A Generalized Multigrid Method for Solving Contact Problems in Lagrange Multiplier based Unfitted Finite Element Method

  title={A Generalized Multigrid Method for Solving Contact Problems in Lagrange Multiplier based Unfitted Finite Element Method},
  author={Hardik Kothari and Rolf H. Krause},

Stability and conditioning of immersed finite element methods: analysis and remedies

This review paper discusses the developments in immersed or unfitted finite element methods over the past decade, and provides a detailed explanation of Schwarz preconditioning, element aggregation, and the ghost penalty formulation.



Multigrid and saddle-point preconditioners for unfitted finite element modelling of inclusions

This work utilizes the Uzawa method for solving the saddle point system and proposes preconditioning strategies for primal and dual systems, and employs the method of Lagrange multipliers for enforcing the interface conditions between the inclusions and matrix.

A Multigrid Method for a Nitsche-based Extended Finite Element Method

  • Hardik KothariR. Krause
  • Computer Science
    International Journal of Computing and Visualization in Science and Engineering
  • 2021
A tailored multigrid method for linear problems stemming from a Nitsche-based extended finite element method (XFEM) that is robust with respect to highly varying coefficients and the number of interfaces in a domain and compares it with other preconditioners.

Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

A geometric multigrid preconditioner for immersed finite element methods, which provides mesh-independent and cut-element-independent convergence rates and enables solving large-scale immersed systems at a computational cost that scales linearly with the number of degrees of freedom.

A Multigrid Method for Unfitted Finite Element Discretizations of Elliptic Interface Problems

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.

Monotone Multigrid Methods on Nonmatching Grids for Nonlinear Multibody Contact Problems

A generalized mortar method based on dual Lagrange multipliers is used for the discretization of a nonlinear contact problem between linear elastic bodies and can be implemented as a multigrid method.

Algebraic multigrid methods for dual mortar finite element formulations in contact mechanics

A basic analysis of the mathematical properties of the linear operators reveals why the naive application of standard iterative solvers shows instabilities and provides new insights of how contact modeling affects the corresponding linear systems.

Efficient simulation of multi‐body contact problems on complex geometries: A flexible decomposition approach using constrained minimization

We consider the numerical simulation of non‐linear multi‐body contact problems in elasticity on complex three‐dimensional geometries. In the case of warped contact boundaries and non‐matching finite

High-order cut finite elements for the elastic wave equation

A high-order cut finite element method is formulated for solving the elastic wave equation and Nitsche’s method is used to enforce boundary and interface conditions, resulting in symmetric bilinear forms.

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

A fully aggregation‐based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach and can easily be combined with segregated transfer operators to preserve the saddle point structure on the coarse levels.