From: shakirbsm Date: Mon, 3 Aug 2015 16:55:47 +0000 (+0200) Subject: advection residuals added and tested X-Git-Tag: v8.4.0-rc2~524^2~2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=68e1b17afa8fb323d2b6596a2388d09b20163dd5;p=dealii.git advection residuals added and tested --- diff --git a/include/deal.II/integrators/advection.h b/include/deal.II/integrators/advection.h index 2c4e84bc91..5f585cf9de 100644 --- a/include/deal.II/integrators/advection.h +++ b/include/deal.II/integrators/advection.h @@ -117,10 +117,15 @@ namespace LocalIntegrators } } + + /** - * Advection residual operator in strong form + * Scalar advection residual operator in strong form * * \f[ r_i = \int_Z (\mathbf w \cdot \nabla)u\, v_i \, dx. \f] + * + * \warning This is not the residual consistent with cell_matrix(), + * but with its transpose. */ template inline void @@ -154,13 +159,17 @@ namespace LocalIntegrators } + /** - * Vector-valued advection residual operator in strong form - * - * - * \f[ r_i = \int_Z \bigl((\mathbf w \cdot \nabla) \mathbf u\bigr) - * \cdot\mathbf v_i \, dx. \f] - */ + * Vector-valued advection residual operator in strong form + * + * + * \f[ r_i = \int_Z \bigl((\mathbf w \cdot \nabla) \mathbf u\bigr) + * \cdot\mathbf v_i \, dx. \f] + * + * \warning This is not the residual consistent with cell_matrix(), + * but with its transpose. + */ template inline void cell_residual ( @@ -195,6 +204,89 @@ namespace LocalIntegrators } } + + + /** + * Scalar advection residual operator in weak form + * + * \f[ r_i = \int_Z (\mathbf w \cdot \nabla)v\, u_i \, dx. \f] + */ + template + inline void + cell_residual ( + Vector &result, + const FEValuesBase &fe, + const std::vector &input, + const VectorSlice > > &velocity, + double factor = 1.) + { + const unsigned int nq = fe.n_quadrature_points; + const unsigned int n_dofs = fe.dofs_per_cell; + Assert(input.size() == nq, ExcDimensionMismatch(input.size(), nq)); + Assert(result.size() == n_dofs, ExcDimensionMismatch(result.size(), n_dofs)); + + AssertDimension(velocity.size(), dim); + const unsigned int v_increment = (velocity[0].size() == 1) ? 0 : 1; + if (v_increment == 1) + { + AssertVectorVectorDimension(velocity, dim, fe.n_quadrature_points); + } + + for (unsigned k=0; k + inline void + cell_residual ( + Vector &result, + const FEValuesBase &fe, + const VectorSlice > > &input, + const VectorSlice > > &velocity, + double factor = 1.) + { + const unsigned int nq = fe.n_quadrature_points; + const unsigned int n_dofs = fe.dofs_per_cell; + const unsigned int n_comp = fe.get_fe().n_components(); + + AssertVectorVectorDimension(input, n_comp, fe.n_quadrature_points); + Assert(result.size() == n_dofs, ExcDimensionMismatch(result.size(), n_dofs)); + + AssertDimension(velocity.size(), dim); + const unsigned int v_increment = (velocity[0].size() == 1) ? 