The Effects of Nonsymmetric Matrix Permutations and Scalings in Semiconductor Device and Circuit Simulation

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The solution of large sparse unsymmetric linear systems is a critical and challenging component of semiconductor device and circuit simulations. The time for a simulation is often dominated by this part. The sparse solver is expected to balance different, and often conflicting requirements. Reliability, a low memory-footprint, and a short solution time are a few of these demands. Currently, no black-box solver exists that can satisfy all criteria. The linear systems from both simulations can be highly ill-conditioned and therefore quite challenging for direct and iterative methods. In this paper, it is shown that nonsymmetric permutations and scalings aimed at placing large entries on the diagonal greatly enhance the reliability of both direct and preconditioned iterative solvers.  The numerical experiments indicate that the overall solution strategy is both reliable and very cost effective for unsymmetric linear systems arising in semiconductor device and circuit simulations.

By: Olaf Schenk, Stefan Rollin, Anshul Gupta

Published in: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, volume 23, (no 3), pages 400-11 in 2004


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