The paper introduces the sweeping preconditioner, which is highly efficient
for iterative solutions of the variable coefficient Helmholtz equation
including very high frequency problems. The first central idea of this novel
approach is to construct an approximate factorization of the discretized
Helmholtz equation by sweeping the domain layer by layer, starting from an
absorbing layer or boundary condition. Given this specific order of
factorization, the second central idea of this approach is to represent the
intermediate matrices in the hierarchical matrix framework.