Despite the potential and the increasing popularity of the boundary element method (BEM), modal analyses based on BEM are not yet put into engineering practice, mainly due to the lack of efficient solvers for the underlying nonlinear eigenvalue problem (EVP). In this article, we review a subspace iteration method based on FEAST for the solution of vibroacoustic EVPs involving the finite element method (FEM) and BEM. The subspace is obtained by applying a spectral projector and is computed by contour integration, whereas the contour is also used to subsequently solve the projected EVP by rational approximation. The computation of the projection matrices is addressed by two approaches. In the case of heavy fluid loading, we solve the underlying coupled linear systems by an iterative block Krylov method. In the case of light fluid loading, we exploit the fact that the coupled system admits accurate model order reduction solely based on the structural subsystem. Applications to a spherical shell and to a musical bell indicate that only a few contour points are required for an accurate solution without inducing spurious eigenvalues. The results are compared with those of a contour integral method and illustrate the efficiency of the proposed eigensolver.

中文翻译：

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基于柯西积分的无界域振动声学问题的子空间迭代特征求解器

尽管边界元法 (BEM) 具有潜力且日益流行，但基于 BEM 的模态分析尚未投入工程实践，这主要是由于缺乏针对潜在非线性特征值问题 (EVP) 的有效求解器。在本文中，我们回顾了一种基于 FEAST 的子空间迭代方法，用于求解涉及有限元法 (FEM) 和 BEM 的振动声 EVP。子空间是通过应用光谱投影仪获得的，并通过轮廓积分计算，而轮廓也用于随后通过有理近似求解投影的 EVP。投影矩阵的计算由两种方法解决。在重流体载荷的情况下，我们通过迭代块 Krylov 方法求解基础耦合线性系统。在轻载流体的情况下，我们利用耦合系统承认仅基于结构子系统的精确模型阶数减少这一事实。球壳和音乐铃的应用表明，在不引入虚假特征值的情况下，精确解只需要几个轮廓点。结果与轮廓积分方法的结果进行了比较，并说明了所提出的特征求解器的效率。