Algebraic multigrid: From academia to industry

Abstract

The research on multigrid in the 1970s opened revolutionary perspectives for the efficient solution of discretized elliptic partial differential equations. In spite of this, it took nearly three decades for it to be seriously recognized and used outside the research community. Surprisingly, not the original geometric multigrid (GMG) but algebraic multigrid (AMG) finally brought the breakthrough. When SCAI (Fraunhofer Institute for Algorithms and Scientific Computing)-formerly an institute of the German National Research Center of Information Technology (GMD)-became a Fraunhofer institute in 2001, applied research at SCAI necessarily got a very strong industrial focus. In particular, the primary goal of SCAI’s further AMG development was to help industrial software developers exploit the scientific progress in numerical solver research to their benefit. In this report, we will review the development of AMG in general as well as the scientific and non-scientific efforts needed to develop SCAI’s software product SAMG (System Algebraic MultiGrid), today used as solver environment in many industrial simulation tools. The development of SAMG has mostly been driven by requests from industrial partners. We will outline some advanced industrial AMG applications, for instance, in semiconductor design, multi-ion transport and reaction applications, as well as oil reservoir simulation.