0 : 1; + if (v_increment == 1) + { + AssertVectorVectorDimension(velocity, dim, fe.n_quadrature_points); + } + + for (unsigned k=0; kvelocity is provided as a VectorSlice, having dim + * vectors, one for each velocity component. Each of the vectors must + * either have only a single entry, if the advection velocity is + * constant, or have an entry for each quadrature point. + * + * The finite element can have several components, in which case each + * component is advected by the same velocity. + */ + template + inline void + upwind_value_residual( + Vector &result, + const FEValuesBase &fe, + const std::vector &input, + const std::vector &data, + const VectorSlice > > &velocity, + double factor = 1.) + { + const unsigned int n_dofs = fe.dofs_per_cell; + + AssertDimension(input.size(), fe.n_quadrature_points); + AssertDimension(data.size(), fe.n_quadrature_points); + + AssertDimension(velocity.size(), dim); + const unsigned int v_increment = (velocity[0].size() == 1) ? 0 : 1; + if (v_increment == 1) + { + AssertVectorVectorDimension(velocity, dim, fe.n_quadrature_points); + } + + + for (unsigned k=0; k 0) + { + for (unsigned i=0; ivelocity is provided as a VectorSlice, having dim + * vectors, one for each velocity component. Each of the vectors must + * either have only a single entry, if t he advection velocity is + * constant, or have an entry for each quadrature point. + * + * The finite element can have several components, in which case each + * component is advected by the same velocity. + */ + template + inline void + upwind_value_residual( + Vector &result, + const FEValuesBase &fe, + const VectorSlice > > &input, + const VectorSlice > > &data, + const VectorSlice > > &velocity, + double factor = 1.) + { + const unsigned int n_dofs = fe.dofs_per_cell; + const unsigned int n_comp = fe.get_fe().n_components(); + + AssertVectorVectorDimension(input, n_comp, fe.n_quadrature_points); + AssertVectorVectorDimension(data, n_comp, fe.n_quadrature_points); + + AssertDimension(velocity.size(), dim); + const unsigned int v_increment = (velocity[0].size() == 1) ? 0 : 1; + if (v_increment == 1) + { + AssertVectorVectorDimension(velocity, dim, fe.n_quadrature_points); + } + + + for (unsigned k=0; k 0) + { + for (unsigned i=0; i &M1 = nbeta > 0. ? M11 : M22; + FullMatrix &M2 = nbeta > 0. ? M21 : M12; + const FEValuesBase &fe = nbeta > 0. ? fe1 : fe2; + const FEValuesBase &fetest = nbeta > 0. ? fetest1 : fetest2; + const FEValuesBase &fetestn = nbeta > 0. ? fetest2 : fetest1; + for (unsigned i=0; ivelocity is provided as a VectorSlice, having dim + * vectors, one for each velocity component. Each of the vectors must + * either have only a single entry, if t he advection velocity is + * constant, or have an entry for each quadrature point. + * + * The finite element can have several components, in which case each + * component is advected the same way. + */ + template + void upwind_face_residual ( + Vector &result1, + Vector &result2, + const FEValuesBase &fe1, + const FEValuesBase &fe2, + const std::vector &input1, + const std::vector &input2, + const VectorSlice > > &velocity, + const double factor = 1.) + { + Assert(fe1.get_fe().n_components() == 1, + ExcDimensionMismatch(fe1.get_fe().n_components(), 1)); + Assert(fe2.get_fe().n_components() == 1, + ExcDimensionMismatch(fe2.get_fe().n_components(), 1)); + + const unsigned int n1 = fe1.dofs_per_cell; + // Multiply the quadrature point + // index below with this factor to + // have simpler data for constant + // velocities. + AssertDimension(velocity.size(), dim); + const unsigned int v_increment = (velocity[0].size() == 1) ? 