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Two Efficient Block Preconditioners for the Mass-Conserved Ohta-Kawasaki Equation

Two Efficient Block Preconditioners for the Mass-Conserved Ohta-Kawasaki Equation

Year:    2025

Author:    Juan Zhang, Shifeng Li, Kai Jiang

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 454–488

Abstract

In this paper, we propose two efficient block preconditioners to solve the mass-conserved Ohta-Kawasaki equation with finite element discretization. We also study the spectral distribution of these two preconditioners, i.e., Schur complement preconditioner and the modified Hermitian and skew-Hermitian splitting (MHSS in short) preconditioner. Besides, Newton method and Picard method are used to address the implicitly nonlinear term. We rigorously analyze the convergence of Newton method. 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

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0066

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 454–488

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:    Mass-conserved Ohta-Kawasaki equation Newton method Schur complement preconditioner MHSS preconditioner.

Author Details

Juan Zhang

Shifeng Li

Kai Jiang