Authors:
Prem Ratan Mohan Ram | TU Braunschweig, Institute of Dynamics and Vibrations | Germany
Shreyas M. Guruprasad | TU Braunschweig, Institute for Acoustics | Germany
Ulrich Römer | TU Braunschweig, Institute of Dynamics and Vibrations | Germany
Christopher Blech | TU Braunschweig, Institute for Acoustics | Germany
Sabine C. Langer | TU Braunschweig, Institute for Acoustics | Germany
To perform uncertainty quantification (UQ) on systems such as acoustic or electromagnetic systems, one is often interested in computing a surrogate model of the response function in the frequency domain. In many cases, this is challenging as these systems exhibit sharp variations in their response for small changes in frequency. Lately two approaches, namely the Padé approximation technique and the generalized polynomial chaos (gPC) method are receiving increasing interest in this context. With a general formulation of Padé-type approximations for multi-variate problems being a work-in-progress, and the gPC method requiring a very high polynomial order for accurate approximation, in [1], the multi element generalized polynomial chaos (MEgPC) method has been proposed. This method adaptively decomposes the domain of the random parameters and performs a piecewise polynomial approximation.
In this work, the MEgPC method has been used to approximate stochastic frequency response functions. We discuss adaptivity criteria and illustrate the performance of the method through both academic benchmark problems and problems from vibroacoustics.
[1] X. Wan, G. E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, Journal of Computational Physics 209 (2005) 617–641.