Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem
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We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing physical parameters into random variables. A random quantity of interest is expanded into the (generalised) polynomial chaos using orthogonal basis polynomials. We investigate the determination of sparse representations, where just a few basis polynomials are required for a sufficiently accurate approximation. Furthermore, we apply model order reduction with proper orthogonal decomposition to obtain a low-dimensional representation in an alternative basis.
The research of the second author is supported by the Excellence Initiative of the German Federal and State Governments and by the Graduate School of Computational Engineering at Technische Universität Darmstadt.
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