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Mathematik für Innovationen in Industrie und Dienstleistungen
MoreSim4Nano> SP 4 (Augsburg)

Research network within the BMBF funded program
Mathematics for Innovations in Industry and Services


Subproject 4: Model order reduction for parametric circuit equations

    Subproject leader:

    Prof. Dr. Heike Faßbender, TU Braunschweig
    Prof. Dr. Tatjana Stykel, University of Augsburg

    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.


    • [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.
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Judith Schneider, judith.schneider@mpi-magdeburg.mpg.de