Coupled Finite And Boundary Element Methods for Fluid-Solid Interaction Eigenvalue Problems

Summary For thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid–structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE–BE) method is developed for the numerical eigenanalysis of the fluid–structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton–Miller formulation is applied to tackle the fictitious eigenfrequency problem of the BEM, and the optimal choice of its coupling parameter is investigated for the coupled FE–BE method. Numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed FE–BE method. Copyright © 2016 John Wiley & Sons, Ltd.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

See 1 more Smart Citation

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

Zheng

Zhang

et al. 2016

“…Peters et al have proposed a frequency approximation of the boundary element impedance matrix 15,16 to overcome this issue, and more recently, the nonlinear structural acoustic eigenvalue problem has been solved using contour integration. 17,18 Despite the abovementioned advances in numerical modal analysis, a frequencywise response analysis is still the most popular procedure for the calculation of vibro-acoustic responses in a frequency range. Moreover, implementations of eigenvalue solvers such as the contour integral method nevertheless require system evaluations at a considerable number of discrete frequency points.…”

Section: Introductionmentioning

confidence: 99%

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

Baydoun

Voigt

Jelich

et al. 2019

Summary The solution of frequency dependent linear systems arising from the discretization of vibro‐acoustic problems requires a significant computational effort in the case of rapidly varying responses. In this paper, we review the use of a greedy reduced basis scheme for the efficient solution in a frequency range. The reduced basis is spanned by responses of the system at certain frequencies that are chosen iteratively based on the response that is currently worst approximated in each step. The approximations at intermediate frequencies as well as the a posteriori estimations of associated errors are computed using a least squares solver. The proposed scheme is applied to the solution of an interior acoustic problem with boundary element method (BEM) and to the solution of coupled structural acoustic problems with finite element method and BEM. The computational times are compared to those of a conventional frequencywise strategy. The results illustrate the efficiency of the method.

“…RSRR can be easily implemented and parallelized. The advantages of the RIA and the performance of RSRR are demonstrated by a variety of benchmark and practical problems.Prepared using nmeauth.cls [Version: 2010/05/13 v3.00] 2 J. XIAO, ET AL independently or in coupled manners [5,6], and NEPs of them reflect the main bottlenecks in the current development of numerical methods for NEPs. However, the methods developed in this paper are rather general and by no means limited to the NEPs in the FEM and BEM.Generally speaking, although there exist a number of numerical methods for NEPs in literature, most of them are restricted by matrix structures, properties of eigenvalues, computational costs, etc.…”

mentioning

confidence: 99%

Solving large‐scale nonlinear eigenvalue problems by rational interpolation and resolvent sampling based Rayleigh–Ritz method

Xiao

Zhang

Huang

et al. 2016

Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of most existing methods is limited by the matrix structures, properties of the eigen-solutions, sizes of the problems, etc. This paper aims to remove those limitations and develop robust and universal NEP solvers for large-scale engineering applications. The novelty lies in two aspects. First, a rational interpolation approach (RIA) is proposed based on the Keldysh theorem for holomorphic matrix functions. Comparing with the existing contour integral approach, the RIA provides the possibility to select sampling points in more general regions and has advantages in improving the accuracy and reducing the computational cost. Second, a resolvent sampling scheme using the RIA is proposed to construct reliable search spaces for the Rayleigh-Ritz procedure, based on which a robust eigen-solver, called resolvent sampling based Rayleigh-Ritz method (RSRR), is developed for solving general NEPs. The RSRR can be easily implemented and parallelized. The advantages of the RIA and the performance of the RSRR are demonstrated by a variety of benchmark and application examples.Generally speaking, although there exist a number of numerical methods for NEPs in literature, most of them are restricted by the matrix structures, properties of eigenvalues, computational costs, etc. Accurate and efficient methods that can robustly and reliably calculate all the eigenpairs within a given region, and at the same time, can be applied to large-scale computations are still lacking [3,4,[7][8][9][10][11].In recent years, the contour integral approach (CIA) based on contour integrals of the probed resolvent T .´/ 1 U has attracted great attention [12][13][14][15][16][17][18][19], where the constant matrix U 2 C n L consists of L random column vectors used to probe T .´/ 1 . The CIA is first developed for solving generalized eigenvalue problems [12,13], and later, extended to NEPs in [20] and [15] based on the Smith form and Keldysh's theorem for analytic matrix-valued functions, respectively. Because [20] and [15] result in similar algorithms, we consider the block Sakurai-Sugiura (SS) algorithm in [20]. This algorithm transforms the original NEP into a small-sized generalized eigenvalue problem involving block Hankel matrices by using the monomial moments of the probed resolvent T .´/ 1 U on a given contour. It becomes unstable and inaccurate when higher order contour moments of T .´/ 1 U are used.To circumvent this problem, the SS method with the Rayleigh-Ritz projection (SSRR) has been recently proposed [16]. The eigenspace of the SSRR is constructed from a matrix M 2 C n K L collecting all the monomial moments of T .´/ 1 U up to a given order K. We refer to this as the resolvent moment scheme (or simply moment scheme) for generating eigenspaces. Numerical results in [16] show that the SSRR has a much better stability and accuracy than the SS algorithm when a small value of L is used. Besides, the...