0 : 1; + if (v_increment == 1) + { + AssertVectorVectorDimension(velocity, dim, fe1.n_quadrature_points); + } + for (unsigned k=0; k 0) { - if (nbeta > 0) - { - M11(i,j) += dx_nbeta - * fe1.shape_value(j,k) - * fetest1.shape_value(i,k); - M21(i,j) -= dx_nbeta - * fe1.shape_value(j,k) - * fetest2.shape_value(i,k); - } - else - { - M22(i,j) -= dx_nbeta - * fe2.shape_value(j,k) - * fetest2.shape_value(i,k); - M12(i,j) += dx_nbeta - * fe2.shape_value(j,k) - * fetest1.shape_value(i,k); - } + result1(i) += dx_nbeta*u1*v1; + result2(i) -= dx_nbeta*u1*v2; } else { - for (unsigned int d=0; d 0) - { - M11(i,j) += dx_nbeta - * fe1.shape_value_component(j,k,d) - * fetest1.shape_value_component(i,k,d); - M21(i,j) -= dx_nbeta - * fe1.shape_value_component(j,k,d) - * fetest2.shape_value_component(i,k,d); - } - else - { - M22(i,j) -= dx_nbeta - * fe2.shape_value_component(j,k,d) - * fetest2.shape_value_component(i,k,d); - M12(i,j) += dx_nbeta - * fe2.shape_value_component(j,k,d) - * fetest1.shape_value_component(i,k,d); - } + + result1(i) += dx_nbeta*u2*v1; + result2(i) -= dx_nbeta*u2*v2; } + } + } + } + + + + /** + * Vector-valued case: Upwind flux in the interior for weak advection operator. Matrix entries + * correspond to the upwind value of the trial function, multiplied by the + * jump of the test functions + * @f[ + * a_{ij} = \int_F \left|\mathbf w + * \cdot \mathbf n\right| + * u^\uparrow + * (v^\uparrow-v^\downarrow) + * \,ds + * @f] + * + * The velocity is provided as a VectorSlice, having dim + * vectors, one for each velocity component. Each of the vectors must + * either have only a single entry, if t he advection velocity is + * constant, or have an entry for each quadrature point. + * + * The finite element can have several components, in which case each + * component is advected the same way. + */ + template + void upwind_face_residual ( + Vector &result1, + Vector &result2, + const FEValuesBase &fe1, + const FEValuesBase &fe2, + const VectorSlice > > &input1, + const VectorSlice > > &input2, + const VectorSlice > > &velocity, + const double factor = 1.) + { + const unsigned int n_comp = fe1.get_fe().n_components(); + const unsigned int n1 = fe1.dofs_per_cell; + AssertVectorVectorDimension(input1, n_comp, fe1.n_quadrature_points); + AssertVectorVectorDimension(input2, n_comp, fe2.n_quadrature_points); + + // Multiply the quadrature point + // index below with this factor to + // have simpler data for constant + // velocities. + AssertDimension(velocity.size(), dim); + const unsigned int v_increment = (velocity[0].size() == 1) ? 0 : 1; + if (v_increment == 1) + { + AssertVectorVectorDimension(velocity, dim, fe1.n_quadrature_points); + } + + for (unsigned k=0; k 0) + { + result1(i) += dx_nbeta*u1*v1; + result2(i) -= dx_nbeta*u1*v2; + } + else + { + + result1(i) += dx_nbeta*u2*v1; + result2(i) -= dx_nbeta*u2*v2; + } + } } } + } } diff --git a/tests/integrators/advection_01.cc b/tests/integrators/advection_01.cc new file mode 100644 index 0000000000..6f9248b7f7 --- /dev/null +++ b/tests/integrators/advection_01.cc @@ -0,0 +1,299 @@ +// --------------------------------------------------------------------- +// +// 