From: Wolfgang Bangerth <bangerth@colostate.edu>
Date: Thu, 22 Apr 2021 19:35:01 +0000 (-0600)
Subject: Simplify some type computations in FEValuesViews.
X-Git-Tag: v9.3.0-rc1~179^2~3
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a52daa9f71fb875df4ebc082ac0f2f42a3fc332a;p=dealii.git

Simplify some type computations in FEValuesViews.

Specifically, instead of using a nested class, just use a template type alias.
While there, also fix a few places where we should have used the existing type
alias but instead had repeated the same type computation used in the definition
of the type alias.
---

diff --git a/include/deal.II/fe/fe_values.h b/include/deal.II/fe/fe_values.h
index 8b5a704d9a..910717389a 100644
--- a/include/deal.II/fe/fe_values.h
+++ b/include/deal.II/fe/fe_values.h
@@ -175,52 +175,53 @@ namespace FEValuesViews
     using third_derivative_type = dealii::Tensor<3, spacedim>;
 
     /**
-     * A struct that provides the output type for the product of the value
-     * and derivatives of basis functions of the Scalar view and any @p Number type.
+     * An alias for the data type of the product of a @p Number and the
+     * values of the view this class provides. This is the data type of
+     * scalar components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
      */
     template <typename Number>
-    struct OutputType
-    {
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * values of the view the Scalar class.
-       */
-      using value_type =
-        typename ProductType<Number,
-                             typename Scalar<dim, spacedim>::value_type>::type;
+    using solution_value_type = typename ProductType<Number, value_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * gradients of the view the Scalar class.
-       */
-      using gradient_type = typename ProductType<
-        Number,
-        typename Scalar<dim, spacedim>::gradient_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * gradients of the view this class provides. This is the data type of
+     * scalar components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_gradient_type =
+      typename ProductType<Number, gradient_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * laplacians of the view the Scalar class.
-       */
-      using laplacian_type =
-        typename ProductType<Number,
-                             typename Scalar<dim, spacedim>::value_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * laplacians of the view this class provides. This is the data type of
+     * scalar components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_laplacian_type =
+      typename ProductType<Number, value_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * hessians of the view the Scalar class.
-       */
-      using hessian_type = typename ProductType<
-        Number,
-        typename Scalar<dim, spacedim>::hessian_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * hessians of the view this class provides. This is the data type of
+     * scalar components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_hessian_type =
+      typename ProductType<Number, hessian_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * third derivatives of the view the Scalar class.
-       */
-      using third_derivative_type = typename ProductType<
-        Number,
-        typename Scalar<dim, spacedim>::third_derivative_type>::type;
-    };
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * third derivatives of the view this class provides. This is the data type
+     * of scalar components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_third_derivative_type =
+      typename ProductType<Number, third_derivative_type>::type;
 
     /**
      * A structure where for each shape function we pre-compute a bunch of
@@ -348,8 +349,7 @@ namespace FEValuesViews
     void
     get_function_values(
       const InputVector &fe_function,
-      std::vector<typename ProductType<value_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -390,8 +390,7 @@ namespace FEValuesViews
     void
     get_function_values_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::value_type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -415,8 +414,7 @@ namespace FEValuesViews
     void
     get_function_gradients(
       const InputVector &fe_function,
-      std::vector<typename ProductType<gradient_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_gradient_type<typename InputVector::value_type>>
         &gradients) const;
 
     /**
@@ -429,8 +427,7 @@ namespace FEValuesViews
     void
     get_function_gradients_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::gradient_type>
+      std::vector<solution_gradient_type<typename InputVector::value_type>>
         &gradients) const;
 
     /**
@@ -454,8 +451,7 @@ namespace FEValuesViews
     void
     get_function_hessians(
       const InputVector &fe_function,
-      std::vector<typename ProductType<hessian_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_hessian_type<typename InputVector::value_type>>
         &hessians) const;
 
     /**
@@ -468,8 +464,7 @@ namespace FEValuesViews
     void
     get_function_hessians_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::hessian_type>
+      std::vector<solution_hessian_type<typename InputVector::value_type>>
         &hessians) const;
 
 
@@ -495,8 +490,7 @@ namespace FEValuesViews
     void
     get_function_laplacians(
       const InputVector &fe_function,
-      std::vector<typename ProductType<value_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_laplacian_type<typename InputVector::value_type>>
         &laplacians) const;
 
     /**
@@ -509,8 +503,7 @@ namespace FEValuesViews
     void
     get_function_laplacians_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::laplacian_type>
+      std::vector<solution_laplacian_type<typename InputVector::value_type>>
         &laplacians) const;
 
 
@@ -536,8 +529,8 @@ namespace FEValuesViews
     void
     get_function_third_derivatives(
       const InputVector &fe_function,
-      std::vector<typename ProductType<third_derivative_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<
+        solution_third_derivative_type<typename InputVector::value_type>>
         &third_derivatives) const;
 
     /**
@@ -549,9 +542,10 @@ namespace FEValuesViews
     template <class InputVector>
     void
     get_function_third_derivatives_from_local_dof_values(
-      const InputVector &                   dof_values,
-      std::vector<typename OutputType<typename InputVector::value_type>::
-                    third_derivative_type> &third_derivatives) const;
+      const InputVector &dof_values,
+      std::vector<
+        solution_third_derivative_type<typename InputVector::value_type>>
+        &third_derivatives) const;
 
 
   private:
@@ -666,76 +660,82 @@ namespace FEValuesViews
     using third_derivative_type = dealii::Tensor<4, spacedim>;
 
