Two efficient block preconditioners for the mass-conserved Ohta-Kawasaki equation

Abstract

In this paper, we propose two efficient block preconditioners to solve the mass-conserved Ohta-Kawasaki equation with finite element dis-cretization. We also study the spectral distribution of these two pre-conditioners, i.e., Schur complement preconditioner and the modified Hermitian and skew-Hermitian splitting (MHSS in short) preconditioner. Besides, the Newton method and its variant are used to address the implicitly nonlinear term. We rigorously analyze the convergence of the Newton iteration methods. Finally, we offer numerical examples to support the theoretical analysis and indicate the efficiency of the proposed preconditioners for the mass-conserved Ohta-Kawasaki equation.