Efficient matrix exponential method based on extended Krylov subspace for transient simulation of large-scale linear circuits

Matrix exponential (MEXP) method has been demonstrated to be a competitive candidate for transient simulation of very large-scale integrated circuits. Nevertheless, the performance of MEXP based on ordinary Krylov subspace is unsatisfactory for stiff circuits, wherein the underlying Arnoldi process tends to oversample the high magnitude part of the system spectrum while undersampling the low magnitude part that is important to the final accuracy. In this work we explore the use of extended Krylov subspace to generate more accurate and efficient approximation for MEXP. We also develop a formulation that allows unequal positive and negative dimensions in the generated Krylov subspace for better performance. Numerical results demonstrate the efficacy of the proposed method.