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

被引:2
作者
Jiang, Bin [1 ]
Yu, Jian [2 ]
Li, Wei [1 ,3 ,4 ]
Chai, Yingbin [1 ]
Gui, Qiang [1 ]
机构
[1] Huazhong Univ Sci & Technol, Sch Naval Architecture & Ocean Engn, Wuhan 430074, Peoples R China
[2] Wuhan Second Ship Design & Res Inst, Wuhan 430205, Peoples R China
[3] Collaborat Innovat Ctr Adv Ship & Deep Sea Explora, Shanghai 200240, Peoples R China
[4] Huazhong Univ Sci & Technol, Hubei Key Lab Naval Architecture & Ocean Engn Hydr, Wuhan 430074, Peoples R China
基金
中国国家自然科学基金;
关键词
overlapping finite element method; underwater acoustic scattering; Helmholtz equation; modified Dirichlet-to-Neumann boundary condition; POINT INTERPOLATION METHOD; HIGH WAVE-NUMBER; HELMHOLTZ-EQUATION; P-VERSION; PROPAGATION; PARTITION; PARADIGM;
D O I
10.3390/jmse11091676
中图分类号
U6 [水路运输]; P75 [海洋工程];
学科分类号
0814 ; 081505 ; 0824 ; 082401 ;
摘要
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.
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页数:22
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