Baur: Created page with "Category:method Category:linear Category:parametric Category:time invariant '''Piecewise H2 tangential interpolation''' (PWH2TanInt) is an approach for parame..."

2015-10-30T10:55:16Z

Created page with "Category:method Category:linear Category:parametric Category:time invariant '''Piecewise H2 tangential interpolation''' (PWH2TanInt) is an approach for parame..."

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[[Category:method]]
[[Category:linear]]
[[Category:parametric]]
[[Category:time invariant]]

'''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.
<ref name="morBauBBetal11"> U. Baur, C. A. Beattie, P. Benner, and S. Gugercin,
"<span class="plainlinks">[http://epubs.siam.org/doi/abs/10.1137/090776925 Interpolatory projection methods for parameterized model reduction]</span>",
SIAM J. Sci. Comput., 33(5):2489-2518, 2011</ref>

IRKA computes optimal (frequency) shifts <math>s_i</math> and corresponding tangential directions <math>b_{ij}</math> and <math>c_{ij}</math> such that

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

:<math>
\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},

</math>
for <math>i=1,\ldots,r',\ j=1,\ldots, K</math>.

Additionally, the usual tangential interpolation properties hold:

:<math>
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).
</math>

==References==

<references/>

==Contact==

[[User:Baur]]

Piecewise H2 Tangential Interpolation - Revision history

Baur: Created page with "Category:method Category:linear Category:parametric Category:time invariant '''Piecewise H2 tangential interpolation''' (PWH2TanInt) is an approach for parame..."