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A key component of a nuclear fusion reactor is the divertor. Its role is to remove impurities from the reactor in order to sustain the fusion reaction. Furthermore, the divertor is responsible for the power exhaust and should be able to handle extreme power loads. Properly understanding plasma-wall interactions is one of the critical problems in development of nuclear fusion. For this purpose, the B2−Eirene code was developed in the late 1980’s. It is computationally very demanding to simulate the behaviour of particles near the plasma edge. Multigrid methods are frequently used in computational fluid dynamics in order to reduce the computation time. Because of the multigrid method’s success in CFD, the usefulness of linear multigrid methods in the nuclear fusion domain is further explored in this thesis. The multigrid algorithm makes use of two concepts: iterative solvers and multiple girds of different sizes. The model that is used in this thesis is a one dimensional simplification which is based on the B2-Eirene code. A one dimensional model is used because it simplifies the implementation of the multigrid method and it allows for rapid testing. Different model problems are set up to test the multigrid methods. Although the linear multigrid methods require more computation time, it is shown that they reduce the amount of iterations. This reduction is attributed to the fact that the multigrid method has a relaxation effect. A second result is that in some cases with statistical noise, the multigrid methods are able to reach convergence where the standard solution method does not. The multigrid method is able to converge because it cancels out statistical noise that is introduced by Monte Carlo simulations. In the one dimensional model, there are two main avenues of investigation. The first is combining the multigrid method with different smoothers, the second is the use on non-linear multigrid method.