     /**
-     * A struct that provides the output type for the product of the value
-     * and derivatives of basis functions of the Vector view and any @p Number type.
+     * An alias for the data type of the product of a @p Number and the
+     * values of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
      */
     template <typename Number>
-    struct OutputType
-    {
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * values of the view the Vector class.
-       */
-      using value_type =
-        typename ProductType<Number,
-                             typename Vector<dim, spacedim>::value_type>::type;
+    using solution_value_type = typename ProductType<Number, value_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * gradients of the view the Vector class.
-       */
-      using gradient_type = typename ProductType<
-        Number,
-        typename Vector<dim, spacedim>::gradient_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * gradients of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_gradient_type =
+      typename ProductType<Number, gradient_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * symmetric gradients of the view the Vector class.
-       */
-      using symmetric_gradient_type = typename ProductType<
-        Number,
-        typename Vector<dim, spacedim>::symmetric_gradient_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * symmetric gradients of the view this class provides. This is the data
+     * type of vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_symmetric_gradient_type =
+      typename ProductType<Number, symmetric_gradient_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * divergences of the view the Vector class.
-       */
-      using divergence_type = typename ProductType<
-        Number,
-        typename Vector<dim, spacedim>::divergence_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * divergences of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_divergence_type =
+      typename ProductType<Number, divergence_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * laplacians of the view the Vector class.
-       */
-      using laplacian_type =
-        typename ProductType<Number,
-                             typename Vector<dim, spacedim>::value_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * laplacians of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_laplacian_type =
+      typename ProductType<Number, value_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * curls of the view the Vector class.
-       */
-      using curl_type =
-        typename ProductType<Number,
-                             typename Vector<dim, spacedim>::curl_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * curls of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_curl_type = typename ProductType<Number, curl_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * hessians of the view the Vector class.
-       */
-      using hessian_type = typename ProductType<
-        Number,
-        typename Vector<dim, spacedim>::hessian_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * hessians of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_hessian_type =
+      typename ProductType<Number, hessian_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * third derivatives of the view the Vector class.
-       */
-      using third_derivative_type = typename ProductType<
-        Number,
-        typename Vector<dim, spacedim>::third_derivative_type>::type;
-    };
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * third derivatives of the view this class provides. This is the data type
+     * of vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_third_derivative_type =
+      typename ProductType<Number, third_derivative_type>::type;
 
     /**
      * A structure where for each shape function we pre-compute a bunch of
@@ -940,8 +940,7 @@ namespace FEValuesViews
     void
     get_function_values(
       const InputVector &fe_function,
-      std::vector<typename ProductType<value_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -982,8 +981,7 @@ namespace FEValuesViews
     void
     get_function_values_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::value_type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -1007,8 +1005,7 @@ namespace FEValuesViews
     void
     get_function_gradients(
       const InputVector &fe_function,
-      std::vector<typename ProductType<gradient_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_gradient_type<typename InputVector::value_type>>
         &gradients) const;
 
     /**
@@ -1021,8 +1018,7 @@ namespace FEValuesViews
     void
     get_function_gradients_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::gradient_type>
+      std::vector<solution_gradient_type<typename InputVector::value_type>>
         &gradients) const;
 
     /**
@@ -1052,8 +1048,8 @@ namespace FEValuesViews
     void
     get_function_symmetric_gradients(
       const InputVector &fe_function,
-      std::vector<typename ProductType<symmetric_gradient_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<
+        solution_symmetric_gradient_type<typename InputVector::value_type>>
         &symmetric_gradients) const;
 
     /**
@@ -1065,9 +1061,10 @@ namespace FEValuesViews
     template <class InputVector>
     void
     get_function_symmetric_gradients_from_local_dof_values(
-      const InputVector &                     dof_values,
-      std::vector<typename OutputType<typename InputVector::value_type>::
-                    symmetric_gradient_type> &symmetric_gradients) const;
+      const InputVector &dof_values,
+      std::vector<
+        solution_symmetric_gradient_type<typename InputVector::value_type>>
+        &symmetric_gradients) const;
 
     /**
      * Return the divergence of the selected vector components of the finite
@@ -1091,8 +1088,7 @@ namespace FEValuesViews
     void
     get_function_divergences(
       const InputVector &fe_function,
-      std::vector<typename ProductType<divergence_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_divergence_type<typename InputVector::value_type>>
         &divergences) const;
 
     /**
@@ -1105,8 +1101,7 @@ namespace FEValuesViews
     void
     get_function_divergences_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::divergence_type>
+      std::vector<solution_divergence_type<typename InputVector::value_type>>
         &divergences) const;
 
     /**
@@ -1131,9 +1126,8 @@ namespace FEValuesViews
     void
     get_function_curls(
       const InputVector &fe_function,
-      std::vector<
-        typename ProductType<curl_type, typename InputVector::value_type>::type>
-        &curls) const;
+      std::vector<solution_curl_type<typename InputVector::value_type>> &curls)
+      const;
 
     /**
      * This function relates to get_function_curls() in the same way
@@ -1145,9 +1139,8 @@ namespace FEValuesViews
     void
     get_function_curls_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::curl_type>
-        &curls) const;
+      std::vector<solution_curl_type<typename InputVector::value_type>> &curls)
+      const;
 
     /**
      * Return the Hessians of the selected vector components of the finite
@@ -1170,8 +1163,7 @@ namespace FEValuesViews
     void
     get_function_hessians(
       const InputVector &fe_function,
-      std::vector<typename ProductType<hessian_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_hessian_type<typename InputVector::value_type>>
         &hessians) const;
 
     /**
@@ -1184,8 +1176,7 @@ namespace FEValuesViews
     void
     get_function_hessians_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::hessian_type>
+      std::vector<solution_hessian_type<typename InputVector::value_type>>
         &hessians) const;
 
     /**
@@ -1210,8 +1201,7 @@ namespace FEValuesViews
     void
     get_function_laplacians(
       const InputVector &fe_function,
-      std::vector<typename ProductType<value_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_laplacian_type<typename InputVector::value_type>>
         &laplacians) const;
 
     /**
@@ -1224,8 +1214,7 @@ namespace FEValuesViews
     void
     get_function_laplacians_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::laplacian_type>
+      std::vector<solution_laplacian_type<typename InputVector::value_type>>
         &laplacians) const;
 
