The goal of this project is the development of passivity-preserving model
reduction methods for parametric differential-algebraic equations (DAEs) arising in circuit
simulation.
First, we will study a model reduction method for parametric linear circuit
equations based on a combination of balanced truncation at certain distinct parameters
with interpolation.
For model reduction of non-parametric DAE systems, we will employ the
PAssivity preserving Balanced Truncation method for Electrical Circuits
(PABTEC).
The optimal choice of interpolation points, exploiting the topological
structure, preservation of passivity, and error analysis will be investigated.
In cooperation with SP3, for problems with multiple parameters, we intend to
use sparse grid techniques to reduce the computational effort.
In balanced truncation for DAE systems, the numerical solution of projected
Lyapunov equations
is required that involve certain spectral projectors. It is planned to analyze
a projector-free
approach for structured circuit equations and also for Maxwell's equations
considered in SP1.
In addition, we will develop efficient numerical methods for solving
parametric Lyapunov equations.
Furthermore, using research results from SP6, we will extend various model
reduction approaches
such as the reduced basis method or the discrete empirical interpolation
technique of
parametric nonlinear circuit equations.
Together with the development and analysis of model reduction methods for
parametric DAE systems,
the implementation of the algorithms, their integration into the simulation
packages of the
industry partners and testing on practical problems are also planned.
Milestones:
[Months 1-15] Development and analysis of passivity-preserving model reduction methods
based on balanced truncation and interpolation for parametric linear DAE systems in
nanoelectronics by exploiting the topological network structure.
[Months 13-21] Development of efficient numerical algorithms for the iterative solution of
the parametric projected Lyapunov equations.
[Months 22-30] Development of model reduction methods for parametric nonlinear circuit
equations.
[Months 31-36] Integration of the developed model reduction methods into the simulation
software of the industry partners, and testing on practice-relevant examples.