The Naval Research Laboratory has been at the forefront of the technique, nearfield acoustic holography (NAH). The frequency-based NAH is well understood, and although there are not many open questions, when we consider laminar flow, numerous questions remain to be addressed for the application of this methodology [1]. The time-dependent application of NAH also contains many open research questions [2,3].

We will address these questions by extending the surface integral theory and developing numerical methodologies that optimize the calculations. The numerical methodologies should address the reconstruction of ill-posed problems where measurement noise amplifies these errors in the reconstruction. We handle the solution to the ill-posed problems using numerical regularization.

[1] N. Valdivia, “The reconstruction of surface vibrations from near-field acoustic pressure measurements under steady flow,” Inverse Problems 40 (2024).

[2] N.P.Valdivia, “Krylov Subspace iterative methods for time domain equivalent sources method based nearfield acoustical holography”, Journal of Sound and Vibration 516, (2022).

[3] N.P.Valdivia, “Krylov Subspace iterative methods for time domain boundary element method based nearfield acoustical holography”, Journal of Sound and Vibration 484, (2020).

nearfield acoustic holography, inverse problems, numerical linear algebra, surface integral equations, numerical methods

citizenship

Open to U.S. citizens and permanent residents

level

Open to Postdoctoral applicants

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