From: Guido Kanschat Date: Mon, 14 Mar 2016 15:28:06 +0000 (-0500) Subject: add weak tangential boundary condition for elasticity X-Git-Tag: v8.5.0-rc1~1214^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=7af6185f5c29586509bac9ce0ce81a4d6e47c95a;p=dealii.git add weak tangential boundary condition for elasticity --- diff --git a/include/deal.II/integrators/elasticity.h b/include/deal.II/integrators/elasticity.h index db3ce2d200..2e6f76be0c 100644 --- a/include/deal.II/integrators/elasticity.h +++ b/include/deal.II/integrators/elasticity.h @@ -106,9 +106,9 @@ namespace LocalIntegrators /** - * The weak boundary condition of Nitsche type for linear elasticity: + * The matrix for the weak boundary condition of Nitsche type for linear elasticity: * @f[ - * \int_F \Bigl(\gamma (u-g) \cdot v - n^T \epsilon(u) v - (u-g) \epsilon(v) n^T\Bigr)\;ds. + * \int_F \Bigl(\gamma u \cdot v - n^T \epsilon(u) v - u \epsilon(v) n\Bigr)\;ds. * @f] */ template @@ -150,6 +150,67 @@ namespace LocalIntegrators } } + /** + * The matrix for the weak boundary condition of Nitsche type for the tangential displacement in linear elasticity: + * @f[ + * \int_F \Bigl(\gamma u_\tau \cdot v_\tau - n^T \epsilon(u_\tau) v_\tau - u_\tau^T \epsilon(v_\tau) n\Bigr)\;ds. + * @f] + */ + template + inline void nitsche_tangential_matrix ( + FullMatrix &M, + const FEValuesBase &fe, + double penalty, + double factor = 1.) + { + const unsigned int n_dofs = fe.dofs_per_cell; + + AssertDimension(fe.get_fe().n_components(), dim); + AssertDimension(M.m(), n_dofs); + AssertDimension(M.n(), n_dofs); + + for (unsigned int k=0; k n = fe.normal_vector(k); + for (unsigned int i=0; iF the vector @@ -208,6 +269,72 @@ namespace LocalIntegrators } } + /** + * The weak boundary condition of Nitsche type for the tangential displacement in linear elasticity: + * @f[ + * \int_F \Bigl(\gamma (u_\tau-g_\tau) \cdot v_\tau - n^T \epsilon(u_\tau) v - (u_\tau-g_\tau) \epsilon(v_\tau) n\Bigr)\;ds. + * @f] + */ + template + inline void nitsche_tangential_residual ( + Vector &result, + const FEValuesBase &fe, + const VectorSlice > > &input, + const VectorSlice > > > &Dinput, + const VectorSlice > > &data, + double penalty, + double factor = 1.) + { + const unsigned int n_dofs = fe.dofs_per_cell; + AssertVectorVectorDimension(input, dim, fe.n_quadrature_points); + AssertVectorVectorDimension(Dinput, dim, fe.n_quadrature_points); + AssertVectorVectorDimension(data, dim, fe.n_quadrature_points); + + for (unsigned int k=0; k n = fe.normal_vector(k); + for (unsigned int i=0; iF the vector diff --git a/tests/integrators/elasticity_02.cc b/tests/integrators/elasticity_02.cc new file mode 100644 index 0000000000..ef9ba82f1c --- /dev/null +++ b/tests/integrators/elasticity_02.cc @@ -0,0 +1,127 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2012 - 2015 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 nitsche_tangential in Elasticity +// Output matrices and assert consistency of residuals + +#include "../tests.h" +#include "../test_grids.h" + +#include +#include + +#include +#include +#include +#include + +using namespace LocalIntegrators::Elasticity; + +template +void test_boundary(const FEValuesBase &fev) +{ + const unsigned int n = fev.dofs_per_cell; + unsigned int d=fev.get_fe().n_components(); + FullMatrix M(n,n); + nitsche_tangential_matrix(M, fev, 17); + { + LogStream::Prefix pre("bdry"); + M.print(deallog,12,8); + } + + Vector u(n), v(n), w(n); + std::vector > + uval (d,std::vector(fev.n_quadrature_points)), + null_val(d,std::vector(fev.n_quadrature_points, 0.)); + std::vector > > + ugrad (d,std::vector >(fev.n_quadrature_points)); + + std::vector indices(n); + for (unsigned int i=0; i > >(uval), true); + fev.get_function_gradients(u, indices, VectorSlice > > >(ugrad), true); + nitsche_tangential_residual(w, fev, make_slice(uval), make_slice(ugrad), make_slice(null_val), 17); + M.vmult(v,u); + w.add(-1., v); + deallog << ' ' << w.l2_norm(); + } + deallog << std::endl; + } +} + + +template +void +test_fe(Triangulation &tr, FiniteElement &fe) +{ + deallog << fe.get_name() << std::endl << "cell matrix" << std::endl; + typename Triangulation::cell_iterator cell1 = tr.begin(1); + + QGauss face_quadrature(fe.tensor_degree()+1); + FEFaceValues fef1(fe, face_quadrature, update_values | update_gradients | update_normal_vectors); + for (unsigned int i=0; i::faces_per_cell; ++i) + { + deallog << "boundary_matrix " << i << std::endl; + fef1.reinit(cell1, i); + test_boundary(fef1); + } +} + + + +template +void +test(Triangulation &tr) +{ + FE_DGQ q1(1); + FESystem fe1(q1,dim); + test_fe(tr, fe1); + + FE_DGQ q2(2); + FESystem fe2(q2,dim); + test_fe(tr, fe2); + + FE_Nedelec n1(1); + test_fe(tr, n1); + + FE_RaviartThomas rt1(1); + test_fe(tr, rt1); +} + + +int main() +{ + initlog(); + deallog.threshold_double(1.e-10); + deallog.precision(8); + + Triangulation<2> tr2; + TestGrids::hypercube(tr2, 1); + test(tr2); + + Triangulation<3> tr3; + TestGrids::hypercube(tr3, 1); + test(tr3); +} diff --git a/tests/integrators/elasticity_02.output b/tests/integrators/elasticity_02.output new file mode 100644 index 0000000000..e3611cd6a0 --- /dev/null +++ b/tests/integrators/elasticity_02.output @@ -0,0 +1,1469 @@ + +DEAL::Triangulation hypercube 2D refinement 1 steps 4 active cells 5 total cells +DEAL::FESystem<2>[FE_DGQ<2>(1)^2] +DEAL::cell matrix +DEAL::boundary_matrix 0 +DEAL:bdry::0 0 0 0 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