Comments on "The boundary point method for the calculation of exterior acoustic radiation problem" S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761-772

Abstract

Zhang and Chen [The boundary point method for the calculation of exterior acoustic radiation problem, Journal of Sound and Vibration 228 (1999) 761–772] proposed a boundary point method (BPM) for exterior acoustic problems. The idea is similar to the CHUNKY CHIEF by Wu [A weighted residual formulation for the CHIEF method in acoustic, Journal of Acoustical Society of America 90 (1991) 1608–1614], but Chunky CHIEF provides constraints using null-field equations while the BPM used the CHUNKY BLOCK singularity outside the domain. The mathematical structure is similar to Trefftz method and method of fundamental solutions [J.T. Chen et al., On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations, Computers & Mathematics with Applications 53 (2007) 851–879], since the interpolation function satisfies the governing equation. Later, Wu commented twice [Sean F. Wu, Comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772), Journal of Sound and Vibration, 298 (2006) 1173]; Sean F. Wu, Comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”, Journal of Sound and Vibration, 298 (2006) 1176–1177] that the formulation of BPM is wrong and the authors replied also twice [X.Z. Chen, C.X. Bi, Reply to the comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772), Journal of Sound and Vibration, 298 (2006) 1174–1175; [X.Z. Chen, C.X. Bi, Reply to the comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”, Journal of Sound and Vibration, 298 (2006) 1178–1179] to defend themselves. Here, we would like to say a few words for the discussions in two aspects. One is the formulation, and the other is the occurrence of fictitious frequencies.