LAUSR

Summary In order to increase the robustness of a Pade-based approximation of parametric solutions to finite element problems, an a priori estimate of the poles is proposed. The resulting original approach is shown to allow for a straightforward, efficient, subsequent Pade-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 Pade 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 i) a component-wise expansion which allows to specifically target subsets of the solution field, and ii) the a priori, simultaneous choice of the Pade 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 in order to demonstrate the potential of the approach proposed. This article is protected by copyright. All rights reserved.