From: Wolfgang Bangerth Date: Wed, 24 Apr 2002 13:21:12 +0000 (+0000) Subject: Implement evaluating the x-derivative at a point. X-Git-Tag: v8.0.0~18121 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f8868334bed07f97f2869eb0340ff2fee92b6f8d;p=dealii.git Implement evaluating the x-derivative at a point. git-svn-id: https://svn.dealii.org/trunk@5727 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-14/step-14.cc b/deal.II/examples/step-14/step-14.cc index 084a5289d7..a9274c154a 100644 --- a/deal.II/examples/step-14/step-14.cc +++ b/deal.II/examples/step-14/step-14.cc @@ -171,6 +171,213 @@ namespace Evaluation }; + // @sect4{The PointXDerivativeEvaluation class} + + // Besides the class implementing + // the evaluation of the solution + // at one point, we here provide + // one which evaluates the gradient + // at a grid point. Since in + // general the gradient of a finite + // element function is not + // continuous at a vertex, we have + // to be a little bit more careful + // here. What we do is to loop over + // all cells, even if we have found + // the point already on once cell, + // and use the mean value of the + // gradient at the vertex taken + // from all adjacent cells. + // + // Given the interface of the + // ``PointValueEvaluation'' class, + // the declaration of this class + // provides little surprise, and + // neither does the constructor: + template + class PointXDerivativeEvaluation : public EvaluationBase + { + public: + PointXDerivativeEvaluation (const Point &evaluation_point, + TableHandler &results_table); + + virtual void operator () (const DoFHandler &dof_handler, + const Vector &solution) const; + + DeclException1 (ExcEvaluationPointNotFound, + Point, + << "The evaluation point " << arg1 + << " was not found among the vertices of the present grid."); + private: + const Point evaluation_point; + TableHandler &results_table; + }; + + + template + PointXDerivativeEvaluation:: + PointXDerivativeEvaluation (const Point &evaluation_point, + TableHandler &results_table) + : + evaluation_point (evaluation_point), + results_table (results_table) + {}; + + + // The more interesting things + // happen inside the function doing + // the actual evaluation: + template + void + PointXDerivativeEvaluation:: + operator () (const DoFHandler &dof_handler, + const Vector &solution) const + { + // This time initialize the + // return value with something + // useful, since we will have to + // add up a number of + // contributions and take the + // mean value afterwards... + double point_derivative = 0; + + // ...then have some objects of + // which the meaning wil become + // clear below... + QTrapez vertex_quadrature; + FEValues fe_values (dof_handler.get_fe(), + vertex_quadrature, + update_gradients | update_q_points); + std::vector > + solution_gradients (vertex_quadrature.n_quadrature_points); + + // ...and next loop over all cells + // and their vertices, and count + // how often the vertex has been + // found: + typename DoFHandler::active_cell_iterator + cell = dof_handler.begin_active(), + endc = dof_handler.end(); + unsigned int evaluation_point_hits = 0; + for (; cell!=endc; ++cell) + for (unsigned int vertex=0; + vertex::vertices_per_cell; + ++vertex) + if (cell->vertex(vertex) == evaluation_point) + { + // Things are now no more + // as simple, since we + // can't get the gradient + // of the finite element + // field as before, where + // we simply had to pick + // one degree of freedom + // at a vertex. + // + // Rather, we have to + // evaluate the finite + // element field on this + // cell, and at a certain + // point. As you know, + // evaluating finite + // element fields at + // certain points is done + // through the + // ``FEValues'' class, so + // we use that. The + // question is: the + // ``FEValues'' object + // needs to be a given a + // quadrature formula and + // can then compute the + // values of finite + // element quantities at + // the quadrature + // points. Here, we don't + // want to do quadrature, + // we simply want to + // specify some points! + // + // Nevertheless, the same + // way is chosen: use a + // special quadrature + // rule with points at + // the vertices, since + // these are what we are + // interested in. The + // appropriate rule is + // the trapezoidal rule, + // so that is the reason + // why we used that one + // above. + // + // Thus: initialize the + // ``FEValues'' object on + // this cell, + fe_values.reinit (cell); + // and extract the + // gradients of the + // solution vector at the + // vertices: + fe_values.get_function_grads (solution, + solution_gradients); + + // Now we have the + // gradients at all + // vertices, so pick out + // that one which belongs + // to the evaluation + // point (note that the + // order of vertices is + // not necessarily the + // same as that of the + // quadrature points): + unsigned int q_point = 0; + for (; q_point 0, + ExcEvaluationPointNotFound(evaluation_point)); + + // We have simply summed up the + // contributions of all adjacent + // cells, so we still have to + // compute the mean value. Once + // this is done, enter the result + // into the provided table: + point_derivative /= evaluation_point_hits; + results_table.add_value ("DoFs", dof_handler.n_dofs()); + results_table.add_value ("d_x u(x_0)", point_derivative); + + std::cout << " Point x-derivative=" << point_derivative //TODO + << std::endl; + }; + + + // @sect4{The GridOutput class} // Since this program has a more @@ -560,7 +767,7 @@ namespace LaplaceSolver void Solver::LinearSystem::solve (Vector &solution) const { - SolverControl solver_control (1000, 1e-16); + SolverControl solver_control (10000, 1e-12); //TODO! PrimitiveVectorMemory<> vector_memory; SolverCG<> cg (solver_control, vector_memory); @@ -2728,8 +2935,8 @@ template void solve_problem () { Triangulation triangulation (Triangulation::smoothing_on_refinement); - const FE_Q primal_fe(3); - const FE_Q dual_fe(4); + const FE_Q primal_fe(1); + const FE_Q dual_fe(2); const QGauss4 quadrature; const QGauss4 face_quadrature; @@ -2755,12 +2962,15 @@ void solve_problem () TableHandler results_table; Evaluation::PointValueEvaluation postprocessor1 (Point(0.75,0.75), results_table); + Evaluation::PointXDerivativeEvaluation + postprocessor2 (Point(0.75,0.75), results_table); Evaluation::GridOutput - postprocessor2 ("grid"); + postprocessor3 ("grid"); std::list *> postprocessor_list; postprocessor_list.push_back (&postprocessor1); - postprocessor_list.push_back (&postprocessor2); + postprocessor_list.push_back (&postprocessor2); + postprocessor_list.push_back (&postprocessor3); run_simulation (*solver, postprocessor_list);