Application of Lippmann-Schwinger Scattering Series with an Adaptive Preconditioner

We present a numerical study of high frequency acoustic wave scattering from two types of rigid scatterers, a circular disk and a red blood cell (RBC) shaped (biconcave) obstacle. Using an iterative frequency domain solver, we compute the steady state pressure and energy density distribution. The sound speed varies inside the source 1350 m/s and 1650 m/s with ambient medium 1500 m/s. Simulations are performed at frequencies up to 366 MHz. Results are sampled along the center line through the source center for direct comparison. Both solver produce nearly identical pressure amplitude profile, with a pronounced central pressure maximum and decaying oscillations toward the edges. As frequency increases, the number of concentric interference rings around the source grows, and the central lobe narrows (for RBC). The number of iterations required for convergence rise sharply with frequency. The simulations capture the expected wave phenomena and demonstrate that the Convergent Born series (CBS) solver remains reliable and robustness for strong scattering contrasts in presence of spatially adaptive preconditioner.