Numerische Simulation von Akustik-Akustik- und Strukturmechanik-Akustik-Kopplungen auf nichtkonformen Gittern
Project description
The project is aimed at investigation and implementation of new numerical methods for efficient solution of the acoustic- and mechanical-acoustic coupled models on nonconforming grids.Current results
Construction and implementation of efficient numerical methods for multiphysics problems require special attention being paid to the nonmatching interfaces between different space-scales regions. In the current project, that is done with a newly implemented Schwarz type domain decomposition method for nonlinear problems. Such methods typically lead to schemes where an outer iteration for the subproblem correction and an inner subspace iteration on each subproblem have to be applied. The proposed method constitutes, by means of a Gauß-Seidel type outer iteration, a multiplicative variant of the straightforward additive scheme. The implemented method was applied to the nonlinear elasto-acoustic problem, yielding two numerical schemes using different solvers for the subproblems, a Newton-like and a fixed point iteration scheme. The essential algorithmic difference is that the Newton method is used for the resolution of the nonlinear elastic subproblem, while a fixed point iteration is employed for the nonlinear acoustic part. We present a test series with varying damping parameter "w" below. Due to symmetry reasons, the computational domain is set to one half of the original one (Figure 1).Figure 1. (left) Computational grid: lower small part = structure, upper part = acoustic, (right) use of nonmatching grids. |
Figure 2. Test of the additive Richardson scheme: average convergence rate versus damping parameter (left) for the nonlinear elastic/linear acoustic system and (right) for the linear elastic/nonlinear acoustic system. |
Figure 3. Test of the multiplicative scheme: average convergence rate versus damping parameter (left) for the nonlinear elastic/linear acoustic system and (right) for the linear elastic/nonlinear acoustic system. |
Figure 4. Computational domain with 4 layers overlap. The thicker horizontal line inside the acoustic domain indicates the upper boundary of the overlapping region. |
Figure 5. Test of overlapping scheme: iteration count versus time step, varying the overlap (left) for the nonlinear elastic/linear acoustic system and (right) for the linear elastic/nonlinear acoustic system. |
Publications
Author(s) | Title | Appeared In | Year | Type | Download |
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Roland Ernst, Bernd Flemisch, Barbara Wohlmuth | A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction | M2AN Math. Model. Numer. Anal. 43, 487--506 | 2009 | Article in Journal |
Abstract
Link ^{} Bibtex |
Bernd Flemisch, Michael Mair, Barbara Wohlmuth | Nonconforming discretization techniques for overlapping domain decompositions | M. Feistauer et. al (eds.), Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2003, Springer, 2004, pp. 316-325 | 2004 | Article in Conference Proceedings |
Abstract
Link ^{} Bibtex |
Maksymilian Dryia, Andreas Gantner, Olof Widlund, Barbara Wohlmuth | Multilevel Additive Schwarz Preconditioner For Nonconforming Mortar Finite Element Methods | Journal of Numerical Mathematics Vol. 12, 23-38 | 2004 | Article in Journal |
Abstract
Link ^{} Bibtex |