A Multigrid Method for Unfitted Finite Element Discretizations of Elliptic Interface Problems
For computational scientists solving interface problems with cut finite elements, this multigrid method offers a robust and efficient solver, though it is an incremental improvement over existing multigrid techniques.
The paper develops a multigrid method for unfitted finite element discretizations of elliptic interface problems, achieving robustness for large jumps in diffusion coefficients. Numerical results demonstrate efficiency and robustness with respect to mesh size, interface location, and coefficient contrast.
We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three methods rely on Nitsche s method to incorporate the interface conditions. The main topic of the paper is the development of a multigrid method, based on a novel prolongation operator for the unfitted finite element space and an interface smoother that is designed to yield robustness for large jumps in the diffusion coefficients. Numerical results are presented which illustrate efficiency of this multigrid method and demonstrate its robustness properties with respect to variation of the mesh size, location of the interface and contrast in the diffusion coefficients.