Fast Alternating BiDirectional Preconditioner for the 2D High-Frequency Lippmann--Schwinger Equation

This paper presents a fast iterative solver for the Lippmann--Schwinger equation for high-frequency waves scattered by a smooth medium with a compactly supported inhomogeneity. The solver is based on the sparsifying preconditioner [L. Ying, Multiscale Model. Simul., 13 (2015), pp. 644--660] and a domain decomposition approach similar to the method of polarized traces [L. Zepeda-Nún͂ez and L. Demanet, J. Comput. Phys., 308 (2016), pp. 347--388.]...