Adaptive algebraic smoothers
Construction of smoothers which are appropriate for a certain problem is a cumbersome task. This paper attempts to automate the process of smoother construction using \textit{local sensitivity analysis} (LSA). A measure based on LSA is introduced as a means of identifying strong coupling between variables. The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coefficient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system of partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem. Furthermore, it is possible to adaptively vary the size and strength of the blocks leading to the construction of a one parameter family of block iterative methods which can be tuned for a problem based on efficiency or convergence criteria.
scientific article; zbMATH DE number 6015744
scientific article