     /**
@@ -1250,8 +1239,8 @@ namespace FEValuesViews
     void
     get_function_third_derivatives(
       const InputVector &fe_function,
-      std::vector<typename ProductType<third_derivative_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<
+        solution_third_derivative_type<typename InputVector::value_type>>
         &third_derivatives) const;
 
     /**
@@ -1263,9 +1252,10 @@ namespace FEValuesViews
     template <class InputVector>
     void
     get_function_third_derivatives_from_local_dof_values(
-      const InputVector &                   dof_values,
-      std::vector<typename OutputType<typename InputVector::value_type>::
-                    third_derivative_type> &third_derivatives) const;
+      const InputVector &dof_values,
+      std::vector<
+        solution_third_derivative_type<typename InputVector::value_type>>
+        &third_derivatives) const;
 
   private:
     /**
@@ -1335,28 +1325,23 @@ namespace FEValuesViews
     using divergence_type = dealii::Tensor<1, spacedim>;
 
     /**
-     * A struct that provides the output type for the product of the value
-     * and derivatives of basis functions of the SymmetricTensor view and any @p Number type.
+     * An alias for the data type of the product of a @p Number and the
+     * values of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
      */
     template <typename Number>
-    struct OutputType
-    {
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * values of the view the SymmetricTensor class.
-       */
-      using value_type = typename ProductType<
-        Number,
-        typename SymmetricTensor<2, dim, spacedim>::value_type>::type;
+    using solution_value_type = typename ProductType<Number, value_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * divergences of the view the SymmetricTensor class.
-       */
-      using divergence_type = typename ProductType<
-        Number,
-        typename SymmetricTensor<2, dim, spacedim>::divergence_type>::type;
-    };
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * divergences of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_divergence_type =
+      typename ProductType<Number, divergence_type>::type;
 
     /**
      * A structure where for each shape function we pre-compute a bunch of
@@ -1484,8 +1469,7 @@ namespace FEValuesViews
     void
     get_function_values(
       const InputVector &fe_function,
-      std::vector<typename ProductType<value_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -1526,8 +1510,7 @@ namespace FEValuesViews
     void
     get_function_values_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::value_type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -1555,8 +1538,7 @@ namespace FEValuesViews
     void
     get_function_divergences(
       const InputVector &fe_function,
-      std::vector<typename ProductType<divergence_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_divergence_type<typename InputVector::value_type>>
         &divergences) const;
 
     /**
@@ -1569,8 +1551,7 @@ namespace FEValuesViews
     void
     get_function_divergences_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::divergence_type>
+      std::vector<solution_divergence_type<typename InputVector::value_type>>
         &divergences) const;
 
   private:
@@ -1635,36 +1616,33 @@ namespace FEValuesViews
     using gradient_type = dealii::Tensor<3, spacedim>;
 
     /**
-     * A struct that provides the output type for the product of the value
-     * and derivatives of basis functions of the Tensor view and any @p Number type.
+     * An alias for the data type of the product of a @p Number and the
+     * values of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
      */
     template <typename Number>
-    struct OutputType
-    {
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * values of the view the Tensor class.
-       */
-      using value_type = typename ProductType<
-        Number,
-        typename Tensor<2, dim, spacedim>::value_type>::type;
+    using solution_value_type = typename ProductType<Number, value_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * divergences of the view the Tensor class.
-       */
-      using divergence_type = typename ProductType<
-        Number,
-        typename Tensor<2, dim, spacedim>::divergence_type>::type;
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * divergences of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_divergence_type =
+      typename ProductType<Number, divergence_type>::type;
 
-      /**
-       * An alias for the data type of the product of a @p Number and the
-       * gradient of the view the Tensor class.
-       */
-      using gradient_type = typename ProductType<
-        Number,
-        typename Tensor<2, dim, spacedim>::gradient_type>::type;
-    };
+    /**
+     * An alias for the data type of the product of a @p Number and the
+     * gradient of the view this class provides. This is the data type of
+     * vector components of a finite element field whose degrees of
+     * freedom are described by a vector with elements of type @p Number.
+     */
+    template <typename Number>
+    using solution_gradient_type =
+      typename ProductType<Number, gradient_type>::type;
 
     /**
      * A structure where for each shape function we pre-compute a bunch of
@@ -1809,8 +1787,7 @@ namespace FEValuesViews
     void
     get_function_values(
       const InputVector &fe_function,
-      std::vector<typename ProductType<value_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -1851,8 +1828,7 @@ namespace FEValuesViews
     void
     get_function_values_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::value_type>
+      std::vector<solution_value_type<typename InputVector::value_type>>
         &values) const;
 
     /**
@@ -1880,8 +1856,7 @@ namespace FEValuesViews
     void
     get_function_divergences(
       const InputVector &fe_function,
-      std::vector<typename ProductType<divergence_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_divergence_type<typename InputVector::value_type>>
         &divergences) const;
 
     /**
@@ -1894,8 +1869,7 @@ namespace FEValuesViews
     void
     get_function_divergences_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::divergence_type>
+      std::vector<solution_divergence_type<typename InputVector::value_type>>
         &divergences) const;
 
     /**
@@ -1918,8 +1892,7 @@ namespace FEValuesViews
     void
     get_function_gradients(
       const InputVector &fe_function,
-      std::vector<typename ProductType<gradient_type,
-                                       typename InputVector::value_type>::type>
+      std::vector<solution_gradient_type<typename InputVector::value_type>>
         &gradients) const;
 
