SBIR Phase I: A Multilevel Method for Rapid Evaluation of Sound Fields

这个小企业创新研究（SBIR）第一阶段项目旨在通过开发先进的计算工具，获得周期性组合结构的声波方程的快速解。提出的新修改利用结构对称性，大大加快了快速多级多极子算法（MLFMA）。此外，提出了几个增强，以提高MLFMA的计算效率。基于FFT的插值和滤波、预处理、迭代求解器的最佳选择以及并行实现等技术将导致效率提高，从而使周期性和非周期性结构都受益。为了在保持解的精度的同时减少未知数，必须扩展到高阶形状函数。半空间公式允许水下声学中的真实的生活情况的建模。将新的MLFMA方法纳入直接和间接公式的框架中，最终将消除声学边界元程序的高频限制，并促进目前不可能的超大型声结构相互作用问题的数值模拟。最后，所提出的解决方案将使用多极方法作为一个基本框架，以统一许多新的理论，在数值声学，如源模拟技术。MLFMA消除了边界元声学中的高频限制，使超大规模的模拟成为可能。该项目的成功实施将极大地影响与计算声学相关的许多领域。例如，它可用于交通噪声和社区噪声模拟，用于声纳等隐身和监控应用，用于设计更好的音乐霍尔斯，用于汽车行业计算发动机，轮胎，消声器辐射的声音，以及优化音频设备和乐器。逆问题（识别噪声源的位置和强度从近场测量）可以解决在大约相同的时间作为直接的问题，使用MLFMA，导致更安静的轮胎设计和车窗密封。一个计算机程序，包含简单的模型创建界面，一系列准确的配方，并根据问题的大小自动选择适当的解决方案的技术将是一个宝贵的资产，声学社区与应用在汽车，国防和航空航天工业。

This Small Business Innovation Research (SBIR) Phase I project aims to obtain rapid solutions to the acoustic wave equation for periodic built-up structures through development of advanced computational tools. The proposed novel modification exploits the structural symmetry to dramatically speedup the Fast Multilevel Multipole Algorithm (MLFMA). In addition several enhancements are proposed to improve the computational efficiency of MLFMA. Techniques such as FFT based interpolation and filtering, preconditioning, optimal selection of iterative solvers, and parallel implementation will result in efficiency improvements that benefit both periodic and non-periodic structures. Extension to higher order shape functions is essential to reduce the number of unknowns while maintaining solution accuracy. Half-space formulations allow modeling of real life situations in under- water acoustics. Incorporating the new MLFMA methodologies into a framework of direct and indirect formulations will finally remove the high frequency limit of acoustic boundary element programs and facilitate numerical simulation of extremely large sound structure interaction problems that are currently not possible. Finally, the proposed solution will use multipole methods as an underlying fundamental framework to unify many new theories in numerical acoustics such as Source Simulation Technique. MLFMA eliminates the high frequency restriction in boundary element acoustics and makes extremely large-scale simulations possible. Successful execution of this project will greatly impact a number of areas related to computational acoustics. For instance, it can be used in traffic noise and community noise simulations, in stealth and monitoring applications like sonar, for designing better concert halls, in the automotive industry for computing sound radiated from engines, tires, mufflers and to optimize audio equipment and musical instruments. Inverse problems (identification of noise source location and strength from near field measurements) could be solved in about the same time as direct problems using MLFMA, leading to quieter tire designs and car window seals. A computer program that contains easy model creation interfaces, an array of accurate formulations, and automatic selection of appropriate solution techniques based on problem size will be an invaluable asset to the acoustics community with applications in Automotive, Defense And Aerospace industries.