Christopher Jelich, M.Sc.

Wissenschaftlicher Mitarbeiter

Akustische Randelementemethode für periodische Strukturen

Periodic structures are known to be very efficient in modifying the propagation of various types of waves, including acoustic, elastic and electromagnetic waves. Applications reach from noise barriers and tuned absorbers to microelectromechanical systems. The wave propagation is controlled by the geometry of the unit cell, its resonances and the periodic layout. Many functionalities that cannot be found in naturally existing materials such as a negative refractive index, cloaking and perfect absorption can be realized. They can be determined ahead of production by means of numerical analyses.

The research project focuses on developing numerical methods to study the propagation of acoustic waves subject to periodic structures. Our recent approach introduces a novel fast multipole boundary element method that achieves significant savings in computational time and memory by meticulously utilizing the regularity found in periodic structures. The method considers structures of finite extent and does not require any periodicity of the boundary conditions or solution.

Jelich, C., Zhao, W., Chen, H., Marburg, S. (2021): Fast multipole boundary element method for the acoustic analysis of periodic structures, submitted to Computer Methods in Applied Mechanics and Engineering.

Lösungsverfahren für parameterabhängige Struktur-Akustik-Probleme

Assessing the vibroacoustic behavior of thin-walled lightweight structures is an important aspect of designing quiet machines and vehicles. The advances in numerical modeling techniques allow accurate predictions of vibroacoustic quantities such as radiated sound power and transmission loss ahead of manufacturing. Including them in design optimization and uncertainty analyses has become a common engineering practice in recent decades. However, repeatedly evaluating vibroacoustic quantities for different parameters and various frequencies poses a significant computational challenge. This especially holds for the popular choice of the combined approach of finite element method (FEM) and boundary element method (BEM) for the analysis of structures in the low frequency range.

The research project targets to develop an efficient scheme for solving fully coupled FEM-BEM structural acoustic problems at predefined parameter and frequency points. The key challenge lies in the consideration of implicit parameter dependence, i.e. non-affine parameterized systems. We address this by parametric model order reduction and propose a greedy reduced basis scheme. The scheme approximates the solution at the predefined points by linear combination of a reduced basis. It iteratively expands the basis by adding the response at the parameter and frequency point that is currently worst approximated. Our greedy reduced basis scheme finds the solution at all predefined parameter and frequency points based on the evaluation of a few high-fidelity solutions. The convergence of the solution is visualized in Figure 1 for an academic example with two parameters: Young’s modulus and frequency.

Jelich, C., Baydoun, S. K., Voigt, M., Marburg, S. (2021): A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence, submitted to International Journal of Numerical Methods in Engineering.

Forschungsschwerpunkte:

  • Numerische Vibroakustik
  • Finite- & Randelementemethode (FEM & BEM)
  • Fast Multipole Methoden und hierarchische Matrizen
  • Iterative Krylow-Unterraumverfahren

Publikationen

2022

  • Jelich, Christopher; Zhao, Wenchang; Chen, Haibo; Marburg, Steffen: Fast multipole boundary element method for the acoustic analysis of finite periodic structures. Computer Methods in Applied Mechanics and Engineering 391, 2022, 114528 mehr… BibTeX Volltext ( DOI )
  • Preuss, Simone; Gurbuz, Caglar; Jelich, Christopher; Baydoun, Suhaib Koji; Marburg, Steffen: Recent Advances in Acoustic Boundary Element Methods. Journal of Theoretical and Computational Acoustics 30 (03), 2022 mehr… BibTeX Volltext ( DOI )

2021

  • Baydoun, Suhaib Koji; Voigt, Matthias; Goderbauer, Benedikt; Jelich, Christopher; Marburg, Steffen: A subspace iteration eigensolver based on Cauchy integrals for vibroacoustic problems in unbounded domains. International Journal for Numerical Methods in Engineering, 2021 mehr… BibTeX Volltext ( DOI )
  • Jelich, C.; Baydoun, S. K.; Voigt, M.; Marburg, S.: A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence. Int. J. Numer. Methods Eng. 122 (24), 2021, 7409--7430 mehr… BibTeX Volltext ( DOI )
  • Jelich, Christopher; Karimi, Mahmoud; Kessissoglou, Nicole; Marburg, Steffen: Efficient solution of block Toeplitz systems with multiple right-hand sides arising from a periodic boundary element formulation. Engineering Analysis with Boundary Elements 130, 2021, 135-144 mehr… BibTeX Volltext ( DOI )
  • Langer, Patrick; Jelich, Christopher; Guist, Christian; Peplow, Andrew; Marburg, Steffen: Simplification of Complex Structural Dynamic Models: A Case Study Related to a Cantilever Beam and a Large Mass Attachment. Applied Sciences 11 (12), 2021, 5428 mehr… BibTeX Volltext ( DOI )

2019

  • Baydoun, Suhaib Koji; Voigt, Matthias; Jelich, Christopher; Marburg, Steffen: A greedy reduced basis scheme for multifrequency solution of structural acoustic systems. International Journal for Numerical Methods in Engineering 121 (2), 2019, 187-200 mehr… BibTeX Volltext ( DOI )
  • Baydoun, Suhaib Koji; Voigt, Matthias; Jelich, Christopher; Marburg, Steffen: A greedy reduced basis scheme for multifrequency solution of structural acoustic systems. International Journal for Numerical Methods in Engineering 121 (2), 2019, 187-200 mehr… BibTeX Volltext ( DOI )
  • Jelich, C.; Baydoun, S. K.; Marburg, S.: Anwendung des Greedy-Verfahrens zur Lösung der akustischen Helmholtzgleichung in einem breiten Frequenzbereich. Fortschritte der Akustik - DAGA: 45. Jahrestagung für Akustik, 18.-21. März, DEGA e.V., 2019 mehr… BibTeX

2018

  • C., Jelich; S., Marburg: Iterative Lösungsverfahren fÜr die Randelementemethode am Beispiel der akustischen Helmholtzgleichung. Fortschritte der Akustik - DAGA 2018 - 44. JAHRESTAGUNG FÜR AKUSTIK,19.-22. MäRZ 2018, DEGA e.V., 2018 mehr… BibTeX
  • Jelich, Christopher; Marburg, Steffen: Iterative Solution Schemes for the Acoustic Boundary Element Method. INTER-NOISE and NOISE-CON Congress and Conference Proceedings 257 (1), 2018, 146-152 mehr… BibTeX

2017

  • Langer, P.; Jelich, C.; Hoppe, A.; Schneider, A.; Guist, C.; Sepahvand, K. and S. Marburg: Finite element model for modal analysis of engine-transmission unit: numerical and experimental investigations. Proceedings of the 46th International Congress and Exposition on Noise Control Engineering, 2017HongKong mehr… BibTeX