Towards a robust a priori choice of Padé approximants for fast frequency sweeps of finite element problems

Overview & Synopsis

In this work, a solution strategy based on the use of Padé approximants is investigated for efficient solution of parametric finite element problems such as, for example, frequency sweep analyses. An improvement to the Padé-based expansion of the solution vector components is proposed, suggesting the advantageous a priori estimate of the poles of the solution. This allows for the intervals of approximation to be chosen a priori in connection with the Padé approximants to be used. The choice of these approximants is supported by the Montessus de Ballore theorem, proving the convergenceof a series of approximants with fixed denominator degrees. An acoustic case study is presented in order to illustrate the potential of the approach proposed by the authors.