解决二维海尔姆霍尔茨方程的双边界元素方法,用于缓和波方程的二维海尔姆霍尔茨方程
Kue-Hong Chen1, Yi-Kui Liu1, Jeng-Tzong Chen2
1Department of Civil Engineering, National Ilan University, Ilan 26047, Taiwan.
The Journal of the Acoustical Society of America
|September 23, 2025
概括
本研究引入了一个双边界积分公式,用于2D尔姆霍尔茨方程与缓冲. 该方法有效地处理复杂的波数和不规则的几何形状,改进了共振分析.
科学领域:
- 计算数学 计算数学 计算数学
- 声学和波浪的传播.
- 数字分析 数字分析
背景情况:
- 赫尔姆霍尔茨方程模型波浪现象,通常涉及由于阻尼而复杂的波浪数.
- 单数和超单数积分在边界积分公式中带来了挑战.
- 了解阻尼系统中的共振现象对于各种应用至关重要.
研究的目的:
- 用复杂波数推导二维海尔姆霍尔茨方程的双边界积分公式.
- 开发一种规范化技术,用于处理单数和超单数积分.
- 为了研究阻尼对共振现象的影响,并验证配方的准确性和适用性.
主要方法:
- 用复杂波数计算赫尔姆霍尔茨方程的双边界积分公式的导数.
- 将加法定理应用于将内核函数扩展到实变量数列中的应用.
- 单数和超单数积分的规则化成正则积分的总结.
- 使用高斯方程计算正则积分的计算.
- 使用基准案例与精确解决方案的验证和不规则几何形状的分析.
主要成果:
- 介绍了一种新的双边界积分公式,用于缓和的赫尔姆霍尔茨方程.
- 单点和超单点积分通过序列扩展和正则化技术成功地转化为正则积分.
- 研究了声对内部和外部赫尔姆霍尔茨问题的固有值和共振的影响.
- 拟议的方法显示了对基准案例和复杂几何学的良好趋同和准确性.
结论:
- 开发的双边界积分公式有效地解决了海尔姆霍尔茨方程中复杂波数和单一积分所带来的挑战.
- 该方法提供了一种强大的方法来分析沉声系统中的共振现象,即使有不规则的边界.
- 该配方显示了在声学,电磁学和其他涉及波浪传播与减噪的领域的应用的巨大潜力.
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