Efficient High-Order Adaptive Finite Element Methods for broadband Helmholtz Solutions in Engineering Applications

"Efficient High-Order Adaptive Finite Element Methods for broadband Helmholtz Solutions in Engineering Applications", organizado por CITMAga. Será impartido por Hadrien Beriot Siemens Industry Software (Belgium)

Data: mércores, 24 de abril

Hora: 11:00 h.

Duración: 45 min

Lugar: En liña (MS Teams)

Abstract:

In many engineering applications, solutions of the Helmholtz equation are required over a broad frequency range. For acoustics applications, one is often interested in modeling the sound field over the full audible frequency range, i.e. from 20 Hz to 20 kHz. The nature of the solution and the requirements in terms of resolution vary drastically over this range.

Instead of using a set of increasingly refined meshes, which poses many practical issues, a more efficient computational framework is proposed, which consists in relying on a single mesh resolved with a high-order adaptive finite element approach. When combined with efficient a-priori error indicators, this strategy allows to naturally adjust the resolution across the frequency range to reach a user defined target accuracy. As a side benefit, resorting to p-FEM also allow to circumvent the accumulation of phase errors which hamper the conventional low-order FEM accuracy at mid to high frequencies.

Anisotropic orders may also be introduced to deal efficiently with problems involving highly inhomogeneous meshes, with curved and/or high-aspect ratio elements. It may also prove beneficial when the dispersion properties of the waves are direction-dependent, like for instance in the presence of a strong background mean flow.

For exterior acoustics applications, p-adaptive FEM may be efficiently combined with the so-called Automatically Matched Layer (AML), which is a locally-conformal implementation of the Perfectly Matched Layers, applicable on convex domains of general shape. Of utmost importance is also the design of the absorbing function, which needs to be generalized to be reliable in the near field and/or at lower frequencies. Finally, for large scale applications, parallelization strategies based on optimized Schwarz methods will be discussed.