diff --git a/nufi/cells.h b/nufi/cells.h
new file mode 100644
index 0000000..76abf15
--- /dev/null
+++ b/nufi/cells.h
@@ -0,0 +1,82 @@
+#ifndef CELLS_H
+#define CELLS_H
+
+#include <algorithm>
+#include <deal.II/base/geometry_info.h>
+#include <deal.II/base/point.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/grid/tria.h>
+#include <vector>
+
+using namespace dealii;
+
+template <int dim> struct CellInfo {
+  typename DoFHandler<dim>::active_cell_iterator cell;
+
+  Point<dim> lower;
+  Point<dim> upper;
+  double h;
+};
+
+template <int dim> class CellLocator {
+public:
+  using CellIterator = typename DoFHandler<dim>::active_cell_iterator;
+
+  void rebuild(const DoFHandler<dim> &dof_handler,
+               const Triangulation<dim> &triangulation);
+
+  CellIterator locate(const Point<dim> &p) const;
+
+private:
+  std::vector<CellInfo<dim>> cells;
+};
+
+template <int dim>
+void CellLocator<dim>::rebuild(const DoFHandler<dim> &dof_handler,
+                               const Triangulation<dim> &triangulation) {
+
+  cells.clear();
+  cells.reserve(triangulation.n_active_cells());
+
+  for (const auto &cell : dof_handler.active_cell_iterators()) {
+    CellInfo<dim> info;
+
+    info.cell = cell;
+    info.lower = cell->vertex(0);
+    info.upper = cell->vertex(GeometryInfo<dim>::vertices_per_cell - 1);
+
+    info.h = info.upper[0] - info.lower[0];
+
+    cells.push_back(info);
+  }
+}
+
+template <int dim>
+typename DoFHandler<dim>::active_cell_iterator
+CellLocator<dim>::locate(const Point<dim> &p) const {
+  static_assert(dim == 1,
+                "Current CellLocator implementation only supports 1D.");
+
+  AssertThrow(!cells.empty(),
+              ExcMessage("CellLocator::rebuild() has not been called."));
+
+  const double x = p[0];
+
+  // const double x_min = cells.front().lower[0];
+  // const double x_max = cells.back().uppper[0];
+  // const double L = x_max - x_min;
+
+  // binary search loop
+  auto it = std::upper_bound(cells.begin(), cells.end(), x,
+                             [](double value, const CellInfo<dim> &cell) {
+                               return value < cell.lower[0];
+                             });
+  if (it == cells.begin())
+    it = cells.begin();
+  else
+    --it;
+
+  return it->cell;
+}
+
+#endif // !CELLS_H
diff --git a/nufi/poisson_problem.h b/nufi/poisson_problem.h
index fb26183..3903126 100644
--- a/nufi/poisson_problem.h
+++ b/nufi/poisson_problem.h
@@ -50,6 +50,7 @@
 #include <utility>
 #include <vector>
 
+#include "nufi/cells.h"
 #include "nufi/parameters.h"
 
 using namespace dealii;
@@ -227,6 +228,16 @@ std::vector<double> PoissonProblem<dim>::eval_vector_grad(
   return values;
 }
 
+// template <int dim>
+// std::vector<double> eval_point_grad(const Mapping<dim> &mapping,
+//                                      const DoFHandler<dim> &dof_handler,
+//                                      const Vector<double> &solution,
+//                                      const Point<dim> &point) {
+//     Tensor Ex = VectorTools::point_gradient(mapping, dof_handler, solution,
+//     points);
+//   return Ex[0];
+// }
+//
 // template <int dim>
 // std::vector<double> eval_vector_grad(const Mapping<dim> &mapping,
 //                                      const DoFHandler<dim> &dof_handler,