1st Edition
by Mohammad Monir Uddin (Author)
These days, computer-based
simulation is considered the quintessential approach to exploring new
ideas in the different disciplines of science, engineering and
technology (SET). To perform simulations, a physical system needs to be
modeled using mathematics; these models are often represented by linear
time-invariant (LTI) continuous-time (CT) systems. Oftentimes these
systems are subject to additional algebraic constraints, leading to
first- or second-order differential-algebraic equations (DAEs),
otherwise known as descriptor systems. Such large-scale systems
generally lead to massive memory requirements and enormous computational
complexity, thus restricting frequent simulations, which are required
by many applications. To resolve these complexities, the
higher-dimensional system may be approximated by a substantially
lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses
computational techniques for the MOR of large-scale sparse LTI CT
systems. Although the book puts emphasis on the MOR of descriptor
systems, it begins by showing and comparing the various MOR techniques
for standard systems.
The book also discusses the low-rank
alternating direction implicit (LR-ADI) iteration and the issues related
to solving the Lyapunov equation of large-scale sparse LTI systems to
compute the low-rank Gramian factors, which are important components for
implementing the Gramian-based MOR.
Although this book is
primarly aimed at post-graduate students and researchers of the various
SET disciplines, the basic contents of this book can be supplemental to
the advanced bachelor's-level students as well. It can also serve as an
invaluable reference to researchers working in academics and industries
alike.
Features:
- Provides an up-to-date,
step-by-step guide for its readers. Each chapter develops theories
and provides necessary algorithms, worked examples, numerical
experiments and related exercises. With the combination of this book and
its supplementary materials, the reader gains a sound understanding of
the topic.
- The MATLAB® codes for some selected algorithms are
provided in the book. The solutions to the exercise problems, experiment
data sets and a digital copy of the software are provided on the book's
website;
- The numerical experiments use real-world data sets obtained from industries and research institutes.
