TensorProductManifold
+  {
+    template <int dim1, int dim2>
+    Tensor<1,dim1+dim2> concat(const Tensor<1,dim1> &p1, const Tensor<1,dim2> &p2)
+    {
+      Tensor<1,dim1+dim2> r;
+      for (unsigned int d=0; d<dim1; ++d)
+        r[d] = p1[d];
+      for (unsigned int d=0; d<dim2; ++d)
+        r[dim1+d] = p2[d];
+      return r;
+    }
+
+    template <int dim1, int dim2>
+    Point<dim1+dim2> concat(const Point<dim1> &p1, const Point<dim2> &p2)
+    {
+      Point<dim1+dim2> r;
+      for (unsigned int d=0; d<dim1; ++d)
+        r[d] = p1[d];
+      for (unsigned int d=0; d<dim2; ++d)
+        r[dim1+d] = p2[d];
+      return r;
+    }
+
+    template <int dim1, int dim2>
+    void split_point(const Point<dim1+dim2> &source, Point<dim1> &p1, Point<dim2> &p2)
+    {
+      for (unsigned int d=0; d<dim1; ++d)
+        p1[d] = source[d];
+      for (unsigned int d=0; d<dim2; ++d)
+        p2[d] = source[dim1+d];
+    }
+
+  }
+}
+
+template <int dim,
+          int dim_A, int spacedim_A, int chartdim_A,
+          int dim_B, int spacedim_B, int chartdim_B>
+TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+::TensorProductManifold(
+  const ChartManifold<dim_A, spacedim_A, chartdim_A> &manifold_A,
+  const ChartManifold<dim_B, spacedim_B, chartdim_B> &manifold_B)
+  : ChartManifold<dim,spacedim_A+spacedim_B,chartdim_A+chartdim_B> (
+    internal::TensorProductManifold::concat(
+      manifold_A.get_periodicity(),
+      manifold_B.get_periodicity())),
+  manifold_A (&manifold_A),
+  manifold_B (&manifold_B)
+{}
+
+template <int dim,
+          int dim_A, int spacedim_A, int chartdim_A,
+          int dim_B, int spacedim_B, int chartdim_B>
+Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim>
+TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+::pull_back(const Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::spacedim> &space_point) const
+{
+  Point<spacedim_A> space_point_A;
+  Point<spacedim_B> space_point_B;
+  internal::TensorProductManifold::split_point(space_point, space_point_A, space_point_B);
+
+  Point<chartdim_A> result_A = manifold_A->pull_back(space_point_A);
+  Point<chartdim_B> result_B = manifold_B->pull_back(space_point_B);
+
+  return internal::TensorProductManifold::concat(result_A, result_B);
+}
+
+template <int dim,
+          int dim_A, int spacedim_A, int chartdim_A,
+          int dim_B, int spacedim_B, int chartdim_B>
+Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::spacedim>
+TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+::push_forward(const Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim> &chart_point) const
+{
+  Point<chartdim_A> chart_point_A;
+  Point<chartdim_B> chart_point_B;
+  internal::TensorProductManifold::split_point(chart_point, chart_point_A, chart_point_B);
+
+  Point<spacedim_A> result_A = manifold_A->push_forward(chart_point_A);
+  Point<spacedim_B> result_B = manifold_B->push_forward(chart_point_B);
+
+  return internal::TensorProductManifold::concat(result_A, result_B);
+}
+
+template <int dim,
+          int dim_A, int spacedim_A, int chartdim_A,
+          int dim_B, int spacedim_B, int chartdim_B>
+DerivativeForm<1,
+               TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim,
