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Download Robust and scalable multiphysics solvers for unfitted finite element
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Robust and scalable multiphysics solvers for unfitted finite element methods Santiago Badia∗,† and Francesc Verdugo∗,† ∗ Universitat Politècnica de Catalunya Campus Nord UPC, 08034 Barcelona, Spain e-mail: [email protected], [email protected], † International Center for Numerical Methods in Engineering (CIMNE) Parc Mediterrani de la Tecnologia, Esteve Terradas 5, Castelldefels, Spain ABSTRACT Embedded boundary methods are very attractive, because eliminate the need to define bodyfitted meshes. In particular, at large scales, the meshing step is a bottleneck of the simulation pipeline, since mesh generators do not usually scale properly. In some other situations, like in additive manufacturing simulations, the geometry evolves in time, and the use of boddy-fitted meshes is not suitable. On the contrary, algorithms to create adaptive cartesian meshes are highly scalable. However, using embedded boundary methods, one can destroy the condition number of the linear systems to be solved, since cut elements can have close to zero support. As a result, these techniques require direct linear solvers, since standard preconditioned iterative solvers are not robust and scalable. In this work, we take as a starting point a balancing domain decomposition by constraints (BDDC) preconditioner. Next, we consider a recent physics-based version of the method that is robust with respect to high variations of the materials. Finally, we show to how to make these preconditioners robust also for embedded boundary methods for coercive PDEs, by a proper modification of the inter-subdomain constraints.
