TY - EJOUR
DO - 10.1051/m2an/2017050
AB - The present work concerns the approximation of the solution map $S$ associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution of the Helmholtz equation. We introduce a least squares rational Padé-type approximation technique applicable to any meromorphic Hilbert space-valued univariate map, and we prove the uniform convergence of the Padé approximation error on any compact subset of the interval of interest that excludes any pole. This general result is then applied to the Helmholtz solution map $S$, which is proven to be meromorphic in $\mathbb{C}$, with a pole of order one in every (single or multiple) eigenvalue of the Laplace operator with the considered boundary conditions. Numerical tests are provided that confirm the theoretical upper bound on the Padé approximation error for the Helmholtz solution map.
T1 - Convergence analysis of Padé approximations for Helmholtz frequency response problems
DA - 2017
AU - Bonizzoni, Francesca
AU - Nobile, Fabio
AU - Perugia, Ilaria
JF - Mathematical Modelling and Numerical Analysis
PB - EDP Sciences
ID - 219986
KW - Hilbert space-valued meromorphic maps
KW - Padé approximants
KW - convergence of Padé approximants
KW - parametric PDEs
KW - Helmholtz equation
SN - 0764-583X
UR - http://infoscience.epfl.ch/record/219986/files/2017_Bonizzoni_Nobile_Perugia_M2AN_Pade_online.pdf
ER -