+               TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::spacedim>
+
+               TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+               ::push_forward_gradient(const Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim> &chart_point) const
+{
+  Point<chartdim_A> chart_point_A;
+  Point<chartdim_B> chart_point_B;
+  internal::TensorProductManifold::split_point(chart_point, chart_point_A, chart_point_B);
+
+  DerivativeForm<1,chartdim_A,spacedim_A> result_A
+    = manifold_A->push_forward_gradient(chart_point_A);
+  DerivativeForm<1,chartdim_B,spacedim_B> result_B
+    = manifold_B->push_forward_gradient(chart_point_B);
+
+
+  DerivativeForm<1,chartdim,spacedim> result;
+  for (unsigned int i = 0; i<chartdim_A; ++i)
+    for (unsigned int j = 0; j<spacedim_A; ++j)
+      result[j][i] = result_A[j][i];
+  for (unsigned int i = 0; i<chartdim_B; ++i)
+    for (unsigned int j = 0; j<spacedim_B; ++j)
+      result[j+spacedim_A][i+chartdim_A] = result_B[j][i];
+
+  return result;
+}
+
+
+
+
+DEAL_II_NAMESPACE_CLOSE
+
+#endif
diff --git a/tests/manifold/tensor_product_manifold_01.cc b/tests/manifold/tensor_product_manifold_01.cc
new file mode 100644
index 0000000000..a1ad09f494
--- /dev/null
+++ b/tests/manifold/tensor_product_manifold_01.cc
@@ -0,0 +1,88 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Test TensorProductManifold
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+#include <deal.II/grid/tensor_product_manifold.h>
+#include <deal.II/grid/manifold_lib.h>
+
+
+void test1()
+{
+  const int dim=2, spacedim=2+1;
+
+  FunctionManifold<1,2,1>    F("x;x^2", "x");
+  FunctionManifold<1,1,1>    G("1.0+2*x", "0.5*(x-1.0)");
+
+  TensorProductManifold<1, 1,2,1, 1,1,1> manifold(F, G);
+
+  // Chart points.
+  Point<2> cp[2];
+  cp[1][0] = 1.0;
+  cp[1][1] = 0.5;
+
+  // Spacedim points
+  std::vector<Point<spacedim> > sp(2);
+
+  // Weights
+  std::vector<double> w(2);
+
+  sp[0] = manifold.push_forward(cp[0]);
+  sp[1] = manifold.push_forward(cp[1]);
+
+  for (unsigned int d=0; d<2; ++d)
+    if (cp[d].distance(manifold.pull_back(sp[d])) > 1e-10)
+      deallog << "Error! "
+              << cp[d] << "->" << sp[d] << "->" << manifold.pull_back(sp[d])
+              << std::endl;
+
+  unsigned int n_intermediates = 8;
+
+  deallog << "P0: " << sp[0]
+          << ", P1: " << sp[1] << std::endl;
+
+  for (unsigned int i=0; i<n_intermediates+1; ++i)
+    {
+      w[0] = 1.0-(double)i/((double)n_intermediates);
+      w[1] = 1.0 - w[0];
+
+      Point<spacedim> ip = manifold.get_new_point(Quadrature<spacedim>(sp, w));
+      Tensor<1,spacedim> t1 = manifold.get_tangent_vector(ip, sp[0]);
+      Tensor<1,spacedim> t2 = manifold.get_tangent_vector(ip, sp[1]);
+
+      deallog << "P: " << ip
+              << ", T(P, P0): " << t1
+              << ", T(P, P1): " << t2 << std::endl;
+
+    }
+}
+
+
+
+int main ()
+{
+  initlog();
+
+  test1();
+
+
+  return 0;
+}
+
diff --git a/tests/manifold/tensor_product_manifold_01.output b/tests/manifold/tensor_product_manifold_01.output
new file mode 100644
index 0000000000..83d9255c81
--- /dev/null
+++ b/tests/manifold/tensor_product_manifold_01.output
@@ -0,0 +1,11 @@
+
+DEAL::P0: 0.00000 0.00000 1.00000, P1: 1.00000 1.00000 2.00000
