feat(utils/projection): infrastructure for projecting some known field into FEM space

src/include/serif/utils/projection/projection.hpp

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+#pragma once
+
+#include "serif/utils/projection/radial.hpp"
+#include "serif/backend/mfem/projection/radial.hpp"

src/include/serif/utils/projection/radial.hpp

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+#pragma once
+
+#include <concepts>
+#include <expected>
+#include <functional>
+#include <string>
+#include <type_traits>
+
+namespace serif::utils::projection {
+    using RadialValue = std::expected<double, std::string>;
+
+    /** @brief A radial profile accepts physical radius and returns a value or a numerical rejection. */
+    template <typename Function>
+    concept RadialFunction = std::invocable<const Function&, double> &&
+        (std::same_as<std::invoke_result_t<const Function&, double>, double> ||
+         std::same_as<std::invoke_result_t<const Function&, double>, RadialValue>);
+
+    namespace detail {
+        /** @brief Borrow a profile for one synchronous projection without requiring it to be copyable. */
+        template <RadialFunction Function>
+        [[nodiscard]] std::function<RadialValue(double)> checked_profile(const Function& function) {
+            return [&function](const double radius) -> RadialValue {
+                return std::invoke(function, radius);
+            };
+        }
+    }
+}