Mathematikgebäude, M 1011

Discontinuous Galerkin (DG) methods have many attractive features such as being naturally of arbitrary order, local mass conservation, or the freedom of choosing local bases and element geometries. Compared to classical discretization methods, however, DG typically yields larger and more ill-conditioned sparse linear systems. Hierarchical scale separation (HSS) is a recently proposed two-scale approximation method for those systems provided basis functions are of modal type. HSS splits the system into a coarse-scale system of reduced size corresponding to the local mean values of the solution and a set of decoupled local fine-scale systems corresponding to the higher order solution components. This reduces the communication overhead, e.g., within sparse matrix-vector multiplications of classical iterative solvers and allows for an optimal parallelization of the fine-scale solves. In this talk, I introduce the ''inexact HSS'' algorithm, which shifts the workload to the parallel fine-scale solver to reduce global synchronization, resulting in a significant speedup. The presented applications are phase-field models for two-phase pore-scale flow simulations.

Dr. Florian Frank

Friedrich-Alexander-Universität Erlangen-Nürnberg