Multigrid method belong to the class of methods that are used for numerical solution of discretized differential equations with superior performance. Multigrid methods were specifically designed for the solution of discretized elliptic Partial Differential Equations earlier. The method was later broaden in different ways to handle other Equations earlier. The method was later broaden in different ways to handle other PDE problems, including nonlinear ones, as well as problems not modeled by PDEs. Multigrid methods use relaxation schemes to damp the high frequency eigenvalues, we use a modified relaxation scheme RUB-Jacobi as our core relaxation scheme. The discussion is broaden to the variable coarsening and comparing them with the standard ones. To achieve accuracy complete Local Fourier Analysis have been established for two Dimensions for a tripling case. In the end complete performance analysis is given with the help of suitable experiments. These experiments are extended to d dimension