  One well adopted power grid simulation methodology is to factorize matrix
once and perform only backward forward substitution with a deliberately chosen
step size along the simulation. Since the required simulation time is usually
long for the power grid design, the costly factorization is amortized. However,
such fixed step size cannot exploit larger step size for the low frequency
response in the power grid to speedup the simulation. In this work, we utilize
the matrix exponential method with the rational Krylov subspace approximation
to enable adaptive step size in the power grid simulation. The kernel operation
in our method only demands one factorization and backward forward
substitutions. Moreover, the rational Krylov subspace approximation can relax
the stiffness constraint of the previous works. The cheap computation of
adaptivity in our method could exploit the long low frequency response in a
power grid and significantly accelerate the simulation. The experimental
results show that our method achieves up to 18X speedup over the trapezoidal
method with fixed step size.