     /**
@@ -1932,8 +1905,7 @@ namespace FEValuesViews
     void
     get_function_gradients_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::gradient_type>
+      std::vector<solution_gradient_type<typename InputVector::value_type>>
         &gradients) const;
 
   private:
diff --git a/include/deal.II/meshworker/scratch_data.h b/include/deal.II/meshworker/scratch_data.h
index 36ab1e1088..9f63419326 100644
--- a/include/deal.II/meshworker/scratch_data.h
+++ b/include/deal.II/meshworker/scratch_data.h
@@ -36,17 +36,6 @@ DEAL_II_NAMESPACE_OPEN
 
 namespace MeshWorker
 {
-  namespace internal
-  {
-    /**
-     * Alias used to deduce the OutputType when asking for values or gradients
-     * of shape functions multiplied with the given @p NumberType.
-     */
-    template <int dim, int spacedim, typename NumberType, typename Extractor>
-    using OutputType = typename FEValuesViews::View<dim, spacedim, Extractor>::
-      template OutputType<NumberType>;
-  } // namespace internal
-
   /**
    * A helper class to simplify the parallel assembly of linear and non-linear
    * problems, and the evaluation of finite element fields.
@@ -606,9 +595,8 @@ namespace MeshWorker
      * the documentation of the FEValues class for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        value_type> &
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_value_type<Number>> &
     get_values(const std::string &global_vector_name,
                const Extractor &  variable,
                const Number       dummy = Number(0));
@@ -635,9 +623,8 @@ namespace MeshWorker
      * the documentation of the FEValues class for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        gradient_type> &
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_gradient_type<Number>> &
     get_gradients(const std::string &global_vector_name,
                   const Extractor &  variable,
                   const Number       dummy = Number(0));
@@ -665,9 +652,8 @@ namespace MeshWorker
      * the documentation of the FEValues class for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        symmetric_gradient_type> &
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_symmetric_gradient_type<Number>> &
     get_symmetric_gradients(const std::string &global_vector_name,
                             const Extractor &  variable,
                             const Number       dummy = Number(0));
@@ -694,9 +680,8 @@ namespace MeshWorker
      * the documentation of the FEValues class for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        divergence_type> &
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_divergence_type<Number>> &
     get_divergences(const std::string &global_vector_name,
                     const Extractor &  variable,
                     const Number       dummy = Number(0));
@@ -723,12 +708,11 @@ namespace MeshWorker
      * the documentation of the FEValues class for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<typename internal::
-                        OutputType<dim, spacedim, Number, Extractor>::curl_type>
-      &
-      get_curls(const std::string &global_vector_name,
-                const Extractor &  variable,
-                const Number       dummy = Number(0));
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_curl_type<Number>> &
+    get_curls(const std::string &global_vector_name,
+              const Extractor &  variable,
+              const Number       dummy = Number(0));
 
     /**
      * For the solution vector identified by @p global_vector_name, compute
@@ -752,9 +736,8 @@ namespace MeshWorker
      * the documentation of the FEValues class for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        hessian_type> &
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_hessian_type<Number>> &
     get_hessians(const std::string &global_vector_name,
                  const Extractor &  variable,
                  const Number       dummy = Number(0));
@@ -781,9 +764,8 @@ namespace MeshWorker
      * the documentation of the FEValues class for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        laplacian_type> &
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_laplacian_type<Number>> &
     get_laplacians(const std::string &global_vector_name,
                    const Extractor &  variable,
                    const Number       dummy = Number(0));
@@ -810,9 +792,8 @@ namespace MeshWorker
      * FiniteElement" in the documentation of the FEValues for more information.
      */
     template <typename Extractor, typename Number = double>
-    const std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        third_derivative_type> &
+    const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                        template solution_third_derivative_type<Number>> &
     get_third_derivatives(const std::string &global_vector_name,
                           const Extractor &  variable,
                           const Number       dummy = Number(0));
@@ -1054,13 +1035,11 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::value_type>
-    &
-    ScratchData<dim, spacedim>::get_values(
-      const std::string &global_vector_name,
-      const Extractor &  variable,
-      const Number       dummy)
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_value_type<Number>> &
+  ScratchData<dim, spacedim>::get_values(const std::string &global_vector_name,
+                                         const Extractor &  variable,
+                                         const Number       dummy)
   {
     const std::vector<Number> &independent_local_dofs =
       get_local_dof_values(global_vector_name, dummy);
@@ -1074,8 +1053,8 @@ namespace MeshWorker
 
     // Now build the return type
     using RetType =
-      std::vector<typename internal::
-                    OutputType<dim, spacedim, Number, Extractor>::value_type>;
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_value_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
@@ -1092,9 +1071,8 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::
-      gradient_type> &
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_gradient_type<Number>> &
   ScratchData<dim, spacedim>::get_gradients(
     const std::string &global_vector_name,
     const Extractor &  variable,
@@ -1111,9 +1089,9 @@ namespace MeshWorker
       global_vector_name, variable, "_gradients_q", n_q_points, dummy);
 
     // Now build the return type
-    using RetType = std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        gradient_type>;
+    using RetType =
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_gradient_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
@@ -1130,9 +1108,8 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::
-      hessian_type> &
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_hessian_type<Number>> &
   ScratchData<dim, spacedim>::get_hessians(
     const std::string &global_vector_name,
     const Extractor &  variable,
@@ -1150,8 +1127,8 @@ namespace MeshWorker
 
     // Now build the return type
     using RetType =
-      std::vector<typename internal::
-                    OutputType<dim, spacedim, Number, Extractor>::hessian_type>;
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_hessian_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
@@ -1169,9 +1146,8 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::
-      laplacian_type> &
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_laplacian_type<Number>> &
   ScratchData<dim, spacedim>::get_laplacians(
     const std::string &global_vector_name,
     const Extractor &  variable,
@@ -1188,9 +1164,9 @@ namespace MeshWorker
       global_vector_name, variable, "_laplacians_q", n_q_points, dummy);
 
     // Now build the return type
-    using RetType = std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        laplacian_type>;
+    using RetType =
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_laplacian_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
@@ -1208,9 +1184,8 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::
-      third_derivative_type> &
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_third_derivative_type<Number>> &
   ScratchData<dim, spacedim>::get_third_derivatives(
     const std::string &global_vector_name,
     const Extractor &  variable,
@@ -1227,9 +1202,9 @@ namespace MeshWorker
       global_vector_name, variable, "_third_derivatives_q", n_q_points, dummy);
 
