Block-Preconditioning for Hybrid Discretizations in Combination With Lagrange-Multiplier Coupling

Hybrid discretization methods based on a domain decomposition exploiting continuous symmetries present in parts of the model aim at a reduction of the computational cost of the related numerical simulations. The resulting linear systems of equations arising from, e.g., the coupling of finite elements (FE) and spectral elements (SE), are sparse and symmetric. However, in case of the use of saddle-point formulations an indefinite system of algebraic equations is obtained. Therefore, the solution requires the application of appropriate iterative solvers and preconditioners. In order to achieve an acceptable solution time, an adapted block-preconditioner based on approximations of the Schur complement is applied. The performance regarding the number of iterations of the Krylov subspace method as well as the solution time is compared for different types of preconditioners.