Localized Sparsifying Preconditioner for Periodic Indefinite Systems
For researchers solving pseudospectral approximations of periodic indefinite systems, this work offers a more efficient preconditioner that reduces computational cost.
This paper improves the sparsifying preconditioner for periodic indefinite systems by incorporating local potential information and an FFT-based method for local stencil computation, achieving iteration counts that grow only mildly with problem size, making pseudospectral approximations nearly as efficient as sparse systems.
This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the recently proposed sparsifying preconditioner with two major modifications. First, the local potential information is utilized to improve the accuracy of the preconditioner. Second, an FFT based method to compute the local stencil is proposed to reduce the setup time of the algorithm. Numerical results show that the iteration number of this improved method grows only mildly as the problem size grows, which implies that solving pseudospectral approximation systems is computationally as efficient as solving sparse systems, up to a mildly growing factor.