scholarly journals Wavenumber-explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers

2022 ◽  
Vol 20 (1) ◽  
pp. 1-52
Author(s):  
Théophile Chaumont-Frelet ◽  
Dietmar Gallistl ◽  
Serge Nicaise ◽  
Jérôme Tomezyk
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Convergence Analysis ◽  
Harmonic Wave ◽  
Perfectly Matched Layers ◽  
Time Harmonic ◽  
Finite Element Discretizations ◽  
Matched Layers ◽  
Element Discretizations

scholarly journals Wavenumber explicit convergence analysis for finite element discretizations of general wave propagation problems

2019 ◽  
Vol 40 (2) ◽  
pp. 1503-1543 ◽  
Author(s):  
T Chaumont-Frelet ◽  
S Nicaise
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Helmholtz Equation ◽  
Error Estimates ◽  
Heterogeneous Media ◽  
Harmonic Wave ◽  
Stability Conditions ◽  
Full Generality ◽  
Finite Element Discretizations ◽  
Element Discretizations

Abstract We analyse the convergence of finite element discretizations of time-harmonic wave propagation problems. We propose a general methodology to derive stability conditions and error estimates that are explicit with respect to the wavenumber $k$. This methodology is formally based on an expansion of the solution in powers of $k$, which permits to split the solution into a regular, but oscillating part, and another component that is rough, but behaves nicely when the wavenumber increases. The method is developed in its full generality and is illustrated by three particular cases: the elastodynamic system, the convected Helmholtz equation and the acoustic Helmholtz equation in homogeneous and heterogeneous media. Numerical experiments are provided, which confirm that the stability conditions and error estimates are sharp.

scholarly journals A Benchmark Study on Eigenfrequencies of Fluid-Loaded Structures

2020 ◽  
Vol 28 (02) ◽  
pp. 2050013
Author(s):  
Felix Kronowetter ◽  
Suhaib Koji Baydoun ◽  
Martin Eser ◽  
Lennart Moheit ◽  
Steffen Marburg
Keyword(s):  
Krylov Subspaces ◽  
Perfectly Matched Layers ◽  
Quadratic Eigenvalue Problem ◽  
Benchmark Study ◽  
Finite Element Discretizations ◽  
Infinite Element Method ◽  
Ritz Procedure ◽  
Quadratic Eigenvalue ◽  
Matched Layers ◽  
Element Discretizations

In this paper, a coupled finite/infinite element method is applied for computing eigenfrequencies of structures in exterior acoustic domains. The underlying quadratic eigenvalue problem is addressed by a contour integral method based on resolvent moments. The numerical framework is applied to an academic example of a hollow sphere submerged in water. Comparisons of the computed eigenfrequencies to those obtained by boundary element discretizations as well as finite element discretizations in conjunction with perfectly matched layers verify the proposed numerical framework. Furthermore, extensive parameter studies are carried out illustrating the performance of the method with regard to both projection and discretization parameters. Finally, we point out that the proposed method achieves significantly smaller residuals of the computed eigenpairs than the Rayleigh Ritz procedure with second-order Krylov subspaces.

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