Piecewise H2 Tangential Interpolation

Piecewise H2 tangential interpolation (PWH2TanInt) is an approach for parametric model order reduction which is based on IRKA and a concatenation of the resulting local bases to a global basis for projection on a low-dimensional subspace. ^[1]

IRKA computes optimal (frequency) shifts $s_i$ and corresponding tangential directions $b_{ij}$ and $c_{ij}$ such that

the reduced-order transfer function matches the p-gradient and p-Hessian of the original system response with respect to the parameters:

\nabla_{\!p}c_{ij}^T G( s_i, p_j)b_{ij} =\nabla_{\!p}c_{ij}^T \hat G ( s_i, p_j)b_{ij}, \quad \nabla^2_{\!p}c_{ij}^T G( s_i, p_j)b_{ij} =\nabla^2_{\!p}c_{ij}^T \hat G ( s_i,p_j)b_{ij},

for $i=1,\ldots,r',\ j=1,\ldots, K$ .

Additionally, the usual tangential interpolation properties hold:

G( s_i, p_j)b_{ij} = \hat G( s_i, p_j)b_{ij},\quad c_{ij}^TG( s_i, p_j) = c_{ij}^T\hat G( s_i, p_j).

References

↑ U. Baur, C. A. Beattie, P. Benner, and S. Gugercin, "Interpolatory projection methods for parameterized model reduction", SIAM J. Sci. Comput., 33(5):2489-2518, 2011

Contact

Ulrike Baur

[morBauBBetal11-1] U. Baur, C. A. Beattie, P. Benner, and S. Gugercin, "Interpolatory projection methods for parameterized model reduction", SIAM J. Sci. Comput., 33(5):2489-2518, 2011

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