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In this paper we present a multigrid approach to solve the Poisson equationin arbitrary domain (identified by a level set function) and mixed boundaryconditions. The discretization is based on finite difference scheme andghost-cell method. This multigrid strategy can be applied also to more generalproblems where a non-eliminated boundary condition approach is used. Arbitrarydomain make the definition of the restriction operator for boundary conditionshard to find. A suitable restriction operator is provided in this work,together with a proper treatment of the boundary smoothing, in order to avoiddegradation of the convergence factor of the multigrid due to boundary effects.Several numerical tests confirm the good convergence property of the newmethod.

A Finite Difference Ghost-Cell Multigrid Approach for Poisson Equation with Mixed Boundary Conditions in Arbitrary Domain