Integral formulas for supersonic reconstruction of the acoustic field

References

• Williams EG. Supersonic acoustic intensity. J Acoust Soc Am. 1995 Jan;97(1):121–127.
   Web of Science ®Google Scholar
• Williams EG. Supersonic acoustic intensity on planar sources. J Acoust Soc Am. 1998 Nov;104(5):2845–2850.
   Web of Science ®Google Scholar
• Williams EG, Houston BH, Herdic PC, et al. Interior NAH in flight. J Acoust Soc Am. 2000;108:1451–1463.
   PubMed Web of Science ®Google Scholar
• Magalhâes M, Tenenbaum R. Supersonic acoustic intensity for arbitrarily shaped sources. Acta Acust. 2006;92:189–201.
   Web of Science ®Google Scholar
• Tenenbaum R, Magalhâes M. A new technique to identify arbitrarily shaped noise sources. Shock Vib. 2006;13:219–232.
   Web of Science ®Google Scholar
• Correa C, Tenenbaum R. Useful intensity: a technique to identify radiating regions on arbitrarily shaped surfaces. J Sound Vib. 2013;332:1567–1584.
   Web of Science ®Google Scholar
• Marburg S, L\"{o}sche E, Peters H, et al. Surface contributions to radiated sound power. J Acoust Soc Am. 2013 Jun;133(6):3700–3705.
   PubMed Web of Science ®Google Scholar
• Williams EG. Convolution formulations for non-negative intensity. J Acoust Soc Am. 2013;134(2):1055–1066.
   PubMed Web of Science ®Google Scholar
• Valdivia NP, Williams EG, Herdic PC. Equivalent sources method for supersonic intensity of arbitrarily shaped geometries. J Sound Vib. 2015;347:46–62.
   Web of Science ®Google Scholar
• Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 3rd ed. Vol. 93, Applied mathematical sciences. Berlin: Springer; 2013.
   Google Scholar
• DeLillo TK, Isakov V, Valdivia N, et al. The detection of the source of acoustical noise in two dimensions. SIAM J Appl Math. 2001;61(6):2104–2121.
   Web of Science ®Google Scholar
• DeLillo TK, Isakov V, Valdivia N, et al. The detection of surface vibrations from interior acoustical pressure. Inverse Prob. 2003;19(3):507–524.
   Web of Science ®Google Scholar
• Valdivia N. Uniqueness in inverse obstacle scattering with conductive boundary conditions. Appl Anal. 2004 Aug;83(8):825–851.
   Google Scholar
• Williams EG. Fourier acoustics: sound radiation and nearfield acoustical holography. London: Academic Press; 1999.
   Google Scholar
• Fahy F, Gardonio P. Sound and structural vibration: radiation, transmission and response. London: Elsevier/Academic; 2007.
   Google Scholar
• Isakov V, Wu SF. On theory and application of the helmholtz equation least squares method in inverse acoustics. Inverse Prob. 2002;18:1147–1159.
   Web of Science ®Google Scholar
• Williams EG, Maynard JD. Holographic imaging without the wavelength resolution limit. Phys Rev Lett. 1980;45:554–557.
   Web of Science ®Google Scholar
• Devaney AJ. Mathematical foundations of imaging, tomography and wavefield inversion.\pagination{\break} New York (NY): Cambridge University Press; 2012.
   Google Scholar
• Colton D, Kress R. Integral equation methods in scattering theory. New York (NY): Wiley-Interscience; 1983.
   Google Scholar
• McLean W. Strongly elliptic systems and boundary integral equations. New York (NY): Cambridge University Press; 2000.
   Google Scholar
• Stratton JA. Electromagnetic theory. IEEE Press Series on Electromagnetic Wave Theory.\pagination{\break} New Jersey (NJ): Wiley; 1941.
   Google Scholar
• Arfken G. Mathematical methods for physicists. 2nd ed. New York (NY): Academic Press; 1970.
   Google Scholar
• Valdivia N, Williams EG. Implicit methods of solution to integral formulations in boundary element methods based near-field acoustic holography. J Acoust Soc Am. 2004 Sep;116(3):1559–1572.
   Web of Science ®Google Scholar
• Valdivia N, Williams EG. Krylov subspace iterative methods for boundary element method based near-field acoustic holography. J Acoust Soc Am. 2005 Feb;117(2):711–724.
   PubMed Web of Science ®Google Scholar
• Valdivia NP. Numerical methods for near-field acoustic holography over arbitrarily shaped surfaces. In: Monroy FA, editor. Holography: different field of application. Rijeka, Croatia: InTech; 2011. p. 122–148.
   Google Scholar
• Fernandez-Grande E, Jacobsen F. Conservation of power of the supersonic acoustic intensity. J Acoust Soc Am. 2014;136(2):461–465.
   PubMed Web of Science ®Google Scholar
• Li J, Liu H, Shang Z. Twoscatterers methods for locating multiple electromagnetic scatterers. SIAM J Appl Math. 2013;73(4):1721–1746.
   Web of Science ®Google Scholar
• Li J, Liu H, Zou J. Locating multiple multiscale acoustic scatterers. Multiscale Model Simul. 2014;12(3):927–952.
   Web of Science ®Google Scholar