  Dynamical systems are pervasive in almost all engineering and scientific
applications. Simulating such systems is computationally very intensive. Hence,
Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most
of the MOR algorithms require solving large sparse sequences of linear systems.
Since using direct methods for solving such systems does not scale well in time
with respect to the increase in the input dimension, efficient preconditioned
iterative methods are commonly used.
  In one of our previous works, we have shown substantial improvements by
reusing preconditioners for the parametric MOR (Singh et al. 2019). Here, we
had proposed techniques for both, the non-parametric and the parametric cases,
but had applied them only to the latter. We have four main contributions here.
First, we demonstrate that preconditioners can be reused more effectively in
the non-parametric case as compared to the parametric one because of the lack
of parameters in the former. Second, we show that reusing preconditioners is an
art and it needs to be fine-tuned for the underlying MOR algorithm. Third, we
describe the pitfalls in the algorithmic implementation of reusing
preconditioners. Fourth, and final, we demonstrate this theory on a real life
industrial problem (of size 1.2 million), where savings of upto 64% in the
total computation time is obtained by reusing preconditioners. In absolute
terms, this leads to a saving of 5 days.
