In this paper, an isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed for the time-domain acoustic wave problem in 3D infinite domain. The fundamental solution of the potential problem is used to establish the boundary-domain integral equation, which avoids the problem of solving the coefficient matrix repeatedly at different times. On the one hand, in order to maintain the dimensionality reduction advantages of the boundary element method, the classical dual reciprocity method is used to transform the domain integral into a boundary integral. On the other hand, for purpose of satisfying the boundary conditions at infinite distance accurately, a reliable integral convergence criterion is established by adopting the approximate variation coefficient. Furthermore, the effects of different approximation functions, variation coefficients, time steps, number of interior points and elements on the results are discussed in detail by several typical examples. Numerical results show that the proposed method has high accuracy and good stability even when analyzing geometrically complex dolphin models.

中文翻译：

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用于解决时域声波问题的等几何双互易边界元法

本文针对三维无限域中的时域声波问题，提出了一种等几何双互易边界元法（IG-DRBEM）。利用潜在问题的根本解来建立边界域积分方程，避免了不同时刻重复求解系数矩阵的问题。一方面，为了保持边界元法的降维优势，采用经典的对偶互易法将域积分转化为边界积分。另一方面，为了准确满足无限远边界条件，采用近似变异系数建立了可靠的积分收敛判据。此外，还通过几个典型例子详细讨论了不同的逼近函数、变异系数、时间步长、内点数和单元对结果的影响。数值结果表明，即使在分析几何复杂的海豚模型时，该方法也具有较高的精度和良好的稳定性。