Macro-elementwise preconditioning methods
For extremely large scale models derived from partial differential equations for heterogeneous media, macro- and micro-preconditioning are discussed. Grouping the variables into macro- and even micro-elements here allows for better modeling and more efficient parallel methods and even for different modeling methods for different portions of the variables. With a system partitioned according to its macro-elements, preconditioners must reflect this and be joined across their elementwise boundaries to ensure their efficiency. This leads to finding good approximate inverses for 2 by 2 block matrix preconditioners via approximate Schur complements for the \((2,1)\) block. The paper considers several incomplete Schur complements in this context and studies their effect on conditioning. Also elementwise approximations for such Schur complements are studied.
scientific article; zbMATH DE number 6107071
scientific article