--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 - 2020 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Header file:
+// Evaluation of a coupled system (vector components + symmetric tensor)
+// using a helper class
+//
+// This is the same as "helper_scalar_coupled_2_components_06", but with
+// the indexing order of the vector and symmetric tensor variable swapped.
+// It tests the robustness of the extract_field_component_indices()
+// function as called from extract_Hessain_component(), as there was
+// previously a bug with the first component offset when the symmetric
+// tensor first component was not zero.
+
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/symmetric_tensor.h>
+#include <deal.II/base/tensor.h>
+
+#include <deal.II/differentiation/ad.h>
+
+#include <deal.II/fe/fe_values_extractors.h>
+
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/vector.h>
+
+#include <iostream>
+
+#include "../tests.h"
+
+namespace AD = dealii::Differentiation::AD;
+
+// Function and its derivatives
+template <int dim, typename NumberType>
+struct FunctionsTestSymmetricTensorVectorCoupled
+{
+ static NumberType
+ det_t(const SymmetricTensor<2, dim, NumberType> &t)
+ {
+ return determinant(t);
+ }
+
+ static SymmetricTensor<2, dim, NumberType>
+ ddet_t_dt(const SymmetricTensor<2, dim, NumberType> &t)
+ {
+ const SymmetricTensor<2, dim, NumberType> t_inv =
+ symmetrize(invert(static_cast<Tensor<2, dim, NumberType>>(t)));
+ return det_t(t) * t_inv;
+ }
+
+ static SymmetricTensor<4, dim, NumberType>
+ d2det_t_dt_dt(const SymmetricTensor<2, dim, NumberType> &t)
+ {
+ const SymmetricTensor<2, dim, NumberType> t_inv =
+ symmetrize(invert(static_cast<Tensor<2, dim, NumberType>>(t)));
+ SymmetricTensor<4, dim, NumberType> dt_inv_dt;
+ // https://en.wikiversity.org/wiki/Introduction_to_Elasticity/Tensors#Derivative_of_the_determinant_of_a_tensor
+ for (unsigned int i = 0; i < dim; ++i)
+ for (unsigned int j = i; j < dim; ++j)
+ for (unsigned int k = 0; k < dim; ++k)
+ for (unsigned int l = k; l < dim; ++l)
+ dt_inv_dt[i][j][k][l] =
+ -0.5 * (t_inv[i][k] * t_inv[j][l] + t_inv[i][l] * t_inv[j][k]);
+
+ return det_t(t) * outer_product(t_inv, t_inv) + det_t(t) * dt_inv_dt;
+ }
+
+ static NumberType
+ v_squ(const Tensor<1, dim, NumberType> &v)
+ {
+ return v * v;
+ }
+
+ static Tensor<1, dim, NumberType>
+ dv_squ_dv(const Tensor<1, dim, NumberType> &v)
+ {
+ return 2.0 * v;
+ }
+
+ static SymmetricTensor<2, dim, NumberType>
+ d2v_squ_dv_dv(const Tensor<1, dim, NumberType> &v)
+ {
+ static const SymmetricTensor<2, dim, NumberType> I(
+ unit_symmetric_tensor<dim, NumberType>());
+ return SymmetricTensor<2, dim, NumberType>(2.0 * I);
+ }
+
+ // -------
+
+ static NumberType
+ psi(const SymmetricTensor<2, dim, NumberType> &t,
+ const Tensor<1, dim, NumberType> & v)
+ {
+ return std::pow(det_t(t), 2) * std::pow(v_squ(v), 3);
+ };
+
+ static SymmetricTensor<2, dim, NumberType>
+ dpsi_dt(const SymmetricTensor<2, dim, NumberType> &t,
+ const Tensor<1, dim, NumberType> & v)
+ {
