  The Lippmann-Schwinger equation is an integral equation formulation for
acoustic and electromagnetic scattering from an inhomogeneous media and quantum
scattering from a localized potential. We present the sparsifying
preconditioner for accelerating the iterative solution of the
Lippmann-Schwinger equation. This new preconditioner transforms the discretized
Lippmann-Schwinger equation into sparse form and leverages the efficient sparse
linear algebra algorithms for computing an approximate inverse. This
preconditioner is efficient and easy to implement. When combined with standard
iterative methods, it results in almost frequency-independent iteration counts.
We provide 2D and 3D numerical results to demonstrate the effectiveness of this
new preconditioner.
