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{\large Heidi K. Thornquist \\
{\bf Linear solver challenges in large-scale circuit simulation}}

Sandia National Laboratories \\ P O Box 5800 \\ MS - 0316 \\ Albuquerque \\ NM 87185
\\
{\tt hkthorn@sandia.gov}\\
Eric R. Keiter\\
Eric G. Boman\\
David M. Day\end{center}

While direct linear solvers have long been regarded as a requirement for
successful circuit simulation, the simulation of large-scale digital
circuits is now necessitating the use of iterative linear solvers.
However, the linear systems generated through circuit simulation prove to
be challenging for the conventional matrix ordering, load balancing, and
preconditioning techniques due to their heterogeneous matrix structure.
We will discuss why these linear systems can be difficult for iterative
methods to solve as well as some of the graph techniques employed by the
Xyce circuit simulation code to address these challenges. Furthermore, we
will also discuss ongoing work in parallel partitioning and
preconditioning techniques, including some multi-level approaches, that
have proven useful for the simulation of large-scale digital circuits.


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