Mathematical Methods for Nearfield Acoustical Holography

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This project seeks to find a surface source of noise in anaircraft from measurements of the acoustical pressure inside ofthe cabin. These measurements are available from experiments.The PIs will make use of integral equations of the potentialtheory for the Helmholtz equation combined with contemporarytheory of inverse problems and recent advances in numericalanalysis including rapid computations of potential type integralsand solution of linear algebraic systems of Toeplitz structure.The problem of reducing noise in (midsize) aircraft is of extremeimportance and a part of it is to find a source of the noise.This project assumes a strong interaction with aviation industry.One outcome of this work will be the delivery of a computer codeto Cessna Aircraft Company. However, the results are expected tobe of value also for car industry and for the U.S.Navy. Thegraduate students will be seriously involved into theoretical andnumerical on the project preparing for future work in industry.This GOALI project is jointly supported by the MPS Office ofMultidisciplinary Activities (OMA) and the Division ofMathematical Sciences (DMS).