Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.
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DOI：
10.1098/rsos.140520
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发表时间：
2015-01
影响因子：
3.5
通讯作者：
Chan DY
中科院分区：
文献类型：
--
作者：
Sun Q;Klaseboer E;Khoo BC;Chan DY
开发了亥姆霍兹方程解的边界积分公式，其中边界积分中的所有传统奇异行为都被解析地消除了。通过计算声波问题中辐射体产生的压力场说明了该方法的数值精度。该方法有利于使用更高阶的表面元素来表示边界，从而显着减小问题规模并提高精度。具有极端几何纵横比的问题也可以在不降低精度的情况下得到解决。与CHIEF方法结合时，无需求解超奇异积分即可保证外部声学问题解的唯一性。
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.