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 # vtk DataFile Version 3.0
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diff --git a/electric_field.vtk b/electric_field.vtk
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+0.00870137 0 0
+0.00870134 0 0
+0.00934135 0 0
+0.00934132 0 0
+0.00994853 0 0
+0.0099485 0 0
+0.0105216 0 0
+0.0105216 0 0
+0.0110592 0 0
+0.0110592 0 0
+0.0115603 0 0
+0.0115603 0 0
+0.0120237 0 0
+0.0120237 0 0
+0.0124484 0 0
+0.0124484 0 0
+0.0128335 0 0
+0.0128335 0 0
+0.0131781 0 0
+0.0131781 0 0
+0.0134815 0 0
+0.0134815 0 0
+0.013743 0 0
+0.013743 0 0
+0.0139621 0 0
+0.0139621 0 0
+0.0141382 0 0
+0.0141381 0 0
+0.0142709 0 0
+0.0142709 0 0
+0.01436 0 0
+0.01436 0 0
+0.0144053 0 0
+0.0144053 0 0
+0.0144067 0 0
+0.0144067 0 0
+0.0143641 0 0
+0.0143641 0 0
+0.0142777 0 0
+0.0142777 0 0
+0.0141477 0 0
+0.0141477 0 0
+0.0139743 0 0
+0.0139743 0 0
+0.0137579 0 0
+0.0137579 0 0
+0.013499 0 0
+0.0134991 0 0
+0.0131982 0 0
+0.0131982 0 0
+0.0128562 0 0
+0.0128562 0 0
+0.0124736 0 0
+0.0124736 0 0
+0.0120513 0 0
+0.0120513 0 0
+0.0115903 0 0
+0.0115903 0 0
+0.0110915 0 0
+0.0110915 0 0
+0.0105561 0 0
+0.0105561 0 0
+0.0099852 0 0
+0.00998522 0 0
+0.00938011 0 0
+0.00938013 0 0
+0.00874214 0 0
+0.00874216 0 0
+0.00807268 0 0
+0.0080727 0 0
+0.00737321 0 0
+0.00737323 0 0
+0.00664527 0 0
+0.00664529 0 0
+0.00589045 0 0
+0.00589047 0 0
+0.00511041 0 0
+0.00511044 0 0
+0.00430687 0 0
+0.0043069 0 0
+0.00348159 0 0
+0.00348162 0 0
+0.00263639 0 0
+0.00263642 0 0
+0.00177311 0 0
+0.00177315 0 0
+0.000893668 0 0
+0.000893701 0 0
+-1.6382e-08 0 0
 SCALARS potential double 1
 LOOKUP_TABLE default
 0 0.000567925 0.000567925 0.00122363 0.00122363 0.00196682 0.00196682 0.00279702 0.00279702 0.00371355 0.00371355 0.00471555 0.00471555 0.00580197 0.00580197 0.00697158 0.00697158 0.00822296 0.00822296 0.0095545 0.0095545 0.0109644 0.0109644 0.0124508 0.0124508 0.0140116 0.0140116 0.0156443 0.0156443 0.0173467 0.0173467 0.0191162 0.0191162 0.0209499 0.0209499 0.0228451 0.0228451 0.0247986 0.0247986 0.0268074 0.0268074 0.0288683 0.0288683 0.0309777 0.0309777 0.0331323 0.0331323 0.0353285 0.0353285 0.0375625 0.0375625 0.0398307 0.0398307 0.0421292 0.0421292 0.0444541 0.0444541 0.0468014 0.0468014 0.0491672 0.0491672 0.0515473 0.0515473 0.0539378 0.0539378 0.0563345 0.0563345 0.0587333 0.0587333 0.0611301 0.0611301 0.0635207 0.0635207 0.0659011 0.0659011 0.0682672 0.0682672 0.070615 0.070615 0.0729403 0.0729403 0.0752394 0.0752394 0.0775082 0.0775082 0.079743 0.079743 0.08194 0.08194 0.0840955 0.0840955 0.0862059 0.0862059 0.0882677 0.0882677 0.0902776 0.0902776 0.0922323 0.0922323 0.0941287 0.0941287 0.0959637 0.0959637 0.0977345 0.0977345 0.0994383 0.0994383 0.101072 0.101072 0.102635 0.102635 0.104123 0.104123 0.105534 0.105534 0.106867 0.106867 0.10812 0.10812 0.109292 0.109292 0.11038 0.11038 0.111383 0.111383 0.112302 0.112302 0.113134 0.113134 0.113879 0.113879 0.114536 0.114536 0.115106 0.115106 0.115588 0.115588 0.115982 0.115982 0.116288 0.116288 0.116508 0.116508 0.116641 0.116641 0.116688 0.116688 0.116652 0.116652 0.116532 0.116532 0.11633 0.11633 0.116048 0.116048 0.115688 0.115688 0.115251 0.115251 0.114739 0.114739 0.114156 0.114156 0.113503 0.113503 0.112783 0.112783 0.111998 0.111998 0.111152 0.111152 0.110248 0.110248 0.109288 0.109288 0.108276 0.108276 0.107215 0.107215 0.10611 0.10611 0.104962 0.104962 0.103777 0.103777 0.102557 0.102557 0.101307 0.101307 0.100031 0.100031 0.0987317 0.0987317 0.0974141 0.0974141 0.0960821 0.0960821 0.0947397 0.0947397 0.093391 0.093391 0.0920401 0.0920401 0.0906911 0.0906911 0.0893482 0.0893482 0.0880154 0.0880154 0.0866968 0.0866968 0.0853966 0.0853966 0.0841186 0.0841186 0.0828668 0.0828668 0.0816452 0.0816452 0.0804575 0.0804575 0.0793076 0.0793076 0.0781991 0.0781991 0.0771356 0.0771356 0.0761206 0.0761206 0.0751575 0.0751575 0.0742495 0.0742495 0.0733997 0.0733997 0.0726113 0.0726113 0.071887 0.071887 0.0712297 0.0712297 0.0706419 0.0706419 0.070126 0.070126 0.0696844 0.0696844 0.0693192 0.0693192 0.0690322 0.0690322 0.0688254 0.0688254 0.0687003 0.0687003 0.0686583 
diff --git a/nufi_poisson b/nufi_poisson
index a81de5b..8063062 100755
Binary files a/nufi_poisson and b/nufi_poisson differ
diff --git a/nufi_poisson.cc b/nufi_poisson.cc
index 54b6339..98e272f 100644
--- a/nufi_poisson.cc
+++ b/nufi_poisson.cc
@@ -71,11 +71,10 @@ double f0(const double x,
 
