Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at high frequencies due to the increase in mesh size with a fixed number of elements per wavelength and ill-conditioning of the linear system due to high material contrasts. This study presents the design of boundary element methods feasible for nonconforming surface meshes at the material interface. The nonconforming algorithm allows for independent grid generation, which improves flexibility and reduces the degrees of freedom. It works for different boundary integral formulations for Helmholtz transmission problems, operator preconditioning, and coupling with finite element solvers. The extensive numerical benchmarks at canonical configurations and an acoustic foam model confirm the significant improvements in computational efficiency when employing the nonconforming grid coupling in the boundary element method.
翻译:声波通过嵌入无界介质的同质材料传播的声波波可形成一个边界整体方程式,并用边界元件方法准确解决。计算效率在高频率下下降,原因是网状尺寸增加,每波长有固定数量,线性系统因材料差异很大而调节不良。本研究提出了在材料界面上不对齐表面模件可行的边界元件方法的设计。不兼容算法允许独立电网生成,从而提高灵活性并降低自由度。它适用于赫尔默尔茨传输问题的不同边界整体配方、操作者设定先决条件和与有限元素解脱器的组合。罐形配置的广泛数字基准和声波泡沫模型证实了在使用边界元件方法不对齐电网连接时计算效率的显著提高。