feat(equations): added material centering equation

this equation provides a residual that weakly enforces that some material point should remain at the origin

src/include/serif/equations/centering.hpp

@@ -0,0 +1,50 @@
+#pragma once
+
+/**
+ * @file centering.hpp
+ * @author Emily M. Boudreaux
+ *
+ * @brief File containing the CenteringConstraint equation, which fixes the material point at the computational origin.
+ *
+ * @note This is probably the simplest equation we have right now and therefore may serve as a useful example to learn from.
+ */
+
+#include <array>
+#include <string_view>
+
+#include "serif/equations/contributions.hpp"
+#include "serif/equations/point.hpp"
+
+namespace serif::equations {
+    /**
+     * @brief Equation that fixes the material point at the computational origin.
+     *
+     * @contribution Residuals to the global displacement vector.
+     *
+     * @note This is a translational gauge, not a center-of-mass constraint.
+     */
+    struct CenteringConstraint final : Contribution<discretization::forms::Operand<discretization::blocks::displacement::vector>> {
+        using Operands = utils::types::TypeList<TestOperand>;                   ///< The list of operands for the centering constraint equation.
+        static constexpr std::string_view name = "centering constraint";        ///< Compile time name for the centering constraint equation, used for debugging and logging.
+        static constexpr bool position_independent = true;                      ///< A centering constraint is position independent, as it does not depend on the spatial location of the material point. This member is only used for compile-time checks.
+        static constexpr std::array<double, 3> reference_position{};            ///< The reference position for the centering constraint equation, which is the origin (0, 0, 0). This member is only used for compile-time checks.
+
+
+        /**
+         * @brief Evaluate the centering constraint equation at a given point. Fundamentally all this this is doing is
+         * returning the displacement of the material point at the origin since to center that the displacement of that point should be zero.
+         * The derivative of the residual with respect to displacement along each axis is then just the identity matrix.
+         *
+         * @param point The point at which to evaluate the centering constraint equation.
+         * @return A PointLinearization object containing the residual and field derivatives for the centering constraint equation at the given point.
+         */
+        [[nodiscard]] static PointLinearization<Operands, discretization::forms::VectorValue> evaluate(const EquationPoint<Operands>& point) {
+            PointLinearization<Operands, discretization::forms::VectorValue> result;
+            result.residual = point.fields.get<Test>();
+            for (int axis = 0; axis < 3; ++axis) {
+                result.field_derivatives.get<Test>()[axis][axis] = 1.0;
+            }
+            return result;
+        }
+    };
+} // namespace serif::equations