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

这个小型企业创新研究(SBIR)第一阶段项目旨在通过开发先进的计算工具来快速求解周期性组合结构的声波方程。该算法利用结构的对称性，大大提高了快速多层多极子算法(MLFMA)的计算速度。此外，为了提高MLFMA的计算效率，本文还提出了几点改进措施。诸如基于FFT的内插和滤波、预处理、迭代求解器的最佳选择和并行实现等技术将导致效率的提高，从而使周期和非周期结构都受益。推广到高阶形函数对于减少未知数的数量，同时保持解的准确性是必不可少的。半空间公式允许对水下声学中的真实生活情况进行建模。将新的MLFMA方法融入到直接和间接公式的框架中，将最终消除声学边界元程序的高频限制，并促进目前不可能实现的超大型声结构相互作用问题的数值模拟。最后，提出的解决方案将使用多极子方法作为基本框架，统一数值声学中的许多新理论，如源模拟技术。MLFMA消除了边界元声学对高频的限制，使超大规模数值模拟成为可能。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，它可以用于交通噪声和社区噪声模拟，用于声纳等隐形和监控应用，用于设计更好的音乐厅，用于汽车行业用于计算发动机、轮胎、消声器的辐射声音，以及优化音频设备和乐器。逆问题(通过近场测量识别噪声源位置和强度)可以与使用MLFMA的直接问题几乎同时解决，从而使轮胎设计和车窗密封更加安静。计算机程序包含简单的模型创建界面、一系列准确的公式以及根据问题大小自动选择合适的解决方案技术，这将是声学社区在汽车、国防和航空航天行业应用的无价之宝。

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.