Model reduction is one of the most valuable
contributions of mathematical system theory to
applied mathematics (Jan C. Willems, 2007).
In this book, Ulrike Baur investigates model
reduction for parabolic PDEs based on balanced
Effective implementations of balanced truncation (and
of related methods such as singular perturbation
cross-Gramian model reduction, balanced truncation
for unstable systems)
are developed by exploiting the structure of the
underlying PDE problem.
This is achieved by a data-sparse approximation of
discretized differential operator using the
hierarchical matrix format and
by using the formatted arithmetic in the developed
solvers for different types of matrix equations such as
(generalized) Lyapunov, Stein, Sylvester and
algebraic Bernoulli equations.
All approaches are well-suited for classes of
problems and allow the application of balanced
truncation and related methods to systems
coming from 2D and 3D FEM and BEM discretizations.