Many applications in engineering and physical sciences call for simulations of acoustic scattering from penetrable objects, i.e., scatterers that internally support nonzero velocity potential and pressure field.1–111. C. Yeh, “ Scattering of acoustic waves by a penetrable prolate spheroid. I. Liquid prolate spheroid,” J. Acoust. Soc. Am. 42(2), 518–521 (1967). https://doi.org/10.1121/1.19106142. D. Brill and G. C. Gaunaurd, “ Acoustic resonance scattering by a penetrable cylinder,” J. Acoust. Soc.