From: Guido Kanschat Date: Tue, 2 Aug 2016 18:31:24 +0000 (+0200) Subject: grad-div residuals added and tested for consistency X-Git-Tag: v8.5.0-rc1~789^2~2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a11f0b629bcc4e1dd44860e5307f29e993c0e753;p=dealii.git grad-div residuals added and tested for consistency grad-div removed from file divergence.h --- diff --git a/include/deal.II/integrators/divergence.h b/include/deal.II/integrators/divergence.h index fcbc72811b..3dedf483cb 100644 --- a/include/deal.II/integrators/divergence.h +++ b/include/deal.II/integrators/divergence.h @@ -1,6 +1,6 @@ // --------------------------------------------------------------------- // -// Copyright (C) 2010 - 2015 by the deal.II authors +// Copyright (C) 2010 - 2016 by the deal.II authors // // This file is part of the deal.II library. // @@ -40,6 +40,7 @@ namespace LocalIntegrators namespace Divergence { /** + * @deprecated Use LocalIntegrators::GradDiv:: * Auxiliary function. Computes the grad-div-operator from a set of * Hessians. * @@ -451,10 +452,8 @@ namespace LocalIntegrators } /** - * The weak form of the grad-div operator penalizing volume changes - * @f[ - * \int_Z \nabla\!\cdot\!u \nabla\!\cdot\!v \,dx - * @f] + * @deprecated Use LocalIntegrators::GradDiv::cell_matrix() + * instead. * * @author Guido Kanschat * @date 2011 @@ -463,7 +462,7 @@ namespace LocalIntegrators void grad_div_matrix ( FullMatrix &M, const FEValuesBase &fe, - double factor = 1.) + double factor = 1.) DEAL_II_DEPRECATED { const unsigned int n_dofs = fe.dofs_per_cell; @@ -491,10 +490,7 @@ namespace LocalIntegrators } /** - * The weak form of the grad-div residual - * @f[ - * \int_Z \nabla\!\cdot\!u \nabla\!\cdot\!v \,dx - * @f] + * @deprecated Use LocalIntegrators::GradDiv::cell_residual() instead. * * @author Guido Kanschat * @date 2014 @@ -504,7 +500,7 @@ namespace LocalIntegrators Vector &result, const FEValuesBase &fetest, const VectorSlice > > > &input, - const double factor = 1.) + const double factor = 1.) DEAL_II_DEPRECATED { const unsigned int n_dofs = fetest.dofs_per_cell; @@ -529,114 +525,6 @@ namespace LocalIntegrators } } - /** - * The matrix for the weak boundary condition of Nitsche type for linear elasticity: - * @f[ - * \int_F \Bigl(\gamma (u \cdot n)(v \cdot n) - \nabla\cdot u - * v\cdot n - u \cdot n \nabla \cdot v \Bigr)\;ds. - * @f] - */ - template - inline void nitsche_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; i - void ip_matrix ( - FullMatrix &M11, - FullMatrix &M12, - FullMatrix &M21, - FullMatrix &M22, - const FEValuesBase &fe1, - const FEValuesBase &fe2, - double penalty, - double factor1 = 1., - double factor2 = -1.) - { - const unsigned int n_dofs = fe1.dofs_per_cell; - AssertDimension(M11.n(), n_dofs); - AssertDimension(M11.m(), n_dofs); - AssertDimension(M12.n(), n_dofs); - AssertDimension(M12.m(), n_dofs); - AssertDimension(M21.n(), n_dofs); - AssertDimension(M21.m(), n_dofs); - AssertDimension(M22.n(), n_dofs); - AssertDimension(M22.m(), n_dofs); - - const double nui = factor1; - const double nue = (factor2 < 0) ? factor1 : factor2; - const double nu = .5*(nui+nue); - - for (unsigned int k=0; k n = fe1.normal_vector(k); - for (unsigned int i=0; i +#include +#include +#include +#include +#include +#include + +DEAL_II_NAMESPACE_OPEN + +namespace LocalIntegrators +{ + /** + * Local integrators related to the grad-div operator and its boundary + * traces + * + * @ingroup Integrators + * @author Guido Kanschat, Timo Heister + * @date 2016 + */ + namespace GradDiv + { + /** + * Auxiliary function. Computes the grad-div-operator from a set of + * Hessians. + * + * @note The third tensor argument is not used in two dimensions and can + * for instance duplicate one of the previous. + * + * @author Guido Kanschat + * @date 2011 + */ + template + Tensor<1,dim> + grad_div( + const Tensor<2,dim> &h0, + const Tensor<2,dim> &h1, + const Tensor<2,dim> &h2) + { + Tensor<1,dim> result; + for (unsigned int d=0; d=2) result[d] += h1[d][1]; + if (dim >=3) result[d] += h2[d][2]; + } + return result; + } + + /** + * The weak form of the grad-div operator penalizing volume changes + * @f[ + * \int_Z \nabla\!\cdot\!u \nabla\!\cdot\!v \,dx + * @f] + * + * @author Guido Kanschat + * @date 2011 + */ + template + void cell_matrix ( + FullMatrix &M, + const FEValuesBase &fe, + 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 + void cell_residual ( + Vector &result, + const FEValuesBase &fetest, + const VectorSlice > > > &input, + const double factor = 1.) + { + const unsigned int n_dofs = fetest.dofs_per_cell; + + AssertDimension(fetest.get_fe().n_components(), dim); + AssertVectorVectorDimension(input, dim, fetest.n_quadrature_points); + + for (unsigned int k=0; k + inline void nitsche_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 + * @f[ + * \int_F \Bigl(\gamma (\mathbf u \cdot \mathbf n- \mathbf g \cdot + * \mathbf n) (\mathbf v \cdot \mathbf n) + * - \nabla \cdot \mathbf u (\mathbf v \cdot \mathbf n) + * - (\mathbf u-\mathbf g) \cdot \mathbf n \nabla \cdot v\Bigr)\;ds. + * @f] + * + * Here, u is the finite element function whose values and gradient + * are given in the arguments input and Dinput, + * respectively. g is the inhomogeneous boundary value in the + * argument data. $\gamma$ is the usual penalty parameter. + * + * @author Guido Kanschat + * @date 2008, 2009, 2010 + */ + template + void nitsche_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; + AssertDimension(fe.get_fe().n_components(), dim) + 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); + + double umgn = 0.; + double divu = 0.; + for (unsigned int d=0; d + void ip_matrix ( + FullMatrix &M11, + FullMatrix &M12, + FullMatrix &M21, + FullMatrix &M22, + const FEValuesBase &fe1, + const FEValuesBase &fe2, + double penalty, + double factor1 = 1., + double factor2 = -1.) + { + const unsigned int n_dofs = fe1.dofs_per_cell; + AssertDimension(M11.n(), n_dofs); + AssertDimension(M11.m(), n_dofs); + AssertDimension(M12.n(), n_dofs); + AssertDimension(M12.m(), n_dofs); + AssertDimension(M21.n(), n_dofs); + AssertDimension(M21.m(), n_dofs); + AssertDimension(M22.n(), n_dofs); + AssertDimension(M22.m(), n_dofs); + + const