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
