diff --git a/src/poly/coeff/private/polyCoeff.cpp b/src/poly/coeff/private/polyCoeff.cpp
index ad4d117..c4076a0 100644
--- a/src/poly/coeff/private/polyCoeff.cpp
+++ b/src/poly/coeff/private/polyCoeff.cpp
@@ -3,16 +3,38 @@
 
 #include "coeff.h"
 
-double xi_coeff_func(const mfem::Vector &x) {
+/**
+ * @brief Computes the xi coefficient function.
+ * 
+ * @param x Input vector.
+ * @return double The computed xi coefficient.
+ */
+double xi_coeff_func(const mfem::Vector &x)
+{
   return std::pow(x(0), 2);
 }
 
-void vec_xi_coeff_func(const mfem::Vector &x, mfem::Vector &v) {
+/**
+ * @brief Computes the vector xi coefficient function.
+ * 
+ * @param x Input vector.
+ * @param v Output vector to store the computed xi coefficient.
+ */
+void vec_xi_coeff_func(const mfem::Vector &x, mfem::Vector &v)
+{
   v.SetSize(1);
   v[0] = -std::pow(x(0), 2);
 }
 
-double theta_initial_guess(const mfem::Vector &x, double root) {
+/**
+ * @brief Computes the initial guess for theta.
+ * 
+ * @param x Input vector.
+ * @param root Root value used in the computation.
+ * @return double The initial guess for theta.
+ */
+double theta_initial_guess(const mfem::Vector &x, double root)
+{
   double xi = x[0];
-  return 1-std::pow(xi/root, 2);
+  return 1 - std::pow(xi / root, 2);
 }
\ No newline at end of file
diff --git a/src/poly/utils/private/polyIO.cpp b/src/poly/utils/private/polyIO.cpp
index 8eaf25b..d540cb0 100644
--- a/src/poly/utils/private/polyIO.cpp
+++ b/src/poly/utils/private/polyIO.cpp
@@ -2,7 +2,7 @@
 #include <string>
 #include<fstream>
 
-#include "io.h"
+#include "polyIO.h"
 
 void write_solution_to_csv(const mfem::GridFunction &u, const mfem::Mesh &mesh, const std::string &filename) {
     std::ofstream file(filename);
diff --git a/src/poly/utils/public/polyIO.h b/src/poly/utils/public/polyIO.h
index e69de29..9ca7ceb 100644
--- a/src/poly/utils/public/polyIO.h
+++ b/src/poly/utils/public/polyIO.h
@@ -0,0 +1,16 @@
+#ifndef POLY_IO_H
+#define POLY_IO_H
+
+#include "mfem.hpp"
+#include <string>
+
+/**
+ * @brief Writes the solution to a CSV file.
+ * 
+ * @param u The GridFunction containing the solution.
+ * @param mesh The mesh associated with the solution.
+ * @param filename The name of the CSV file to write to.
+ */
+void write_solution_to_csv(const mfem::GridFunction &u, const mfem::Mesh &mesh, const std::string &filename);
+
+#endif // POLY_IO_H
\ No newline at end of file
diff --git a/src/poly/utils/public/polyMFEMUtils.h b/src/poly/utils/public/polyMFEMUtils.h
index 33985aa..ac07264 100644
--- a/src/poly/utils/public/polyMFEMUtils.h
+++ b/src/poly/utils/public/polyMFEMUtils.h
@@ -4,40 +4,125 @@
 
 void write_solution_to_csv(const mfem::GridFunction &u, const mfem::Mesh &mesh, const std::string &filename);
 
+/**
+ * @brief A class for nonlinear power integrator.
+ */
 class NonlinearPowerIntegrator: public mfem::NonlinearFormIntegrator {
 private: 
   mfem::FunctionCoefficient coeff_;
   double polytropicIndex;
 public:
+  /**
+   * @brief Constructor for NonlinearPowerIntegrator.
+   * 
+   * @param coeff The function coefficient.
+   * @param n The polytropic index.
+   */
   NonlinearPowerIntegrator(mfem::FunctionCoefficient &coeff, double n);
 
+  /**
+   * @brief Assembles the element vector.
+   * 
+   * @param el The finite element.
+   * @param Trans The element transformation.
+   * @param elfun The element function.
+   * @param elvect The element vector to be assembled.
+   */
   virtual void AssembleElementVector(const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::Vector &elvect) override;
+
+  /**
+   * @brief Assembles the element gradient.
+   * 
+   * @param el The finite element.
+   * @param Trans The element transformation.
+   * @param elfun The element function.
+   * @param elmat The element matrix to be assembled.
+   */
   virtual void AssembleElementGrad (const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::DenseMatrix &elmat) override;
 };
 
+/**
+ * @brief A wrapper class for bilinear integrator.
+ */
 class BilinearIntegratorWrapper : public mfem::NonlinearFormIntegrator
 {
 private:
    mfem::BilinearFormIntegrator *integrator;
 public:
+   /**
+    * @brief Constructor for BilinearIntegratorWrapper.
+    * 
+    * @param integratorInput The bilinear form integrator input.
+    */
    BilinearIntegratorWrapper(mfem::BilinearFormIntegrator *integratorInput);
 
-   virtual ~BilinearIntegratorWrapper() ;
+   /**
+    * @brief Destructor for BilinearIntegratorWrapper.
+    */
+   virtual ~BilinearIntegratorWrapper();
 
+   /**
+    * @brief Assembles the element vector.
+    * 
+    * @param el The finite element.
+    * @param Trans The element transformation.
+    * @param elfun The element function.
+    * @param elvect The element vector to be assembled.
+    */
    virtual void AssembleElementVector(const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::Vector &elvect) override;
-   virtual void AssembleElementGrad(const mfem::FiniteElement &el,mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::DenseMatrix &elmat) override;
+
+   /**
+    * @brief Assembles the element gradient.
+    * 
+    * @param el The finite element.
+    * @param Trans The element transformation.
+    * @param elfun The element function.
+    * @param elmat The element matrix to be assembled.
+    */
+   virtual void AssembleElementGrad(const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::DenseMatrix &elmat) override;
 };
 
+/**
+ * @brief A class for composite nonlinear integrator.
+ */
 class CompositeNonlinearIntegrator: public mfem::NonlinearFormIntegrator {
   private:
     std::vector<mfem::NonlinearFormIntegrator*> integrators;
   public:
+    /**
+     * @brief Constructor for CompositeNonlinearIntegrator.
+     */
     CompositeNonlinearIntegrator();
 
+    /**
+     * @brief Destructor for CompositeNonlinearIntegrator.
+     */
     virtual ~CompositeNonlinearIntegrator();
 
+    /**
+     * @brief Adds an integrator to the composite integrator.
+     * 
+     * @param integrator The nonlinear form integrator to add.
+     */
     void add_integrator(mfem::NonlinearFormIntegrator *integrator);
 
+    /**
+     * @brief Assembles the element vector.
+     * 
+     * @param el The finite element.
+     * @param Trans The element transformation.
+     * @param elfun The element function.
+     * @param elvect The element vector to be assembled.
+     */
     virtual void AssembleElementVector(const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::Vector &elvect) override;
+
+    /**
+     * @brief Assembles the element gradient.
+     * 
+     * @param el The finite element.
+     * @param Trans The element transformation.
+     * @param elfun The element function.
+     * @param elmat The element matrix to be assembled.
+     */
     virtual void AssembleElementGrad(const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::DenseMatrix &elmat) override;
 };
\ No newline at end of file