A Coupled Overlapping Finite Element Method for Analyzing Underwater Acoustic Scattering Problems

Abstract

It is found that the classic finite element method (FEM) requires much time for adequate meshes to acquire satisfactory numerical solutions, and is restricted to acoustic problems with low and middle frequencies. In this work, a coupled overlapping finite element method (OFEM) is employed by combining the overlapping finite element and the modified Dirichlet-to-Neumann (mDtN) boundary condition to solve underwater acoustic scattering problems. The main difference between the OFEM and the FEM lies in the construction of the local field approximation. In the OFEM, virtual nodes are utilized to form the partition of unity functions while no degree of freedom is assigned to these virtual nodes, which suppresses the linear dependence issue in other generalized finite element methods. Moreover, the user-defined enrichment functions can be flexibly utilized in the local field, and thus the numerical dispersions can be significantly mitigated. To truncate the infinite problem domain and satisfy the Sommerfeld radiation condition, an artificial boundary is constructed by incorporating the mDtN technique. Several numerical examples are studied and it is shown that the proposed method can greatly diminish the numerical error and is insensitive to distorted meshes, indicating that the proposed method is promising in predicting underwater acoustic scattering.

Review of Underwater Anechoic Coating Technology Under Hydrostatic Pressure

“…In the theoretical study of underwater acoustic cladding, numerous methods to calculate its acoustic performance are available, each demonstrating its own characteristics and applicable acoustic structure types. These methods mainly include the transfer matrix method (TMM) (Chahr-Eddine and Yassine, 2014; Lee et al, 2021b), multiple scattering method (MSM) (Li et al, 2006), plane-wave expansion (PWE) (Ponge et al, 2017), finite-difference time-domain (FDTD) (Grinenko et al, 2012;Tsukui et al, 2022), concentrated mass method (CMM) (Bambill et al, 2004), finite element method (FEM) (Hammad et al, 2021;Jiang et al, 2023), and Jacobi -Ritz method (Li et al, 2019b;Pang et al, 2023). The advantages and weaknesses of various typical calculation methods for readers to consider are summarized in Table 1.…”