     // Now build the return type
-    using RetType = std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        third_derivative_type>;
+    using RetType =
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_third_derivative_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
@@ -1247,9 +1222,8 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::
-      symmetric_gradient_type> &
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_symmetric_gradient_type<Number>> &
   ScratchData<dim, spacedim>::get_symmetric_gradients(
     const std::string &global_vector_name,
     const Extractor &  variable,
@@ -1267,9 +1241,9 @@ namespace MeshWorker
 
 
     // Now build the return type
-    using RetType = std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        symmetric_gradient_type>;
+    using RetType =
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_symmetric_gradient_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
@@ -1286,9 +1260,8 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::
-      divergence_type> &
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_divergence_type<Number>> &
   ScratchData<dim, spacedim>::get_divergences(
     const std::string &global_vector_name,
     const Extractor &  variable,
@@ -1305,9 +1278,9 @@ namespace MeshWorker
       global_vector_name, variable, "_divergence_q", n_q_points, dummy);
 
     // Now build the return type
-    using RetType = std::vector<
-      typename internal::OutputType<dim, spacedim, Number, Extractor>::
-        divergence_type>;
+    using RetType =
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_divergence_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
@@ -1325,12 +1298,11 @@ namespace MeshWorker
 
   template <int dim, int spacedim>
   template <typename Extractor, typename Number>
-  const std::vector<
-    typename internal::OutputType<dim, spacedim, Number, Extractor>::curl_type>
-    &
-    ScratchData<dim, spacedim>::get_curls(const std::string &global_vector_name,
-                                          const Extractor &  variable,
-                                          const Number       dummy)
+  const std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                      template solution_curl_type<Number>> &
+  ScratchData<dim, spacedim>::get_curls(const std::string &global_vector_name,
+                                        const Extractor &  variable,
+                                        const Number       dummy)
   {
     const std::vector<Number> &independent_local_dofs =
       get_local_dof_values(global_vector_name, dummy);
@@ -1344,8 +1316,8 @@ namespace MeshWorker
 
     // Now build the return type
     using RetType =
-      std::vector<typename internal::
-                    OutputType<dim, spacedim, Number, Extractor>::curl_type>;
+      std::vector<typename FEValuesViews::View<dim, spacedim, Extractor>::
+                    template solution_curl_type<Number>>;
 
     RetType &ret =
       internal_data_storage.template get_or_add_object_with_name<RetType>(
diff --git a/source/fe/fe_values.cc b/source/fe/fe_values.cc
index fb39b05f08..e2391ee2c8 100644
--- a/source/fe/fe_values.cc
+++ b/source/fe/fe_values.cc
@@ -525,17 +525,18 @@ namespace FEValuesViews
       const ArrayView<Number> &                    dof_values,
       const Table<2, dealii::Tensor<2, spacedim>> &shape_hessians,
       const std::vector<typename Scalar<dim, spacedim>::ShapeFunctionData>
-        &                         shape_function_data,
-      std::vector<typename Scalar<dim, spacedim>::template OutputType<
-        Number>::laplacian_type> &laplacians)
+        &shape_function_data,
+      std::vector<typename Scalar<dim, spacedim>::
+                    template solution_laplacian_type<Number>> &laplacians)
     {
       const unsigned int dofs_per_cell       = dof_values.size();
       const unsigned int n_quadrature_points = laplacians.size();
 
-      std::fill(laplacians.begin(),
-                laplacians.end(),
-                typename Scalar<dim, spacedim>::template OutputType<
-                  Number>::laplacian_type());
+      std::fill(
+        laplacians.begin(),
+        laplacians.end(),
+        typename Scalar<dim,
+                        spacedim>::template solution_laplacian_type<Number>());
 
       for (unsigned int shape_function = 0; shape_function < dofs_per_cell;
            ++shape_function)
@@ -763,17 +764,18 @@ namespace FEValuesViews
       const ArrayView<Number> &                    dof_values,
       const Table<2, dealii::Tensor<1, spacedim>> &shape_gradients,
       const std::vector<typename Vector<dim, spacedim>::ShapeFunctionData>
-        &                          shape_function_data,
-      std::vector<typename Vector<dim, spacedim>::template OutputType<
-        Number>::divergence_type> &divergences)
+        &shape_function_data,
+      std::vector<typename Vector<dim, spacedim>::
+                    template solution_divergence_type<Number>> &divergences)
     {
       const unsigned int dofs_per_cell       = dof_values.size();
       const unsigned int n_quadrature_points = divergences.size();
 
-      std::fill(divergences.begin(),
-                divergences.end(),
-                typename Vector<dim, spacedim>::template OutputType<
-                  Number>::divergence_type());
+      std::fill(
+        divergences.begin(),
+        divergences.end(),
+        typename Vector<dim,
+                        spacedim>::template solution_divergence_type<Number>());
 
       for (unsigned int shape_function = 0; shape_function < dofs_per_cell;
            ++shape_function)
@@ -1087,17 +1089,18 @@ namespace FEValuesViews
       const ArrayView<Number> &                    dof_values,
       const Table<2, dealii::Tensor<2, spacedim>> &shape_hessians,
       const std::vector<typename Vector<dim, spacedim>::ShapeFunctionData>
-        &                         shape_function_data,
-      std::vector<typename Vector<dim, spacedim>::template OutputType<
-        Number>::laplacian_type> &laplacians)
+        &shape_function_data,
+      std::vector<typename Vector<dim, spacedim>::
+                    template solution_laplacian_type<Number>> &laplacians)
     {
       const unsigned int dofs_per_cell       = dof_values.size();
       const unsigned int n_quadrature_points = laplacians.size();
 
