Simulated Highly Parallel Solution of Versatile Companion Model Graph Equations

Oriented linear graphs have already half a century ago been considered suitable to describe lumped physical systems /1/. Usually matrix equations arising from partial differential equations describing physical networks are very sparse. Companion models arising from linear electrical circuits are introductory presented. /2/. Specific versatile companion model graph eguations can be applied when, for instance, discontinuities and nonlinear dependencies have to be considered /3/. Present sequential solvers for relevant sparse equation systems are not very suited for highly parallel computing. A general concern for developers of industrial process analysis codes is: How to make the code running efficiently on future multi core processor chips /4/. In this study relevant algorithms and architectures are applied on a simulated highly parallel computer. The lessons learned are supposed to guide the transportation or re-programming of millions of lines of present sequential codes.