double fi = factor1; + const double fe = (factor2 < 0) ? factor1 : factor2; + const double f = .5*(fi+fe); + + for (unsigned int k=0; k n = fe1.normal_vector(k); + for (unsigned int i=0; i + void + ip_residual( + Vector &result1, + Vector &result2, + const FEValuesBase &fe1, + const FEValuesBase &fe2, + const VectorSlice > > &input1, + const VectorSlice > > > &Dinput1, + const VectorSlice > > &input2, + const VectorSlice > > > &Dinput2, + double pen, + double int_factor = 1., + double ext_factor = -1.) + { + const unsigned int n1 = fe1.dofs_per_cell; + + AssertDimension(fe1.get_fe().n_components(), dim); + AssertVectorVectorDimension(input1, dim, fe1.n_quadrature_points); + AssertVectorVectorDimension(Dinput1, dim, fe1.n_quadrature_points); + AssertVectorVectorDimension(input2, dim, fe2.n_quadrature_points); + AssertVectorVectorDimension(Dinput2, dim, fe2.n_quadrature_points); + + const double fi = int_factor; + const double fe = (ext_factor < 0) ? int_factor : ext_factor; + const double penalty = .5 * pen * (fi + fe); + + + for (unsigned int k=0; k n = fe1.normal_vector(k); + double uni = 0.; + double une = 0.; + double divui = 0.; + double divue = 0.; + for (unsigned int d=0; d + +#include +#include +#include +#include + +#include "tbb/task_scheduler_init.h" +#include + +using namespace LocalIntegrators::GradDiv; + +template +void test_cell(const FEValuesBase &fev) +{ + const unsigned int n = fev.dofs_per_cell; + FullMatrix M(n,n); + cell_matrix(M,fev); + { + LogStream::Prefix pre("cell"); + M.print(deallog,12,8); + } + + Vector u(n), v(n), w(n); + std::vector > > + ugrad(dim,std::vector >(fev.n_quadrature_points)); + + std::vector indices(n); + for (unsigned int i=0; i > > >(ugrad), true); + cell_residual(w, fev, make_slice(ugrad)); + M.vmult(v,u); + w.add(-1., v); + deallog << ' ' << w.l2_norm(); + } + deallog << std::endl; + } +} + + +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_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_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_face(const FEValuesBase &fev1, + const FEValuesBase &fev2) +{ + const unsigned int n1 = fev1.dofs_per_cell; + const unsigned int n2 = fev1.dofs_per_cell; + unsigned int d=fev1.get_fe().n_components(); + FullMatrix M11(n1,n1); + FullMatrix M12(n1,n2); + FullMatrix M21(n2,n1); + FullMatrix M22(n2,n2); + + ip_matrix(M11, M12, M21, M22, fev1, fev2, 17); + + { + LogStream::Prefix pre("M11"); + M11.print(deallog,12,8); + } + { + LogStream::Prefix pre("M12"); + M12.print(deallog,12,8); + } + { + LogStream::Prefix pre("M21"); + M21.print(deallog,12,8); + } + { + LogStream::Prefix pre("M22"); + M22.print(deallog,12,8); + } + + Vector u1(n1), v1(n1), w1(n1); + Vector u2(n2), v2(n2), w2(n2); + std::vector > + u1val (d,std::vector(fev1.n_quadrature_points)), + nullval (d,std::vector(fev2.n_quadrature_points, 0.)); + std::vector > > + u1grad(d,std::vector >(fev1.n_quadrature_points)), + nullgrad(d,std::vector >(fev2.n_quadrature_points, Tensor<1,dim>())); + + std::vector