@article{,
    author = {Wiesner, Tobias A.; Popp, Alexander; Gee, Michael W.; Wall, Wolfgang A.},
    title = {Algebraic multigrid methods for dual mortar finite element formulations in contact mechanics},
    editor = {},
    booktitle = {},
    series = {},
    journal = {International Journal for Numerical Methods in Engineering},
    address = {},
    publisher = {},
    edition = {},
    year = {2018},
    isbn = {},
    volume = {114},
    number =  {4},
    pages = {399-430},
    url = {http://dx.doi.org/10.1002/nme.5748},
    doi = {10.1002/nme.5748},
    keywords = {Algebraic multigrid methods ; Structural contact problems ; Mortar methods ; Dual mortar approach ; Iterative linear solvers},
    abstract = {This paper proposes novel strategies to enable multigrid preconditioners within iterative solvers for linear systems arising from contact problems based on mortar finite element formulations. The so-called dual mortar approach that is exclusively employed here allows for an easy condensation of the discrete Lagrange multipliers. Therefore, it has the advantage over standard mortar methods that linear systems with saddle point structure are avoided, which generally require special preconditioning techniques. However, even with the dual mortar approach the resulting linear systems turn out to be hard to solve using iterative linear solvers. 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 how the contact modeling affects the corresponding linear systems. This information is used to develop new strategies which make multigrid methods efficient preconditioners for the class of contact problems based on dual mortar methods. It is worth mentioning that these strategies primarily adapt the input of the multigrid preconditioners in a way, that no contact-specific enhancements are necessary in the multigrid algorithms. This makes the implementation comparably easy. With the proposed method we are able to solve large contact problems which is an important step towards the application of dual mortar based contact formulations in industry. Numerical results are presented illustrating the performance of the presented algebraic multigrid method.},
    note = {},
    institution = {Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften, BAU 1 - Institut für Mathematik und Computergestützte Simulation, Professur: Popp, Alexander},
    
    
}