Sparsifying Preconditioner for the Lippmann-Schwinger Equation
For researchers solving acoustic, electromagnetic, or quantum scattering problems, this preconditioner offers an efficient and easy-to-implement method to accelerate iterative solvers.
The paper presents a sparsifying preconditioner for the Lippmann-Schwinger equation that transforms the discretized equation into sparse form, enabling efficient iterative solution with almost frequency-independent iteration counts, as demonstrated in 2D and 3D numerical results.
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.