We present a multigrid method for an unfitted finite element discretization of the Dirichlet boundary value problem. The discretization employs Nitsche's method to implement the boundary condition and additional face based ghost penalties for stabilization. We apply standard intergrid operators, relying on the fact that the relevant domain of computation does not grow under mesh refinement. The smoother is a parallel implementation of the multiplicative vertex-patch smoother with inconsistent treatment of ghost penalties. Our computational results show that we obtain a fast converging method. Furthermore, runtime comparison to fitted methods show that the losses are moderate although many optimizations for Cartesian vertex patches cannot be applied on cut patches.

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