 // =-=-=-=-= Compute rho(x) =-=-=-=-=
 
-double compute_rho(const double x)
+double compute_rho(const double x, const unsigned int Nv=NV)
 {
   const double v_min = V_DOMAIN_LEFT;
   const double v_max = V_DOMAIN_RIGHT;
-  const double Nv = NV;
 
   const double dv = std::abs(v_min - v_max)/Nv;
 
@@ -98,30 +97,35 @@ template <int dim>
 class ChargeDensity : public Function<dim>
 {
 public:
-  ChargeDensity(double eps, double k)
-    : Function<dim>(1), eps(eps), k(k) {}
+  ChargeDensity(double eps,
+                double k,
+                unsigned int Nv)
+    : Function<dim>(1), eps(eps), k(k), Nv(Nv) {}
 
   virtual double value(const Point<dim> &p,
-                       const unsigned int component = 0) const override
+                       [[maybe_unused]] const unsigned int component = 0) const override
   {
-    return compute_rho(p[0]);
+    return compute_rho(p[0], Nv);
   }
 
 private:
   const double eps;
   const double k;
+  const unsigned int Nv;
 };
 
-/* ------------------------------
-   Poisson Solver
---------------------------------*/
+
+// =-=-=-=-= Poisson Solver =-=-=-=-=
+
 template <int dim>
 class PoissonProblem
 {
 public:
-  PoissonProblem(unsigned int degree);
+  PoissonProblem(unsigned int degree, unsigned int Nv);
   void run();
 
+  void set_Nv(unsigned int new_Nv);
+
 private:
   void setup_system();
   void assemble_system();
@@ -139,13 +143,21 @@ private:
 
   Vector<double> solution;      // phi
   Vector<double> system_rhs;
+
+  unsigned int Nv;
 };
 
