A linearized contrast source method for full-wave modeling of nonlinear acoustic wave fields in media with strong and inhomogeneous attenuation

Abstract

The iterative nonlinear contrast source (INCS) method is a numerical method originally developed for modeling transient nonlinear acoustic wave fields in homogeneous (i.e., spatially independent) lossless or lossy media. This method is based on the Westervelt equation and assumes that the nonlinear term describes a distributed contrast source in a linear background medium. Next, the equivalent nonlinear integral equation is iteratively solved by means of a Neumann scheme. In medical diagnostic ultrasound, the observed acoustic nonlinearity is weak, resulting in a weak nonlinear contrast source and a fast convergence of the scheme. To model spatially dependent attenuation, the Westervelt equation has recently been extended with an attenuative contrast source. This presentation deals with the situation of strong local attenuation. In that case, the attenuative contrast source is large and the Neumann scheme may fail to converge. By linearizing the nonlinear contrast source, the integral equation becomes linear and can be solved with more robust schemes, e.g., Bi-CGSTAB. Numerical simulations show that this approach yields convergent results for nonlinear acoustic fields in realistic media with strong local attenuation. Moreover, it is shown that in practical situations, the error due to the linearization remains sufficiently small for the first few harmonics.