-      std::fill(laplacians.begin(),
-                laplacians.end(),
-                typename Vector<dim, spacedim>::template OutputType<
-                  Number>::laplacian_type());
+      std::fill(
+        laplacians.begin(),
+        laplacians.end(),
+        typename Vector<dim,
+                        spacedim>::template solution_laplacian_type<Number>());
 
       for (unsigned int shape_function = 0; shape_function < dofs_per_cell;
            ++shape_function)
@@ -1228,15 +1231,15 @@ namespace FEValuesViews
         typename SymmetricTensor<2, dim, spacedim>::ShapeFunctionData>
         &shape_function_data,
       std::vector<typename SymmetricTensor<2, dim, spacedim>::
-                    template OutputType<Number>::divergence_type> &divergences)
+                    template solution_divergence_type<Number>> &divergences)
     {
       const unsigned int dofs_per_cell       = dof_values.size();
       const unsigned int n_quadrature_points = divergences.size();
 
       std::fill(divergences.begin(),
                 divergences.end(),
-                typename SymmetricTensor<2, dim, spacedim>::template OutputType<
-                  Number>::divergence_type());
+                typename SymmetricTensor<2, dim, spacedim>::
+                  template solution_divergence_type<Number>());
 
       for (unsigned int shape_function = 0; shape_function < dofs_per_cell;
            ++shape_function)
@@ -1402,17 +1405,18 @@ namespace FEValuesViews
       const ArrayView<Number> &                    dof_values,
       const Table<2, dealii::Tensor<1, spacedim>> &shape_gradients,
       const std::vector<typename Tensor<2, dim, spacedim>::ShapeFunctionData>
-        &                          shape_function_data,
-      std::vector<typename Tensor<2, dim, spacedim>::template OutputType<
-        Number>::divergence_type> &divergences)
+        &shape_function_data,
+      std::vector<typename Tensor<2, dim, spacedim>::
+                    template solution_divergence_type<Number>> &divergences)
     {
       const unsigned int dofs_per_cell       = dof_values.size();
       const unsigned int n_quadrature_points = divergences.size();
 
-      std::fill(divergences.begin(),
-                divergences.end(),
-                typename Tensor<2, dim, spacedim>::template OutputType<
-                  Number>::divergence_type());
+      std::fill(
+        divergences.begin(),
+        divergences.end(),
+        typename Tensor<2, dim, spacedim>::template solution_divergence_type<
+          Number>());
 
       for (unsigned int shape_function = 0; shape_function < dofs_per_cell;
            ++shape_function)
@@ -1471,17 +1475,18 @@ namespace FEValuesViews
       const ArrayView<Number> &                    dof_values,
       const Table<2, dealii::Tensor<1, spacedim>> &shape_gradients,
       const std::vector<typename Tensor<2, dim, spacedim>::ShapeFunctionData>
-        &                        shape_function_data,
-      std::vector<typename Tensor<2, dim, spacedim>::template OutputType<
-        Number>::gradient_type> &gradients)
+        &shape_function_data,
+      std::vector<typename Tensor<2, dim, spacedim>::
+                    template solution_gradient_type<Number>> &gradients)
     {
       const unsigned int dofs_per_cell       = dof_values.size();
       const unsigned int n_quadrature_points = gradients.size();
 
-      std::fill(gradients.begin(),
-                gradients.end(),
-                typename Tensor<2, dim, spacedim>::template OutputType<
-                  Number>::gradient_type());
+      std::fill(
+        gradients.begin(),
+        gradients.end(),
+        typename Tensor<2, dim, spacedim>::template solution_gradient_type<
+          Number>());
 
