"Inexact Hierarchical Scale Separation: A Two-Scale Approach for Linear Systems from Discontinuous Galerkin Discretizations"
Hierarchical scale separation (HSS) is an iterative two-scale approximation method for large sparse systems of linear equations arising from discontinuous Galerkin (DG) discretizations. HSS splits the linear 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. The scheme then alternates between coarse-scale and fine-scale system solves until both components converge. The motivation of HSS is to promote parallelism by decoupling the fine-scale systems, and to reduce the communication overhead from classical linear solvers by only applying them to the coarse-scale system.
Inexact HSS (IHSS) is a modification of the original HSS algorithm that improves computational performance by only approximating the coarse-scale systems and by shifting more work to the highly parallel fine-scale solver. The tolerance for the coarse-scale solver is adapted in each IHSS iteration to maintain a balance between both solvers. Stability and performance are further improved by augmenting the repeated fine-scale solves with an Anderson acceleration.