+DEAL::P: 0.00000 0.00000 1.00000, T(P, P0): 0.00000 0.00000 0.00000, T(P, P1): 1.00000 0.00000 1.00000
+DEAL::P: 0.125000 0.0156250 1.12500, T(P, P0): -0.125000 -0.0312500 -0.125000, T(P, P1): 0.875000 0.218750 0.875000
+DEAL::P: 0.250000 0.0625000 1.25000, T(P, P0): -0.250000 -0.125000 -0.250000, T(P, P1): 0.750000 0.375000 0.750000
+DEAL::P: 0.375000 0.140625 1.37500, T(P, P0): -0.375000 -0.281250 -0.375000, T(P, P1): 0.625000 0.468750 0.625000
+DEAL::P: 0.500000 0.250000 1.50000, T(P, P0): -0.500000 -0.500000 -0.500000, T(P, P1): 0.500000 0.500000 0.500000
+DEAL::P: 0.625000 0.390625 1.62500, T(P, P0): -0.625000 -0.781250 -0.625000, T(P, P1): 0.375000 0.468750 0.375000
+DEAL::P: 0.750000 0.562500 1.75000, T(P, P0): -0.750000 -1.12500 -0.750000, T(P, P1): 0.250000 0.375000 0.250000
+DEAL::P: 0.875000 0.765625 1.87500, T(P, P0): -0.875000 -1.53125 -0.875000, T(P, P1): 0.125000 0.218750 0.125000
+DEAL::P: 1.00000 1.00000 2.00000, T(P, P0): -1.00000 -2.00000 -1.00000, T(P, P1): 0.00000 0.00000 0.00000
diff --git a/tests/manifold/tensor_product_manifold_02.cc b/tests/manifold/tensor_product_manifold_02.cc
new file mode 100644
index 0000000000..65b79a5a18
--- /dev/null
+++ b/tests/manifold/tensor_product_manifold_02.cc
@@ -0,0 +1,82 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Test TensorProductManifold by refining and generating normals for
+// a manually constructed cylinder hull.
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+#include <deal.II/grid/tensor_product_manifold.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+
+
+void test()
+{
+  std::ostream &out = deallog.get_file_stream();
+
+  FunctionManifold<1,1> F("x","x");
+  SphericalManifold<2,2> G;
+
+  TensorProductManifold<2, 1,1,1, 2,2,2> manifold(F, G);
+
+  // make a hull of a cylinder
+  Triangulation<2,3> tria;
+  {
+    Triangulation<3,3> volume_tria;
+    GridGenerator::cylinder(volume_tria);
+    std::set<types::boundary_id> boundary_ids;
+    boundary_ids.insert(0);
+    GridGenerator::extract_boundary_mesh(volume_tria, tria, boundary_ids);
+  }
+  tria.set_all_manifold_ids(0);
+  tria.set_manifold(0, manifold);
+
+  tria.refine_global(1);
+
+  out << "set view equal xyz" << std::endl
+      << "splot '-' with lines, '-' with vectors " << std::endl;
+  GridOut().write_gnuplot (tria, out);
+  out << "e" << std::endl;
+
+  Triangulation<2,3>::active_cell_iterator it = tria.begin_active();
+  for (; it!=tria.end(); ++it)
+    {
+      Point<3> p = it->center(true);
+      Tensor<1,3> t1 = manifold.get_tangent_vector(p, it->vertex(0));
+      Tensor<1,3> t2 = manifold.get_tangent_vector(p, it->vertex(1));
+      Tensor<1,3> n = cross_product_3d(t1, t2);
+      n/=-n.norm();
+      out << it->center() << " " << n << std::endl;
+    }
+  out << "e" << std::endl;
+}
+
+
+
+int main ()
+{
+  initlog();
+
+  test();
+
+  return 0;
+}
+
diff --git a/tests/manifold/tensor_product_manifold_02.output b/tests/manifold/tensor_product_manifold_02.output
new file mode 100644
index 0000000000..0b91e642a5
--- /dev/null
+++ b/tests/manifold/tensor_product_manifold_02.output
@@ -0,0 +1,261 @@
+
+set view equal xyz
+splot '-' with lines, '-' with vectors 
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+
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-- 
2.39.5