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 the functions in integrators/laplace.h +// Output matrices and assert consistency of residuals + +#include "../tests.h" +#include "../test_grids.h" + +#include +#include +#include + +#include +#include + +using namespace LocalIntegrators::Advection; + +template +void test_cell(const FEValuesBase &fev) +{ + const unsigned int n = fev.dofs_per_cell; + unsigned int d=fev.get_fe().n_components(); + FullMatrix M(n,n); + std::vector > vel(dim,std::vector(1)); + vel[0][0]=1.; + vel[1][0]=1.; + if (dim > 2) + vel[2][0]=1.; + cell_matrix(M,fev,fev,vel); + { + LogStream::Prefix pre("cell"); + M.print(deallog,8); + } + + Vector u(n), v(n), w(n); + std::vector > + uval (d,std::vector(fev.n_quadrature_points)); + + std::vector indices(n); + for (unsigned int i=0; i > >(uval), true); + cell_residual(w, fev, make_slice(uval),vel); + M.vmult(v,u); + w.add(-1., v); + deallog << ' ' << w.l2_norm(); + if (d==1) + { + cell_residual(w, fev, uval[0],vel); + M.vmult(v,u); + w.add(-1., v); + deallog << " e" << 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); + std::vector > vel(dim ,std::vector(1)); + vel[0][0]=1.; + vel[1][0]=1.; + if (dim > 2) + vel[2][0]=1.; + upwind_value_matrix(M, fev, fev, vel); + { + LogStream::Prefix pre("bdry"); + M.print(deallog,8); + } + + Vector u(n), v(n), w(n); + std::vector > + uval(d, std::vector(fev.n_quadrature_points)); + std::vector > + 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); + upwind_value_residual(w, fev, make_slice(uval), make_slice(null_val), vel); + M.vmult(v,u); + w.add(-1., v); + deallog << ' ' << w.l2_norm(); + if (d==1) + { + upwind_value_residual(w, fev, uval[0], null_val[0], vel); + M.vmult(v,u); + w.add(-1., v); + deallog << " e" << 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 = fev2.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); + std::vector > vel(dim ,std::vector(1)); + vel[0][0]=1.; + vel[1][0]=1.; + if (dim > 2) + vel[2][0]=1.; + + upwind_value_matrix(M11, M12, M21, M22, fev1, fev2, fev1, fev2, vel); + + { + LogStream::Prefix pre("M11"); + M11.print(deallog,8); + } + { + LogStream::Prefix pre("M12"); + M12.print(deallog,8); + } + { + LogStream::Prefix pre("M21"); + M21.print(deallog,8); + } + { + LogStream::Prefix pre("M22"); + M22.print(deallog,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 indices1(n1), indices2(n2); + for (unsigned int i=0; i > >(u1val), true); + upwind_face_residual(w1, w2, fev1, fev2, + make_slice(u1val), + make_slice(nullval), + vel); + M11.vmult(v1,u1); + w1.add(-1., v1); + M21.vmult(v2,u1); + w2.add(-1., v2); + deallog << "sys a " << w1.l2_norm() << ' ' << w2.l2_norm() << std::endl; + if (d==1) + { + w1 = 0.; + w2 = 0.; + upwind_face_residual(w1, w2, fev1, fev2, u1val[0], nullval[0], vel); + M11.vmult(v1,u1); + w1.add(-1., v1); + M21.vmult(v2,u1); + w2.add(-1., v2); + deallog << "sing a " << w1.l2_norm() << ' ' << w2.l2_norm() << std::endl; + } + w1 = 0.; + w2 = 0.; + fev2.get_function_values(u1, indices2, VectorSlice > >(u1val), true); + upwind_face_residual(w1, w2, fev1, fev2, + make_slice(nullval), + make_slice(u1val), + vel); + M12.vmult(v1,u1); + w1.add(-1., v1); + M22.vmult(v2,u1); + w2.add(-1., v2); + deallog << "sys b " << w1.l2_norm() << ' ' << w2.l2_norm() << std::endl; + if (d==1) + { + w1 = 0.; + w2 = 0.; + upwind_face_residual(w1, w2, fev1, fev2, nullval[0], u1val[0], vel); + M12.vmult(v1,u1); + w1.add(-1., v1); + M22.vmult(v2,u1); + w2.add(-1., v2); + deallog << "sing b " << w1.l2_norm() << ' ' << w2.l2_norm() << std::endl; + } + } + 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()); + FEValues fev(fe, quadrature, update_values | 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 | update_normal_vectors); + 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); + test_face(fef2, fef1); +} + + +template +void +test(Triangulation &tr) +{ + FE_DGQ q1(1); + test_fe(tr, q1); + + FE_DGQ q2(2); + test_fe(tr, q2); + + FE_Nedelec n1(1); + test_fe(tr, n1); +} + + +int main() +{ + initlog(); + deallog.threshold_double(1.e-10); + + Triangulation<2> tr2; + TestGrids::hypercube(tr2, 1); + test(tr2); + + Triangulation<3> tr3; + TestGrids::hypercube(tr3, 1); + test(tr3); +} diff --git a/tests/integrators/advection_01.output b/tests/integrators/advection_01.output new file mode 100644 index 0000000000..5cfda9b11e --- /dev/null +++ b/tests/integrators/advection_01.output @@ -0,0 +1,2407 @@ + +DEAL::Triangulation hypercube 2D refinement 1 steps 4 active cells 5 total cells +DEAL::FE_DGQ<2>(1) +DEAL::cell matrix +DEAL:cell::0.25 0.25 0.25 0.25 +DEAL:cell::0 0 0 0 +DEAL:cell::0 0 0 0 +DEAL:cell::-0.25 -0.25 -0.25 -0.25 +DEAL:Residuals:: 0 e0 0 e0 0 e0 0 e0 +DEAL::boundary_matrix 0 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0 0 +DEAL:Residuals:: 0 e0 0 e0 0 e0 0 e0 +DEAL::boundary_matrix 1 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0.33 0 0.17 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0.17 0 0.33 +DEAL:Residuals:: 0 e0 0 e0 0 e0 0 e0 +DEAL::boundary_matrix 2 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0 0 +DEAL:Residuals:: 0 e0 0 e0 0 e0 0 e0 +DEAL::boundary_matrix 3 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0 0 +DEAL:bdry::0 0 0.33 0.17 +DEAL:bdry::0 0 0.17 0.33 +DEAL:Residuals:: 0 e0 0 e0 0 e0 0 e0 +DEAL::face_matrix 0 +DEAL:M11::0 0 0 0 +DEAL:M11::0 0.33 0 0.17 +DEAL:M11::0 0 0 0 +DEAL:M11::0 0.17 0 0.33 +DEAL:M12::0 0 0 0 +DEAL:M12::0 0 0 0 +DEAL:M12::0 0 0 0 +DEAL:M12::0 0 0 0 +DEAL:M21::0 -0.33 0 -0.17 +DEAL:M21::0 0 0 0 +DEAL:M21::0 -0.17 0 -0.33 +DEAL:M21::0 0 0 0 +DEAL:M22::0 0 0 0 +DEAL:M22::0 0 0 0 +DEAL:M22::0 0 0 0 +DEAL:M22::0 0 0 0 +DEAL:Residuals::sys a 0 0 +DEAL:Residuals::sing a 0 0 +DEAL:Residuals::sys b 0 0 +DEAL:Residuals::sing b 0 0 +DEAL:Residuals::sys a 0 0 +DEAL:Residuals::sing a 0 0 +DEAL:Residuals::sys b 0 0 +DEAL:Residuals::sing b 0 0 +DEAL:Residuals::sys a 0 0 +DEAL:Residuals::sing a 0 0 +DEAL:Residuals::sys b 0 0 +DEAL:Residuals::sing b 0 0 +DEAL:Residuals::sys a 0 0 +DEAL:Residuals::sing a 0 0 +DEAL:Residuals::sys b 0 0 +DEAL:Residuals::sing b 0 0 +DEAL:Residuals:: +DEAL:M11::0 0 0 0 +DEAL:M11::0 0 0 0 +DEAL:M11::0 0 0 0 +DEAL:M11::0 0 0 0 +DEAL:M12::0 -0.33 0 -0.17 +DEAL:M12::0 0 0 0 +DEAL:M12::0 -0.17 0 -0.33 +DEAL:M12::0 0 0 0 +DEAL:M21::0 0 0 0 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