Numerical schemes for the Iterative Nonlinear Contrast Source method

Nonlinear acoustics is gaining importance for medical acoustical imaging and high intensity focused ultrasound. With the latter one, high-amplitude acoustic wave fields are used to damage or kill cancer cells. For accurate treatment planning, a full-wave method which can model the propagation and scattering of the nonlinear field in attenuative, heterogeneous media is required. The Iterative Nonlinear Contrast Source (INCS) method is a full-wave method originally developed for homogeneous medium. It recasts the Westervelt equation into an integral equation which can be solved using a Neumann scheme. For heterogeneous media, the same approach results in additional contrast source terms. When these additional contrast sources become strong, convergence of the Neumann scheme may become an issue. To overcome this problem, the Westervelt equation may be linearized and the resulting linear integral equation may be solved with more advanced schemes such as Bi-CGSTAB. Restart strategies may be applied to eliminate systematic errors in the higher harmonics caused by the linearization. However, for realistic wave speed contrasts convergence remains problematic. To overcome these limitations, schemes such as steepest descent may be applied on the original nonlinear integral equation. In the present talk, the different schemes and their pros and cons will be discussed.