+template <int dim>
+void PoissonProblem<dim>::set_Nv(unsigned int new_Nv)
+{
+  Nv = new_Nv;
+}
 
 template <int dim>
-PoissonProblem<dim>::PoissonProblem(unsigned int degree)
+PoissonProblem<dim>::PoissonProblem(unsigned int degree, unsigned int Nv)
   : fe(degree)
   , dof_handler(triangulation)
+  , Nv(Nv)
 {}
 
 
@@ -176,6 +188,35 @@ void PoissonProblem<dim>::setup_system()
 }
 
 
+// =-=-=-=-= E_field = -dPhi/dx =-=-=-=-=
+
+template <int dim>
+class ElectricFieldPostprocessor : public DataPostprocessorVector<dim>
+{
+public:
+  ElectricFieldPostprocessor()
+    : DataPostprocessorVector<dim>("electric_field", update_gradients)
+  {}
+
+  virtual void evaluate_scalar_field(
+    const DataPostprocessorInputs::Scalar<dim> &input_data,
+    std::vector<Vector<double>> &computed_quantities) const override
+  {
+    AssertDimension(input_data.solution_gradients.size(),
+                    computed_quantities.size());
+
+    for (unsigned int p = 0; p < input_data.solution_gradients.size(); ++p)
+      {
+        AssertDimension(computed_quantities[p].size(), dim);
+        for (unsigned int d = 0; d < dim; ++d)
+          computed_quantities[p][d] = -input_data.solution_gradients[p][d];
+      }
+  }
+};
+
+
+// =-=-=-=-= Poisson equation solver =-=-=-=-=
+
 template <int dim>
 void PoissonProblem<dim>::assemble_system()
 {
@@ -193,7 +234,7 @@ void PoissonProblem<dim>::assemble_system()
   Vector<double>     cell_rhs(dofs_per_cell);
   std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
 
-  ChargeDensity<dim> rhs_function(EPS, WAVE_NR);
+  ChargeDensity<dim> rhs_function(EPS, WAVE_NR, Nv);
 
   for (const auto &cell : dof_handler.active_cell_iterators())
   {
@@ -261,9 +302,8 @@ void PoissonProblem<dim>::output_results() const
   for (unsigned int i = 0; i < support_points.size(); ++i)
     x_coordinate[i] = support_points[i][0];  // x-component in 1D
                                              
-
-  /* ---- Output density ---- */
-  ChargeDensity<dim> rho(EPS, WAVE_NR);
+  //---- Output density ----
+  ChargeDensity<dim> rho(EPS, WAVE_NR, Nv);
   Vector<double> density(triangulation.n_active_cells());
 
   DataOut<dim> data_out_rho;
@@ -280,25 +320,15 @@ void PoissonProblem<dim>::output_results() const
   std::ofstream out1("density.vtk");
   data_out_rho.write_vtk(out1);
 
-
-  /* ---- Output electric field ---- */
+  //---- Output electric field & potential ----
   DataOut<dim> data_out_E;
   data_out_E.attach_dof_handler(dof_handler);
 
-  std::vector<std::string> E_names(dim, "E");
-  std::vector<DataComponentInterpretation::DataComponentInterpretation>
-      interpretation(dim,
-                     DataComponentInterpretation::component_is_part_of_vector);
-
+  ElectricFieldPostprocessor<dim> electric_field;
   Vector<double> dummy(solution.size() * dim);
 
-  data_out_E.add_data_vector(solution,
-                             "potential");
-
-  data_out_E.add_data_vector(solution,
-                             "E_field",
-                             DataOut<dim>::type_dof_data,
-                             interpretation);
+  data_out_E.add_data_vector(solution, "potential");
+  data_out_E.add_data_vector(solution, electric_field);
   data_out_E.add_data_vector(x_coordinate, "x_coordinate");
 
   data_out_E.build_patches();
@@ -328,7 +358,8 @@ int main()
 {
   try
   {
-    PoissonProblem<DIMENSION> poisson_problem(FE_DEGREE);
+    PoissonProblem<DIMENSION> poisson_problem(FE_DEGREE, NV);
+    poisson_problem.set_Nv(NV);
     poisson_problem.run();
   }
   catch (std::exception &exc)