--- /dev/null
+New: FE_Nedelec<2> now includes the function get_embedding_dofs(),
+which permits direct identification of DoF indices between two
+realizations of the FE_Nedelec cell.
+<br>
+(Jake Harmon, 2022/01/25)
virtual std::unique_ptr<FiniteElement<dim, dim>>
clone() const override;
+ /**
+ * For a finite element of degree larger than @p sub_degree, we return a
+ * vector which maps the numbering on an FE of degree @p sub_degree into the
+ * numbering on this element.
+ *
+ * Note that for the Nedelec element, by @p sub_degree,
+ * we refer to the maximal polynomial degree (in any coordinate direction) as
+ * opposed to the Nedelec degree.
+ */
+ std::vector<unsigned int>
+ get_embedding_dofs(const unsigned int sub_degree) const;
+
private:
/**
* Only for internal use. Its full name is @p get_dofs_per_object_vector
return 0;
}
+template <int dim>
+std::vector<unsigned int>
+FE_Nedelec<dim>::get_embedding_dofs(const unsigned int sub_degree) const
+{
+ Assert((sub_degree > 0) && (sub_degree <= this->degree),
+ ExcIndexRange(sub_degree, 1, this->degree));
+
+ switch (dim)
+ {
+ case 2:
+ {
+ // The Nedelec cell has only Face (Line) and Cell DoFs...
+ const unsigned int n_face_dofs_sub =
+ GeometryInfo<dim>::lines_per_cell * sub_degree;
+ const unsigned int n_cell_dofs_sub =
+ 2 * (sub_degree - 1) * sub_degree;
+
+ std::vector<unsigned int> embedding_dofs(n_face_dofs_sub +
+ n_cell_dofs_sub);
+
+ unsigned int i = 0;
+
+ // Identify the Face/Line DoFs
+ while (i < n_face_dofs_sub)
+ {
+ const unsigned int face_index = i / sub_degree;
+ embedding_dofs[i] = i % sub_degree + face_index * this->degree;
+ ++i;
+ }
+
+ // Identify the Cell DoFs
+ if (sub_degree >= 2)
+ {
+ const unsigned int n_face_dofs =
+ GeometryInfo<dim>::lines_per_cell * this->degree;
+ // For the first component
+ for (unsigned ku = 0; ku < sub_degree; ++ku)
+ for (unsigned kv = 2; kv <= sub_degree; ++kv)
+ embedding_dofs[i++] =
+ n_face_dofs + ku * (this->degree - 1) + (kv - 2);
+
+ // For the second component
+ for (unsigned ku = 2; ku <= sub_degree; ++ku)
+ for (unsigned kv = 0; kv < sub_degree; ++kv)
+ embedding_dofs[i++] = n_face_dofs +
+ this->degree * (this->degree - 1) +
+ (ku - 2) * (this->degree) + kv;
+ }
+ Assert(i == (n_face_dofs_sub + n_cell_dofs_sub), ExcInternalError());
+ return embedding_dofs;
+ }
+ default:
+ Assert(false, ExcNotImplemented());
+ return std::vector<unsigned int>();
+ }
+}
//----------------------------------------------------------------------//
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 - 2021 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.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+// Checks if get_embedding_dofs() correctly maps the local DoF indices
+// of an FE_Nedelec element of sub_degree to an element of sup_degree,
+// where sub_degree <= sup_degree
+
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/fe/fe_nedelec.h>
+
+#include "interpolate_common.h"
+
+template <int dim>
+void
+check_nedelec_embed(const unsigned int sub_degree,
+ const unsigned int sup_degree)
+{
+ Assert((sub_degree > 0) && (sub_degree <= sup_degree),
+ ExcIndexRange(sub_degree, 1, sup_degree));
+
+ const FE_Nedelec<dim> fe_sub(sub_degree - 1);
+ const FE_Nedelec<dim> fe_sup(sup_degree - 1);
+
+ deallog << fe_sub.get_name() << ' ' << fe_sup.get_name() << ' '
+ << fe_sub.dofs_per_cell << ' ' << fe_sup.dofs_per_cell;
+
+ // Set the quadrature sufficiently high for the enriched finite element space
+ const QGauss<dim> quadrature(fe_sup.degree + 1);
+
+ std::vector<double> dofs_sub(fe_sub.dofs_per_cell, 0.);
+ std::vector<double> dofs_sup(fe_sup.dofs_per_cell, 0.);
+
+ // Assign arbitrary values to dofs_sub
+ for (unsigned int i = 0; i < dofs_sub.size(); ++i)
+ dofs_sub[i] = std::sin(i + 0.5);
+
+
+ // Map the DoFs from fe_sub to fe_sup
+ const std::vector<unsigned int> embedding_dofs =
+ fe_sup.get_embedding_dofs(fe_sub.degree);
+ for (unsigned int i = 0; i < dofs_sub.size(); ++i)
+ dofs_sup[embedding_dofs[i]] = dofs_sub[i];
+
+ // Compare the values at each quadrature point
+ double result = 0.;
+ for (unsigned int k = 0; k < quadrature.size(); ++k)
+ for (unsigned int comp = 0; comp < fe_sup.n_components(); ++comp)
+ {
+ double eval_sub = 0., eval_sup = 0.;
+
+ for (unsigned int i = 0; i < dofs_sub.size(); ++i)
+ eval_sub +=
+ dofs_sub[i] *
+ fe_sub.shape_value_component(i, quadrature.point(k), comp);
+
+ for (unsigned int i = 0; i < dofs_sup.size(); ++i)
+ eval_sup +=
+ dofs_sup[i] *
+ fe_sup.shape_value_component(i, quadrature.point(k), comp);
+
+ const double diff = std::abs(eval_sub - eval_sup);
+ result = std::max(result, diff);
+ }
+ deallog << " max diff " << result << std::endl;
+}
+
+int
+main()
+{
+ initlog();
+
+ // For 2-D
+ {
+ for (unsigned int low_deg = 1; low_deg <= 5; ++low_deg)
+ for (unsigned int high_deg = low_deg; high_deg <= 10; ++high_deg)
+ check_nedelec_embed<2>(low_deg, high_deg);
+ }
+}
--- /dev/null
+
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(0) 4 4 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(1) 4 12 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(2) 4 24 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(3) 4 40 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(4) 4 60 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(5) 4 84 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(6) 4 112 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(7) 4 144 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(8) 4 180 max diff 0.00000
+DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(9) 4 220 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(1) 12 12 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(2) 12 24 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(3) 12 40 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(4) 12 60 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(5) 12 84 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(6) 12 112 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(7) 12 144 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(8) 12 180 max diff 0.00000
+DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(9) 12 220 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(2) 24 24 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(3) 24 40 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(4) 24 60 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(5) 24 84 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(6) 24 112 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(7) 24 144 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(8) 24 180 max diff 0.00000
+DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(9) 24 220 max diff 0.00000
+DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(3) 40 40 max diff 0.00000
+DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(4) 40 60 max diff 0.00000
+DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(5) 40 84 max diff 0.00000
+DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(6) 40 112 max diff 0.00000
+DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(7) 40 144 max diff 0.00000
+DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(8) 40 180 max diff 0.00000
+DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(9) 40 220 max diff 0.00000
+DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(4) 60 60 max diff 0.00000
+DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(5) 60 84 max diff 0.00000
+DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(6) 60 112 max diff 0.00000
+DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(7) 60 144 max diff 0.00000
+DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(8) 60 180 max diff 0.00000
+DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(9) 60 220 max diff 0.00000
projects / dealii.git / commitdiff