A Preconditioner for the Ohta--Kawasaki Equation

DOI10.1137/16M1065483zbMath1365.65221arXiv1603.04570OpenAlexW2964111278MaRDI QIDQ5346750

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Publication date: 29 May 2017

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.04570

zbMATH Keywords

Schur complementfinite elementpreconditionernonlocal Cahn-Hilliard equationdiblock copolymer meltsKrylov iterationsOhta-Kawasaki equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Statistical mechanics of polymers (82D60) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Preconditioners for iterative methods (65F08) PDEs in connection with statistical mechanics (35Q82)

Related Items (9)

Well-posedness and large time behavior for Cahn-Hilliard-Oono equation ⋮ The Cahn–Hilliard–Oono equation with singular potential ⋮ Solver Composition Across the PDE/Linear Algebra Barrier ⋮ Fast solver of optimal control problems constrained by Ohta-Kawasaki equations ⋮ Matching Schur Complement Approximations for Certain Saddle-Point Systems ⋮ Preconditioned iterative methods for the convective FitzHugh-Nagumo equations ⋮ Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction ⋮ A note on preconditioner for the Ohta-Kawasaki equation ⋮ A Globally Convergent Modified Newton Method for the Direct Minimization of the Ohta--Kawasaki Energy with Application to the Directed Self-Assembly of Diblock Copolymers

Uses Software

• BoomerAMG
• FEniCS

Cites Work

• Automated solution of differential equations by the finite element method. The FEniCS book
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• Chebyshev semi-iteration in preconditioning for problems including the mass matrix
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• \textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner
• A Note on Preconditioning Nonsymmetric Matrices
• A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
• Fast Solvers for Cahn--Hilliard Inpainting
• Spectral estimates for unreduced symmetric KKT systems arising from Interior Point methods
• Field-of-Values Convergence Analysis of Augmented Lagrangian Preconditioners for the Linearized Navier–Stokes Problem
• On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn–Hilliard Functional
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Solution of Sparse Indefinite Systems of Linear Equations
• A Note on Preconditioning for Indefinite Linear Systems
• Any Nonincreasing Convergence Curve is Possible for GMRES
• An Implicit Midpoint Spectral Approximation of Nonlocal Cahn--Hilliard Equations

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