Adaptative scheme for diffuse field response of multilayered structures

The computation of the diffuse field response of multilayered homogeneous structures leads to integrals which should be computed efficiently. This is all the more true as the frequency increases, since the integrand has localized peaks. The objective of this communication is to propose an adaptive integration scheme that aims to limit the number of resolutions of the physical problem and to maximize the reuse of previous evaluations in the course of the method. After discussing the usual integration methods, the proposed method will be presented. A first approximation of the integral is performed with two nested integration schemes with a coarse mesh of the initial integration domain. A local error indicator is derived and leads to a first partition. On each set of the latter, and depending on the local error estimated previously, an adequate numerical scheme is chosen. The error is controlled during all the process and it is iterated until convergence. The method is tested first on academic cases and then on industrial cases. The performance of the method is discussed, taking into account not only the number of evaluations of the physical function, but also the additional numerical cost generated by the adaptation process.