BibTeX
@ARTICLE{
         Towara2018Sam,
       crossref = "Christianson2018Sio",
       author = "Markus Towara and Uwe Naumann",
       title = "{SIMPLE} adjoint message passing",
       journal = "Optimization Methods \& Software",
       volume = "33",
       number = "4--6",
       pages = "1232--1249",
       year = "2018",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2018.1435653",
       url = "https://doi.org/10.1080/10556788.2018.1435653",
       eprint = "https://doi.org/10.1080/10556788.2018.1435653",
       abstract = "In the context of numerical simulation a system of partial differential equations
         is typically solved by discretizing it into a set of linear equations. The non-linear effects in the
         solution are then approximated by repeatedly discretizing, solving and correcting the equations
         using some outer iteration scheme. One example for such a scheme is the SIMPLE algorithm. In this
         paper, we show how we obtained an algorithmic adjoint version of the SIMPLE algorithm in OpenFOAM
         with particular focus on the adjoint message passing interface communication inside the linear
         solvers. Due to the sparse matrix storage and specifics of the implementation of the linear solvers,
         this method requires special attention to the inner workings of said structures and algorithms. We
         show the feasibility of the chosen method by presenting two case studies. In addition to the SIMPLE
         algorithm, the presented ideas are applicable to a wide range of algorithms whenever linear systems
         are embedded into an overlying non-linear context.",
       booktitle = "Special issue of Optimization Methods \& Software: Advances in
         Algorithmic Differentiation",
       editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}