Block Inverse Preconditioner for Implicit Time Integration in Finite Element Micromagnetic Solvers
Sidi Fu, Ruinan Chang, Iana Volvach, Majd Kuteifan, Marco Menarini, Vitaliy Lomakin · IEEE Transactions on Magnetics · 2019
A block-inverse preconditioner (BIP) is proposed to accelerate solving implicit time integration in the context of Newton-Krylov approach used in micromagnetic simulations for solving the Landau-Lifshitz-Gilbert equation. A coefficient matrix is generated and stored for the linear system of Newton method. BIP is formulated by subdividing the coefficient matrix into small blocks and directly inverting them. The cost of preconditioning is low since inverting and multiplying small blocks is fast, which can be further minimized by parallel computing on multicore CPUs or GPUs. The effectiveness, speed, robustness, and scalability of BIP is demonstrated by numerical simulation experiments. Comparisons to incomplete LU preconditioning methods are conducted to demonstrate the effectiveness of BIP.