+ return SymmetricTensor<2, dim, NumberType>(
+ 2.0 * std::pow(det_t(t), 1) * ddet_t_dt(t) * std::pow(v_squ(v), 3));
+ };
+
+ static Tensor<1, dim, NumberType>
+ dpsi_dv(const SymmetricTensor<2, dim, NumberType> &t,
+ const Tensor<1, dim, NumberType> & v)
+ {
+ return std::pow(det_t(t), 2) * 3.0 * std::pow(v_squ(v), 2) * dv_squ_dv(v);
+ };
+
+ static SymmetricTensor<4, dim, NumberType>
+ d2psi_dt_dt(const SymmetricTensor<2, dim, NumberType> &t,
+ const Tensor<1, dim, NumberType> & v)
+ {
+ return SymmetricTensor<4, dim, NumberType>(
+ 2.0 * std::pow(v_squ(v), 3) *
+ (pow(det_t(t), 0) * outer_product(ddet_t_dt(t), ddet_t_dt(t)) +
+ std::pow(det_t(t), 1) * d2det_t_dt_dt(t)));
+ };
+
+ static Tensor<3, dim, NumberType>
+ d2psi_dv_dt(const SymmetricTensor<2, dim, NumberType> &t,
+ const Tensor<1, dim, NumberType> & v)
+ {
+ return 2.0 * std::pow(det_t(t), 1) * 3.0 * std::pow(v_squ(v), 2) *
+ outer_product(static_cast<Tensor<2, dim, NumberType>>(ddet_t_dt(t)),
+ dv_squ_dv(v));
+ };
+
+ static Tensor<3, dim, NumberType>
+ d2psi_dt_dv(const SymmetricTensor<2, dim, NumberType> &t,
+ const Tensor<1, dim, NumberType> & v)
+ {
+ return 2.0 * std::pow(det_t(t), 1) * 3.0 * std::pow(v_squ(v), 2) *
+ outer_product(dv_squ_dv(v),
+ static_cast<Tensor<2, dim, NumberType>>(ddet_t_dt(t)));
+ };
+
+ static Tensor<2, dim, NumberType>
+ d2psi_dv_dv(const SymmetricTensor<2, dim, NumberType> &t,
+ const Tensor<1, dim, NumberType> & v)
+ {
+ return std::pow(det_t(t), 2) * 3.0 *
+ (2.0 * std::pow(v_squ(v), 1) *
+ outer_product(dv_squ_dv(v), dv_squ_dv(v)) +
+ std::pow(v_squ(v), 2) * d2v_squ_dv_dv(v));
+ };
+};
+
+template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+void
+test_symmetric_tensor_vector_coupled()
+{
+ typedef AD::ScalarFunction<dim, ad_type_code, number_t> ADHelper;
+ typedef typename ADHelper::ad_type ADNumberType;
+ typedef typename ADHelper::scalar_type ScalarNumberType;
+
+ std::cout << "*** Test variables: SymmetricTensor + Vector (coupled), "
+ << "dim = " << Utilities::to_string(dim) << ", "
+ << "Type code: " << static_cast<int>(ad_type_code) << std::endl;
+
+ // Values computed from the AD energy function
+ ScalarNumberType psi;
+ Vector<ScalarNumberType> Dpsi;
+ FullMatrix<ScalarNumberType> D2psi;
+
+ // Function and its derivatives
+ typedef FunctionsTestSymmetricTensorVectorCoupled<dim, ADNumberType> func_ad;
+
+ // Setup the variable components and choose a value at which to
+ // evaluate the tape
+ const FEValuesExtractors::Vector v_dof(0);
+ const FEValuesExtractors::SymmetricTensor<2> t_dof(
+ Tensor<1, dim>::n_independent_components);
+ const unsigned int n_AD_components =
+ Tensor<1, dim>::n_independent_components +
+ SymmetricTensor<2, dim>::n_independent_components;
+ ADHelper ad_helper(n_AD_components);
+ ad_helper.set_tape_buffer_sizes(); // Increase the buffer size from the
+ // default values
+
+ SymmetricTensor<2, dim, ScalarNumberType> t =
+ unit_symmetric_tensor<dim, ScalarNumberType>();
+ for (unsigned int i = 0; i < t.n_independent_components; ++i)
