A generalized multigrid method for solving contact problems in Lagrange multiplier based unfitted Finite Element method
نویسندگان
چکیده
Internal interfaces in a domain could exist as material defect or they can appear due to propagations of cracks. Discretization such geometries and solution the contact problem on internal be computationally challenging. We employ an unfitted Finite Element (FE) framework for discretization domains develop tailored, globally convergent, efficient multigrid method solving problems interfaces. In FE methods, structured background meshes are used only underlying finite element space has modified incorporate discontinuities. The non-penetration conditions embedded discretized using Lagrange multipliers. reformulate arising variational inequality quadratic minimization with linear constraints. Our solve by employing tailored multilevel hierarchy spaces novel approach tackling conditions. pseudo-$L^2$ projection-based transfer operators construct nested from non-nested meshes. essential component our is technique that decouples constraints orthogonal transformation basis. decoupled handled variant projected Gauss-Seidel method, which we smoother method. These components allow us enforce locally ensure global convergence will demonstrate robustness, efficiency, level independent property proposed Signorini's two-body problems.
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ژورنال
عنوان ژورنال: Computer Methods in Applied Mechanics and Engineering
سال: 2022
ISSN: ['0045-7825', '1879-2138']
DOI: https://doi.org/10.1016/j.cma.2022.114630