Padé approximants and the modal connection: Towards increased robustness for fast parametric sweeps

Romain Rumpler
2017 International Journal for Numerical Methods in Engineering  
Pade approximants and the modal connection: Towards increased robustness for fast parametric sweeps International Journal for Numerical Methods in Engineering, 113(1): 65-81 https://doi.org/10.1002/nme.5603 Access to the published version may require subscription. N.B. When citing this work, cite the original published paper. Permanent link to this version: Summary To increase the robustness of a Padé-based approximation of parametric solutions to finite element problems, an a priori estimate
more » ... a priori estimate of the poles is proposed. The resulting original approach is shown to allow for a straightforward, efficient, subsequent Padé-based expansion of the solution vector components, overcoming some of the current convergence and robustness limitations. In particular, this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of Padé approximants. The choice of these approximants, as shown in the present work, is theoretically supported by the Montessus de Ballore theorem, concerning the convergence of a series of approximants with fixed denominator degrees. Key features and originality of the proposed approach are (1) a component-wise expansion which allows to specifically target subsets of the solution field and (2) the a priori, simultaneous choice of the Padé approximants and their associated interval of convergence for an effective and more robust approximation. An academic acoustic case study, a structural-acoustic application, and a larger acoustic problem are presented to demonstrate the potential of the approach proposed.
doi:10.1002/nme.5603 fatcat:xyzf2nb6kjanlpidy4utk6hx34