+ t[t.unrolled_to_component_indices(i)] += 0.165 * (i + 0.1);
+ Tensor<1, dim, ScalarNumberType> v;
+ for (unsigned int i = 0; i < dim; ++i)
+ v[i] = 1.3 + 0.5 * i;
+
+ const int tape_no = 1;
+ const bool is_recording =
+ ad_helper.start_recording_operations(tape_no /*material_id*/,
+ true /*overwrite_tape*/,
+ true /*keep*/);
+ if (is_recording == true)
+ {
+ ad_helper.register_independent_variable(t, t_dof);
+ ad_helper.register_independent_variable(v, v_dof);
+
+ const SymmetricTensor<2, dim, ADNumberType> t_ad =
+ ad_helper.get_sensitive_variables(t_dof);
+ const Tensor<1, dim, ADNumberType> v_ad =
+ ad_helper.get_sensitive_variables(v_dof);
+
+ const ADNumberType psi(func_ad::psi(t_ad, v_ad));
+
+ ad_helper.register_dependent_variable(psi);
+ ad_helper.stop_recording_operations(false /*write_tapes_to_file*/);
+
+ std::cout << "Recorded data..." << std::endl;
+ std::cout << "independent variable values: " << std::flush;
+ ad_helper.print_values(std::cout);
+ std::cout << "t_ad: " << t_ad << std::endl;
+ std::cout << "v_ad: " << v_ad << std::endl;
+ std::cout << "psi: " << psi << std::endl;
+ std::cout << std::endl;
+ }
+ else
+ {
+ Assert(is_recording == true, ExcInternalError());
+ }
+
+ // Do some work :-)
+ // Set a new evaluation point
+ if (AD::ADNumberTraits<ADNumberType>::is_taped == true)
+ {
+ std::cout
+ << "Using tape with different values for independent variables..."
+ << std::endl;
+ ad_helper.activate_recorded_tape(tape_no);
+ t *= 0.9;
+ v *= 0.63;
+ ad_helper.set_independent_variable(t, t_dof);
+ ad_helper.set_independent_variable(v, v_dof);
+ }
+
+ std::cout << "independent variable values: " << std::flush;
+ ad_helper.print_values(std::cout);
+
+ // Compute the function value, gradient and hessian for the new evaluation
+ // point
+ psi = ad_helper.compute_value();
+ ad_helper.compute_gradient(Dpsi);
+ if (AD::ADNumberTraits<ADNumberType>::n_supported_derivative_levels >= 2)
+ {
+ ad_helper.compute_hessian(D2psi);
+ }
+
+ // Output the full stored function, gradient vector and hessian matrix
+ std::cout << "psi: " << psi << std::endl;
+ std::cout << "Dpsi: \n";
+ Dpsi.print(std::cout);
+ if (AD::ADNumberTraits<ADNumberType>::n_supported_derivative_levels >= 2)
+ {
+ std::cout << "D2psi: \n";
+ D2psi.print_formatted(std::cout, 3, true, 0, "0.0");
+ }
+
+ // Extract components of the solution
+ const SymmetricTensor<2, dim, ScalarNumberType> dpsi_dt =
+ ad_helper.extract_gradient_component(Dpsi, t_dof);
+ const Tensor<1, dim, ScalarNumberType> dpsi_dv =
+ ad_helper.extract_gradient_component(Dpsi, v_dof);
+ std::cout << "extracted Dpsi (t): " << dpsi_dt << "\n"
+ << "extracted Dpsi (v): " << dpsi_dv << "\n";
+
+ // Verify the result
+ typedef FunctionsTestSymmetricTensorVectorCoupled<dim, ScalarNumberType> func;
+ static const ScalarNumberType tol =
+ 1e5 * std::numeric_limits<ScalarNumberType>::epsilon();
+ std::cout << "dpsi_dt: " << dpsi_dt << std::endl;
+ std::cout << "func::dpsi_dt(t,v): " << func::dpsi_dt(t, v) << std::endl;
