Multigrid Methods for Ghost Finite Element Formulations
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We present an unfitted finite element framework enhanced with multigrid techniques for efficient and accurate numerical simulations of problems involving complex and moving geometries. The framework employs a ghost finite element approach, ensuring robustness and preserving second-order accuracy regardless of cut locations. We investigate key numerical properties of the framework, including stability, convergence, and computational performance. Furthermore, we analyze the influence of the stabilization constant on the behavior and efficiency of the multigrid method.