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 $b_{i j}$ and $c_{i j}$ 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_{i j}^{T} G (s_{i}, p_{j}) b_{i j} = \nabla_{p} c_{i j}^{T} \hat{G} (s_{i}, p_{j}) b_{i j}, \nabla_{p}^{2} c_{i j}^{T} G (s_{i}, p_{j}) b_{i j} = \nabla_{p}^{2} c_{i j}^{T} \hat{G} (s_{i}, p_{j}) b_{i j},

for $i = 1, \dots, r^{'}, j = 1, \dots, K$ .

Additionally, the usual tangential interpolation properties hold:

G (s_{i}, p_{j}) b_{i j} = \hat{G} (s_{i}, p_{j}) b_{i j}, c_{i j}^{T} G (s_{i}, p_{j}) = c_{i j}^{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

User: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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