From 3b00b36dc6d223e148c583894a05ecef075a1b33 Mon Sep 17 00:00:00 2001
From: Julian Litz <91479202+julianlitz@users.noreply.github.com>
Date: Wed, 11 Feb 2026 20:55:02 +0100
Subject: [PATCH] Update fmg_interpolation.cpp

---
 src/Interpolation/fmg_interpolation.cpp | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/src/Interpolation/fmg_interpolation.cpp b/src/Interpolation/fmg_interpolation.cpp
index 4e7f0c7c..738ccb7f 100644
--- a/src/Interpolation/fmg_interpolation.cpp
+++ b/src/Interpolation/fmg_interpolation.cpp
@@ -1,10 +1,13 @@
 #include "../../include/Interpolation/interpolation.h"
 
 /*
- * Bicubic FMG Interpolator Using Lagrange Polynomial
- * ----------------------------------------------------
- * This implementation computes an interpolated value using a bicubic Full Multigrid (FMG)
- * scheme. The interpolator applies a scaling factor of 1/16 with the coefficient vector [-1, 9, 9, -1].
+ * Bicubic FMG Interpolator using the Lagrange Interpolating Polynomial
+ * --------------------------------------------------------------------
+ * In contrast to the interpolation of the multigrid cycle, which is applied to corrections,
+ * the FMG interpolation transfers approximations of the solution to the fine grid.
+ * The FMG scheme requires interpolation of higher order than the discretization order 
+ * of the PDE. For second-order discretizations, bicubic interpolation is commonly used.
+ * For a uniform grid, this reduces to the 1D stencil: 1/16 * [-1, 9, 9, -1]
  *
  * The method uses Lagrange interpolation with 4 coarse grid nodes to calculate a single interpolated value.
  * Nodes with an X are the 4 coarse interpolation points used for the interpolation.