Stability analysis of inverse time domain boundary element method for near-field acoustic holography.

Abstract

Stability of the inverse time domain boundary element method (ITBEM) for near-field acoustic holography is investigated. An eigenvalue system is built by reformulating the ITBEM to an iterative format. Through the analysis of the eigenvalue system, a stabilization criterion is derived. Then the stabilization criterion is utilized to reveal the stabilization mechanism of the TSVD method which plays an important role in the ITBEM. Furthermore, a method for properly choosing the ratio of truncated singular values to ensure the stability is provided. Although stability can be managed by using the TSVD method, the accuracy of the results cannot always be guaranteed. To overwhelm this difficulty, an averaging technique is further introduced, and its stabilization mechanism is investigated by incorporating it into the ITBEM formulations. Numerical simulations are carried out to validate the stabilization criterion, and the stabilization mechanisms of TSVD and averaging are shown specifically with extensive eigenvalue analyses.