通过边界元法求解稳态Liouville方程
Solving the stationary Liouville equation via a boundary element method
AI总结：
针对复杂多组件结构的高频振动声学问题，提出一种基于边界元法的稳态Liouville方程求解方法，该方法是动态能量分析技术的改进版，在统计能量分析和全射线追踪之间插值，能高效处理大规模问题并提供良好的能量分布近似。
摘要：
线性波场的强度分布在高频极限下通常用相空间中的流动或输运方程来近似。求解时间相关和稳态问题的流动方程的常用技术是射线追踪或水平集方法。在预测复杂工程结构的振动声学响应中，简化的射线追踪方法如统计能量分析或其变体已得到广泛应用。直接从稳态Liouville方程出发，我们开发了一种边界元法来求解复杂多组件结构的输运方程。该方法是作者最近引入的动态能量分析技术的改进版本，在标准统计能量分析和全射线追踪之间插值，包含这两种方法作为极限情况。我们证明，该方法可以有效地处理复杂的大规模问题，与底层波动方程的精确解相比，能给出能量分布的良好近似。
英文摘要：
Intensity distributions of linear wave fields are, in the high frequency limit, often approximated in terms of flow or transport equations in phase space. Common techniques for solving the flow equations for both time dependent and stationary problems are ray tracing or level set methods. In the context of predicting the vibro-acoustic response of complex engineering structures, reduced ray tracing methods such as Statistical Energy Analysis or variants thereof have found widespread applications. Starting directly from the stationary Liouville equation, we develop a boundary element method for solving the transport equations for complex multi-component structures. The method, which is an improved version of the Dynamical Energy Analysis technique introduced recently by the authors, interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. We demonstrate that the method can be used to efficiently deal with complex large scale problems giving good approximations of the energy distribution when compared to exact solutions of the underlying wave equation.
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