+ std::cout << "diff: " << std::abs((dpsi_dt - func::dpsi_dt(t, v)).norm())
+ << std::endl;
+ std::cout << "dpsi_dv: " << dpsi_dv << std::endl;
+ std::cout << "func::dpsi_dv(t,v): " << func::dpsi_dv(t, v) << std::endl;
+ std::cout << "diff: " << std::abs((dpsi_dv - func::dpsi_dv(t, v)).norm())
+ << std::endl;
+ Assert(std::abs(psi - func::psi(t, v)) < tol,
+ ExcMessage("No match for function value."));
+ Assert(std::abs((dpsi_dt - func::dpsi_dt(t, v)).norm()) < tol,
+ ExcMessage("No match for first derivative."));
+ Assert(std::abs((dpsi_dv - func::dpsi_dv(t, v)).norm()) < tol,
+ ExcMessage("No match for first derivative."));
+ if (AD::ADNumberTraits<ADNumberType>::n_supported_derivative_levels >= 2)
+ {
+ const SymmetricTensor<4, dim, ScalarNumberType> d2psi_dt_dt =
+ ad_helper.extract_hessian_component(D2psi, t_dof, t_dof);
+ const Tensor<3, dim, ScalarNumberType> d2psi_dv_dt =
+ ad_helper.extract_hessian_component(D2psi, t_dof, v_dof);
+ const Tensor<3, dim, ScalarNumberType> d2psi_dt_dv =
+ ad_helper.extract_hessian_component(D2psi, v_dof, t_dof);
+ const Tensor<2, dim, ScalarNumberType> d2psi_dv_dv =
+ ad_helper.extract_hessian_component(D2psi, v_dof, v_dof);
+ std::cout << "extracted Dpsi (t): " << dpsi_dt << "\n"
+ << "extracted Dpsi (v): " << dpsi_dv << "\n"
+ << "extracted D2psi (t,t): " << d2psi_dt_dt << "\n"
+ << "extracted D2psi (t,v): " << d2psi_dv_dt << "\n"
+ << "extracted D2psi (v,t): " << d2psi_dt_dv << "\n"
+ << "extracted D2psi (v,v): " << d2psi_dv_dv << "\n"
+ << std::endl;
+ std::cout << "d2psi_dt_dt: " << d2psi_dt_dt << std::endl;
+ std::cout << "func::d2psi_dt_dt(t,v): " << func::d2psi_dt_dt(t, v)
+ << std::endl;
+ std::cout << "diff: "
+ << std::abs((d2psi_dt_dt - func::d2psi_dt_dt(t, v)).norm())
+ << std::endl;
+ std::cout << "d2psi_dv_dt: " << d2psi_dv_dt << std::endl;
+ std::cout << "func::d2psi_dv_dt(t,v): " << func::d2psi_dv_dt(t, v)
+ << std::endl;
+ std::cout << "diff: "
+ << std::abs((d2psi_dv_dt - func::d2psi_dv_dt(t, v)).norm())
+ << std::endl;
+ std::cout << "d2psi_dt_dv: " << d2psi_dt_dv << std::endl;
+ std::cout << "func::d2psi_dt_dv(t,v): " << func::d2psi_dt_dv(t, v)
+ << std::endl;
+ std::cout << "diff: "
+ << std::abs((d2psi_dt_dv - func::d2psi_dt_dv(t, v)).norm())
+ << std::endl;
+ std::cout << "d2psi_dv_dv: " << d2psi_dv_dv << std::endl;
+ std::cout << "func::d2psi_dv_dv(t,v): " << func::d2psi_dv_dv(t, v)
+ << std::endl;
+ std::cout << "diff: "
+ << std::abs((d2psi_dv_dv - func::d2psi_dv_dv(t, v)).norm())
+ << std::endl;
+ Assert(std::abs((d2psi_dt_dt - func::d2psi_dt_dt(t, v)).norm()) < tol,
+ ExcMessage("No match for second derivative."));
+ Assert(std::abs((d2psi_dv_dt - func::d2psi_dv_dt(t, v)).norm()) < tol,
+ ExcMessage("No match for second derivative."));
+ Assert(std::abs((d2psi_dt_dv - func::d2psi_dt_dv(t, v)).norm()) < tol,
+ ExcMessage("No match for second derivative."));
+ Assert(std::abs((d2psi_dv_dv - func::d2psi_dv_dv(t, v)).norm()) < tol,
+ ExcMessage("No match for second derivative."));
+ }
+}
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