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.

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:

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

Contact

Ulrike Baur