Moment Matching Based Model Order Reduction for Quadratic-Bilinear Systems
For model order reduction of quadratic-bilinear systems a moment matching approach has been recently proposed where univariate frequency responses are constructed by means of the associated transform onto the multivariate transfer functions. This approach comes with the obvious advantage of only one-dimensional interpolation frequencies to be considered, but suffers from the arising large size of the involved equation systems and the high computational demands that make the approach impractical for most applications. In this paper, by exploiting the problem-underlying sparse tensor structure, we propose a splitting algorithm that overcomes this curse of dimensionality. We demonstrate the performance of the extended univariate frequency approach and compare it with the well-established multimoment matching approach regarding accuracy, efficiency and need of memory.
Supported by the German Federal Ministry for Economic Affairs and Energy, in the joint project: MathEnergy – Mathematical Key Technologies for Evolving Energy Grids.
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