indices1(n1), indices2(n2); + for (unsigned int i=0; i > >(u1val), true); + fev1.get_function_gradients(u1, indices1, VectorSlice > > >(u1grad), true); + ip_residual(w1, w2, fev1, fev2, + make_slice(u1val), make_slice(u1grad), + make_slice(nullval), make_slice(nullgrad), + 17); + M11.vmult(v1,u1); + w1.add(-1., v1); + M21.vmult(v2,u1); + w2.add(-1., v2); + deallog << ' ' << w1.l2_norm() + w2.l2_norm(); + + w1 = 0.; + w2 = 0.; + fev2.get_function_values(u1, indices2, VectorSlice > >(u1val), true); + fev2.get_function_gradients(u1, indices2, VectorSlice > > >(u1grad), true); + ip_residual(w1, w2, fev1, fev2, + make_slice(nullval), make_slice(nullgrad), + make_slice(u1val), make_slice(u1grad), + 17); + M12.vmult(v1,u1); + w1.add(-1., v1); + M22.vmult(v2,u1); + w2.add(-1., v2); + deallog << ' ' << w1.l2_norm() + w2.l2_norm(); + } + deallog << std::endl; + } +} + + +template +void +test_fe(Triangulation &tr, FiniteElement &fe) +{ + deallog << fe.get_name() << std::endl << "cell matrix" << std::endl; + QGauss quadrature(fe.tensor_degree()+1); + FEValues fev(fe, quadrature, update_gradients); + typename Triangulation::cell_iterator cell1 = tr.begin(1); + fev.reinit(cell1); + test_cell(fev); + + 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); + } + + FEFaceValues fef2(fe, face_quadrature, update_values | update_gradients); + typename Triangulation::cell_iterator cell2 = cell1->neighbor(1); + + deallog << "face_matrix " << 0 << std::endl; + cell1 = tr.begin(1); + fef1.reinit(cell1, 1); + fef2.reinit(cell2, 0); + test_face(fef1, fef2); +} + + +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/grad_div_01.output b/tests/integrators/grad_div_01.output new file mode 100644 index 0000000000..69639cbe15 --- /dev/null +++ b/tests/integrators/grad_div_01.output @@ -0,0 +1,2718 @@ + +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:cell::0.33333333 -0.33333333 0.16666667 -0.16666667 0.25000000 0.25000000 -0.25000000 -0.25000000 +DEAL:cell::-0.33333333 0.33333333 -0.16666667 0.16666667 -0.25000000 -0.25000000 0.25000000 0.25000000 +DEAL:cell::0.16666667 -0.16666667 0.33333333 -0.33333333 0.25000000 0.25000000 -0.25000000 -0.25000000 +DEAL:cell::-0.16666667 0.16666667 -0.33333333 0.33333333 -0.25000000 -0.25000000 0.25000000 0.25000000 +DEAL:cell::0.25000000 -0.25000000 0.25000000 -0.25000000 0.33333333 0.16666667 -0.33333333 -0.16666667 +DEAL:cell::0.25000000 -0.25000000 0.25000000 -0.25000000 0.16666667 0.33333333 -0.16666667 -0.33333333 +DEAL:cell::-0.25000000 0.25000000 -0.25000000 0.25000000 -0.33333333 -0.16666667 0.33333333 0.16666667 +DEAL:cell::-0.25000000 0.25000000 -0.25000000 0.25000000 -0.16666667 -0.33333333 0.16666667 0.33333333 +DEAL:Residuals:: 0 0 0 0 0 0 0 0 +DEAL::boundary_matrix 0 +DEAL:bdry::10.666667 0.33333333 5.3333333 0.16666667 -0.50000000 0 0.50000000 0 +DEAL:bdry::0.33333333 0 0.16666667 0 0 0 0 0 +DEAL:bdry::5.3333333 0.16666667 10.666667 0.33333333 -0.50000000 0 0.50000000 0 +DEAL:bdry::0.16666667 0 0.33333333 0 0 0 0 0 +DEAL:bdry::-0.50000000 0 -0.50000000 0 0 0 0 0 