A parallelizable GMRES-type method for p-cyclic matrices, with applications in circuit simulation

Abstract

In this paper we propose a GMRES-type method for the solution of linear systems with a p-cyclic coecient matrix. These p-cyclic matrices arise in the periodic steady state simulation of circuits, assuming that the DAE is discretized in the time domain. The method has similarities with existing GMRES approaches for p-cyclic matrices, but in contrast to these methods the method is eciently parallelizable, even if the p-cyclic matrix has a small block size. However, the serial costs of the method may be somewhat higher. Numerical experiments demonstrate the eectiveness of the method.