       for (unsigned int shape_function = 0; shape_function < dofs_per_cell;
            ++shape_function)
@@ -1541,9 +1546,8 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_values(
     const InputVector &fe_function,
-    std::vector<
-      typename ProductType<value_type, typename InputVector::value_type>::type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -1573,9 +1577,8 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_values_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::value_type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -1598,8 +1601,7 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_gradients(
     const InputVector &fe_function,
-    std::vector<typename ProductType<gradient_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_gradient_type<typename InputVector::value_type>>
       &gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -1629,8 +1631,7 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_gradients_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::gradient_type>
+    std::vector<solution_gradient_type<typename InputVector::value_type>>
       &gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -1654,8 +1655,7 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_hessians(
     const InputVector &fe_function,
-    std::vector<typename ProductType<hessian_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_hessian_type<typename InputVector::value_type>>
       &hessians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -1685,8 +1685,7 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_hessians_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::hessian_type>
+    std::vector<solution_hessian_type<typename InputVector::value_type>>
       &hessians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -1710,8 +1709,7 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_laplacians(
     const InputVector &fe_function,
-    std::vector<
-      typename ProductType<value_type, typename InputVector::value_type>::type>
+    std::vector<solution_laplacian_type<typename InputVector::value_type>>
       &laplacians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -1741,8 +1739,7 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_laplacians_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::laplacian_type>
+    std::vector<solution_laplacian_type<typename InputVector::value_type>>
       &laplacians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -1766,8 +1763,8 @@ namespace FEValuesViews
   void
   Scalar<dim, spacedim>::get_function_third_derivatives(
     const InputVector &fe_function,
-    std::vector<typename ProductType<third_derivative_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<
+      solution_third_derivative_type<typename InputVector::value_type>>
       &third_derivatives) const
   {
     Assert(fe_values->update_flags & update_3rd_derivatives,
@@ -1796,9 +1793,10 @@ namespace FEValuesViews
   template <class InputVector>
   void
   Scalar<dim, spacedim>::get_function_third_derivatives_from_local_dof_values(
-    const InputVector &                   dof_values,
-    std::vector<typename OutputType<typename InputVector::value_type>::
-                  third_derivative_type> &third_derivatives) const
+    const InputVector &dof_values,
+    std::vector<
+      solution_third_derivative_type<typename InputVector::value_type>>
+      &third_derivatives) const
   {
     Assert(fe_values->update_flags & update_3rd_derivatives,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -1821,9 +1819,8 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_values(
     const InputVector &fe_function,
-    std::vector<
-      typename ProductType<value_type, typename InputVector::value_type>::type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -1852,9 +1849,8 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_values_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::value_type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -1877,8 +1873,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_gradients(
     const InputVector &fe_function,
-    std::vector<typename ProductType<gradient_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_gradient_type<typename InputVector::value_type>>
       &gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -1908,8 +1903,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_gradients_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::gradient_type>
+    std::vector<solution_gradient_type<typename InputVector::value_type>>
       &gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -1933,8 +1927,8 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_symmetric_gradients(
     const InputVector &fe_function,
-    std::vector<typename ProductType<symmetric_gradient_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<
+      solution_symmetric_gradient_type<typename InputVector::value_type>>
       &symmetric_gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -1963,9 +1957,10 @@ namespace FEValuesViews
   template <class InputVector>
   void
   Vector<dim, spacedim>::get_function_symmetric_gradients_from_local_dof_values(
-    const InputVector &                     dof_values,
-    std::vector<typename OutputType<typename InputVector::value_type>::
-                  symmetric_gradient_type> &symmetric_gradients) const
+    const InputVector &dof_values,
+    std::vector<
+      solution_symmetric_gradient_type<typename InputVector::value_type>>
+      &symmetric_gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -1988,8 +1983,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_divergences(
     const InputVector &fe_function,
-    std::vector<typename ProductType<divergence_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_divergence_type<typename InputVector::value_type>>
       &divergences) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2020,8 +2014,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_divergences_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::divergence_type>
+    std::vector<solution_divergence_type<typename InputVector::value_type>>
       &divergences) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2045,9 +2038,8 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_curls(
     const InputVector &fe_function,
-    std::vector<
-      typename ProductType<curl_type, typename InputVector::value_type>::type>
-      &curls) const
+    std::vector<solution_curl_type<typename InputVector::value_type>> &curls)
+    const
   {
     Assert(fe_values->update_flags & update_gradients,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -2076,8 +2068,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_curls_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::curl_type> &curls)
+    std::vector<solution_curl_type<typename InputVector::value_type>> &curls)
     const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2101,8 +2092,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_hessians(
     const InputVector &fe_function,
-    std::vector<typename ProductType<hessian_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_hessian_type<typename InputVector::value_type>>
       &hessians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -2132,8 +2122,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_hessians_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::hessian_type>
+    std::vector<solution_hessian_type<typename InputVector::value_type>>
       &hessians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -2157,8 +2146,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_laplacians(
     const InputVector &fe_function,
-    std::vector<
-      typename ProductType<value_type, typename InputVector::value_type>::type>
+    std::vector<solution_value_type<typename InputVector::value_type>>
       &laplacians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -2193,8 +2181,7 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_laplacians_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::laplacian_type>
+    std::vector<solution_laplacian_type<typename InputVector::value_type>>
       &laplacians) const
   {
     Assert(fe_values->update_flags & update_hessians,
@@ -2221,8 +2208,8 @@ namespace FEValuesViews
   void
   Vector<dim, spacedim>::get_function_third_derivatives(
     const InputVector &fe_function,
-    std::vector<typename ProductType<third_derivative_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<
+      solution_third_derivative_type<typename InputVector::value_type>>
       &third_derivatives) const
   {
     Assert(fe_values->update_flags & update_3rd_derivatives,
@@ -2251,9 +2238,10 @@ namespace FEValuesViews
   template <class InputVector>
   void
   Vector<dim, spacedim>::get_function_third_derivatives_from_local_dof_values(
-    const InputVector &                   dof_values,
-    std::vector<typename OutputType<typename InputVector::value_type>::
-                  third_derivative_type> &third_derivatives) const
+    const InputVector &dof_values,
+    std::vector<
+      solution_third_derivative_type<typename InputVector::value_type>>
+      &third_derivatives) const
   {
     Assert(fe_values->update_flags & update_3rd_derivatives,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -2276,9 +2264,8 @@ namespace FEValuesViews
   void
   SymmetricTensor<2, dim, spacedim>::get_function_values(
     const InputVector &fe_function,
-    std::vector<
-      typename ProductType<value_type, typename InputVector::value_type>::type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -2307,9 +2294,8 @@ namespace FEValuesViews
   void
   SymmetricTensor<2, dim, spacedim>::get_function_values_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::value_type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -2332,8 +2318,7 @@ namespace FEValuesViews
   void
   SymmetricTensor<2, dim, spacedim>::get_function_divergences(
     const InputVector &fe_function,
-    std::vector<typename ProductType<divergence_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_divergence_type<typename InputVector::value_type>>
       &divergences) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2365,8 +2350,7 @@ namespace FEValuesViews
   SymmetricTensor<2, dim, spacedim>::
     get_function_divergences_from_local_dof_values(
       const InputVector &dof_values,
-      std::vector<
-        typename OutputType<typename InputVector::value_type>::divergence_type>
+      std::vector<solution_divergence_type<typename InputVector::value_type>>
         &divergences) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2390,9 +2374,8 @@ namespace FEValuesViews
   void
   Tensor<2, dim, spacedim>::get_function_values(
     const InputVector &fe_function,
-    std::vector<
-      typename ProductType<value_type, typename InputVector::value_type>::type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -2421,9 +2404,8 @@ namespace FEValuesViews
   void
   Tensor<2, dim, spacedim>::get_function_values_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::value_type>
-      &values) const
+    std::vector<solution_value_type<typename InputVector::value_type>> &values)
+    const
   {
     Assert(fe_values->update_flags & update_values,
            (typename FEValuesBase<dim, spacedim>::ExcAccessToUninitializedField(
@@ -2446,8 +2428,7 @@ namespace FEValuesViews
   void
   Tensor<2, dim, spacedim>::get_function_divergences(
     const InputVector &fe_function,
-    std::vector<typename ProductType<divergence_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_divergence_type<typename InputVector::value_type>>
       &divergences) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2478,8 +2459,7 @@ namespace FEValuesViews
   void
   Tensor<2, dim, spacedim>::get_function_divergences_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::divergence_type>
+    std::vector<solution_divergence_type<typename InputVector::value_type>>
       &divergences) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2503,8 +2483,7 @@ namespace FEValuesViews
   void
   Tensor<2, dim, spacedim>::get_function_gradients(
     const InputVector &fe_function,
-    std::vector<typename ProductType<gradient_type,
-                                     typename InputVector::value_type>::type>
+    std::vector<solution_gradient_type<typename InputVector::value_type>>
       &gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
@@ -2535,8 +2514,7 @@ namespace FEValuesViews
   void
   Tensor<2, dim, spacedim>::get_function_gradients_from_local_dof_values(
     const InputVector &dof_values,
-    std::vector<
-      typename OutputType<typename InputVector::value_type>::gradient_type>
+    std::vector<solution_gradient_type<typename InputVector::value_type>>
       &gradients) const
   {
     Assert(fe_values->update_flags & update_gradients,
diff --git a/source/fe/fe_values.inst.in b/source/fe/fe_values.inst.in
index 675d2bbb89..fceba81020 100644
--- a/source/fe/fe_values.inst.in
+++ b/source/fe/fe_values.inst.in
@@ -249,119 +249,110 @@ for (VEC : GENERAL_CONTAINER_TYPES; Number : ALL_SCALAR_TYPES;
     template void
     FEValuesViews::Scalar<deal_II_dimension, deal_II_space_dimension>::
       get_function_values_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::value_type> &) const;
+        const VEC<Number> &, std::vector<solution_value_type<Number>> &) const;
 