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:bdry::0.50000000 0 0.50000000 0 0 0 0 0 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:Residuals:: 0 0 0 0 0 0 0 0 +DEAL::boundary_matrix 1 +DEAL:bdry::0 0.33333333 0 0.16666667 0 0 0 0 +DEAL:bdry::0.33333333 10.666667 0.16666667 5.3333333 0 0.50000000 0 -0.50000000 +DEAL:bdry::0 0.16666667 0 0.33333333 0 0 0 0 +DEAL:bdry::0.16666667 5.3333333 0.33333333 10.666667 0 0.50000000 0 -0.50000000 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:bdry::0 0.50000000 0 0.50000000 0 0 0 0 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:bdry::0 -0.50000000 0 -0.50000000 0 0 0 0 +DEAL:Residuals:: 0 0 0 0 0 0 0 0 +DEAL::boundary_matrix 2 +DEAL:bdry::0 0 0 0 -0.50000000 -0.50000000 0 0 +DEAL:bdry::0 0 0 0 0.50000000 0.50000000 0 0 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:bdry::-0.50000000 0.50000000 0 0 10.666667 5.3333333 0.33333333 0.16666667 +DEAL:bdry::-0.50000000 0.50000000 0 0 5.3333333 10.666667 0.16666667 0.33333333 +DEAL:bdry::0 0 0 0 0.33333333 0.16666667 0 0 +DEAL:bdry::0 0 0 0 0.16666667 0.33333333 0 0 +DEAL:Residuals:: 0 0 0 0 0 0 0 0 +DEAL::boundary_matrix 3 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:bdry::0 0 0 0 0 0 0 0 +DEAL:bdry::0 0 0 0 0 0 0.50000000 0.50000000 +DEAL:bdry::0 0 0 0 0 0 -0.50000000 -0.50000000 +DEAL:bdry::0 0 0 0 0 0 0.33333333 0.16666667 +DEAL:bdry::0 0 0 0 0 0 0.16666667 0.33333333 +DEAL:bdry::0 0 0.50000000 -0.50000000 0.33333333 0.16666667 10.666667 5.3333333 +DEAL:bdry::0 0 0.50000000 -0.50000000 0.16666667 0.33333333 5.3333333 10.666667 +DEAL:Residuals:: 0 0 0 0 0 0 0 0 +DEAL::face_matrix 0 +DEAL:M11::0 0.16666667 0 0.083333333 0 0 0 0 +DEAL:M11::0.16666667 5.3333333 0.083333333 2.6666667 0 0.25000000 0 -0.25000000 +DEAL:M11::0 0.083333333 0 0.16666667 0 0 0 0 +DEAL:M11::0.083333333 2.6666667 0.16666667 5.3333333 0 0.25000000 0 -0.25000000 +DEAL:M11::0 0 0 0 0 0 0 0 +DEAL:M11::0 0.25000000 0 0.25000000 0 0 0 0 +DEAL:M11::0 0 0 0 0 0 0 0 +DEAL:M11::0 -0.25000000 0 -0.25000000 0 0 0 0 +DEAL:M12::-0.16666667 0 -0.0833333330 0 0 0 0 +DEAL:M12::-5.3333333 -0.16666667 -2.6666667 -0.0833333330.25000000 0 -0.25000000 0 +DEAL:M12::-0.0833333330 -0.16666667 0 0 0 0 0 +DEAL:M12::-2.6666667 -0.083333333-5.3333333 -0.16666667 0.25000000 0 -0.25000000 0 +DEAL:M12::0 0 0 0 0 0 0 0 +DEAL:M12::-0.25000000 0 -0.25000000 0 0 0 0 0 +DEAL:M12::0 0 0 0 0 0 0 0 +DEAL:M12::0.25000000 0 0.25000000 0 0 0 0 0 +DEAL:M21::-0.16666667 -5.3333333 -0.083333333-2.6666667 0 -0.25000000 0 0.25000000 +DEAL:M21::0 -0.16666667 0 -0.0833333330 0 0 0 +DEAL:M21::-0.083333333-2.6666667 -0.16666667 -5.3333333 0 -0.25000000 0 0.25000000 +DEAL:M21::0 -0.0833333330 -0.16666667 0 0 0 0 +DEAL:M21::0 0.25000000 0 0.25000000 0 0 0 0 +DEAL:M21::0 0 0 0 0 0 0 0 +DEAL:M21::0 -0.25000000 0 -0.25000000 0 0 0 0 +DEAL:M21::0 0 0 0 0 0 0 0 +DEAL:M22::5.3333333 0.16666667 2.6666667 0.083333333 -0.25000000 0 0.25000000 0 +DEAL:M22::0.16666667 0 0.083333333 0 0 0 0 0 +DEAL:M22::2.6666667 0.083333333 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