An iterative method for nonsymmetric systems with multiple right-hand sides
SIAM Journal on Scientific Computing
Efficient AC and noise analysis of two-tone RF circuits
DAC '96 Proceedings of the 33rd annual Design Automation Conference
IES3: a fast integral equation solver for efficient 3-dimensional extraction
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
A fast hierarchical algorithm for 3-D capacitance extraction
DAC '98 Proceedings of the 35th annual Design Automation Conference
GLS '99 Proceedings of the Ninth Great Lakes Symposium on VLSI
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Incremental large-scale electrostatic analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Incremental solution of power grids using random walks
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
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In this paper we propose methods for fast iterative solution of multiple related linear systems of equations. Such systems arise, for example, in building pattern libraries for interconnect parasitic extraction, parasitic extraction under process variation, and parameterized interconnect characterization. Our techniques are based on a generalized form of "recycled" Krylov subspace methods that use sharing of information between related systems of equations to accelerate the iterative solution. Experimental results on electromagnetics problems demonstrate that the proposed method can achieve a speed-up of 5X~30X compared to direct GMRES applied sequentially to the individual systems. These methods are generic, fully treat nonlinear perturbations without approximation, and can be applied in a wide variety of application domains outside electromagnetics.