Generalized Krylov recycling methods for solution of multiple related linear equation systems in electromagnetic analysis

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.