     template void
     FEValuesViews::Scalar<deal_II_dimension, deal_II_space_dimension>::
       get_function_gradients_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::gradient_type> &) const;
+        const VEC<Number> &, std::vector<solution_gradient_type<Number>> &)
+        const;
 
     template void
     FEValuesViews::Scalar<deal_II_dimension, deal_II_space_dimension>::
       get_function_hessians_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::hessian_type> &) const;
+        const VEC<Number> &, std::vector<solution_hessian_type<Number>> &)
+        const;
 
     template void
     FEValuesViews::Scalar<deal_II_dimension, deal_II_space_dimension>::
       get_function_laplacians_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::value_type> &) const;
+        const VEC<Number> &, std::vector<solution_value_type<Number>> &) const;
 
     template void
     FEValuesViews::Scalar<deal_II_dimension, deal_II_space_dimension>::
       get_function_third_derivatives_from_local_dof_values<VEC<Number>>(
         const VEC<Number> &,
-        std::vector<typename OutputType<Number>::third_derivative_type> &)
-        const;
+        std::vector<solution_third_derivative_type<Number>> &) const;
 
 
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_values_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::value_type> &) const;
+        const VEC<Number> &, std::vector<solution_value_type<Number>> &) const;
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_gradients_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::gradient_type> &) const;
+        const VEC<Number> &, std::vector<solution_gradient_type<Number>> &)
+        const;
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_symmetric_gradients_from_local_dof_values<VEC<Number>>(
         const VEC<Number> &,
-        std::vector<typename OutputType<Number>::symmetric_gradient_type> &)
-        const;
+        std::vector<solution_symmetric_gradient_type<Number>> &) const;
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_divergences_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::divergence_type> &) const;
+        const VEC<Number> &, std::vector<solution_divergence_type<Number>> &)
+        const;
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_curls_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::curl_type> &) const;
+        const VEC<Number> &, std::vector<solution_curl_type<Number>> &) const;
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_hessians_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::hessian_type> &) const;
+        const VEC<Number> &, std::vector<solution_hessian_type<Number>> &)
+        const;
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_laplacians_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::value_type> &) const;
+        const VEC<Number> &, std::vector<solution_value_type<Number>> &) const;
 
     template void
     FEValuesViews::Vector<deal_II_dimension, deal_II_space_dimension>::
       get_function_third_derivatives_from_local_dof_values<VEC<Number>>(
         const VEC<Number> &,
-        std::vector<typename OutputType<Number>::third_derivative_type> &)
-        const;
+        std::vector<solution_third_derivative_type<Number>> &) const;
 
 
 
-    template void FEValuesViews::
-      SymmetricTensor<2, deal_II_dimension, deal_II_space_dimension>::
-        get_function_values_from_local_dof_values<VEC<Number>>(
-          const VEC<Number> &,
-          std::vector<typename OutputType<Number>::value_type> &) const;
+    template void FEValuesViews::SymmetricTensor<2,
+                                                 deal_II_dimension,
+                                                 deal_II_space_dimension>::
+      get_function_values_from_local_dof_values<VEC<Number>>(
+        const VEC<Number> &, std::vector<solution_value_type<Number>> &) const;
 
     template void FEValuesViews::
       SymmetricTensor<2, deal_II_dimension, deal_II_space_dimension>::
         get_function_divergences_from_local_dof_values<VEC<Number>>(
-          const VEC<Number> &,
-          std::vector<typename OutputType<Number>::divergence_type> &) const;
+          const VEC<Number> &, std::vector<solution_divergence_type<Number>> &)
+          const;
 
 
 
     template void
     FEValuesViews::Tensor<2, deal_II_dimension, deal_II_space_dimension>::
       get_function_values_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::value_type> &) const;
+        const VEC<Number> &, std::vector<solution_value_type<Number>> &) const;
 
     template void
     FEValuesViews::Tensor<2, deal_II_dimension, deal_II_space_dimension>::
       get_function_divergences_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::divergence_type> &) const;
+        const VEC<Number> &, std::vector<solution_divergence_type<Number>> &)
+        const;
 
     template void
     FEValuesViews::Tensor<2, deal_II_dimension, deal_II_space_dimension>::
       get_function_gradients_from_local_dof_values<VEC<Number>>(
-        const VEC<Number> &,
-        std::vector<typename OutputType<Number>::gradient_type> &) const;
+        const VEC<Number> &, std::vector<solution_gradient_type<Number>> &)
+        const;
 #endif
   }