Speaker
Description
CANCELLED
Many modern applications in engineering are faced to deal with heterogeneous and often anisotropic material behavior, relevant for thermal diffusion, groundwater flow or electrostatics. The numerical solution of these types of problems is challenging, as applying the finite element method results in badly scaled and ill-conditioned linear systems to be solved. To maintain efficiency and scalability of the linear solver, iterative solution techniques preconditioned by algebraic multigrid methods (AMG) are widely used. However, traditional AMG lacks a proper handling of the material information and thus converges slowly, if at all, for these types of problems. While recent advances have been made for anisotropy related to stretched meshes, the proper handling of heterogeneous and anisotropic materials remains an open topic for now.
This talk will propose a new smoothed aggregation procedure in the context of AMG to incorporate the material information into the coarsening process for the coarse level construction. While classical strength-of-connection measures struggle with coefficient jumps and anisotropy, the new approach shows robustness and ease-of-use in the envisaged scenarios. Especially in cases with a strongly directional material component, it can be shown that the iteration count is independent of the material property. In addition, care has to be taken in regard to the Jacobi based prolongator smoothing step, especially for ill-conditioned fine level operators. Matrix filtering based on the proposed dropping scheme can control the operator complexity of the multigrid hierarchy and thus keeps the cost of applying the preconditioner low.
