An Energy-Minimization Finite-Element Approach for the Frank--Oseen Model of Nematic Liquid Crystals

DOI10.1137/140956567zbMath1327.76015arXiv1402.3310OpenAlexW1879810993MaRDI QIDQ3192576

D. B. Emerson, J. H. Adler, Scott MacLachlan, T. J. Atherton

Publication date: 13 October 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.3310

zbMATH Keywords

nematic liquid crystalsmixed finite elementssaddle-point problemenergy optimizationNewton linearization

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical computation of solutions to systems of equations (65H10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Liquid crystals (76A15) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (12)

Block preconditioners for saddle point systems arising from liquid crystal directors modeling ⋮ Modelling and computation of liquid crystals ⋮ Constrained Optimization for Liquid Crystal Equilibria ⋮ An Energy-Minimization Finite-Element Approach for the Frank--Oseen Model of Nematic Liquid Crystals ⋮ Energy Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects ⋮ The Ericksen model of liquid crystals with colloidal and electric effects ⋮ A structure-preserving FEM for the uniaxially constrained \(\mathbf{Q} \)-tensor model of nematic liquid crystals ⋮ Combining Deflation and Nested Iteration for Computing Multiple Solutions of Nonlinear Variational Problems ⋮ A finite element method for the generalized Ericksen model of nematic liquid crystals ⋮ The Q-tensor model with uniaxial constraint ⋮ Augmented Lagrangian preconditioners for the Oseen-Frank model of nematic and cholesteric liquid crystals ⋮ \(Q\)-tensor gradient flow with quasi-entropy and discretizations preserving physical constraints

Uses Software

• deal.ii
• NewtonLib

Cites Work

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• A numerical investigation on configurational distortions in nematic liquid crystals
• A preconditioning technique for a class of PDE-constrained optimization problems
• Theory and applications of liquid crystals
• Hydrostatic theory of liquid crystals
• On energetic variational approaches in modeling the nematic liquid crystal flows
• Existence and partial regularity of static liquid crystal configurations
• Simple \(C^ 0\) approximations for the computation of incompressible flows
• Stabilized finite element methods. II: The incompressible Navier-Stokes equations
• Solvability of the Navier-Stokes system with \(L^2\) boundary data
• Gauss-Newton multilevel methods for least-squares finite element computations of variably saturated subsurface flow
• On the general Ericksen-Leslie system: Parodi's relation, well-posedness and stability
• On the Navier-Stokes initial value problem. I
• An energy law preserving \(C^0\) finite element scheme for simulating the kinematic effects in liquid crystal dynamics
• Error-bounds for finite element method
• A Renormalized Newton Method for Liquid Crystal Director Modeling
• An Energy-Minimization Finite-Element Approach for the Frank--Oseen Model of Nematic Liquid Crystals
• Numerical solution of saddle point problems
• deal.II—A general-purpose object-oriented finite element library
• A Saddle Point Approach to the Computation of Harmonic Maps
• A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces
• Finite Element Methods for Navier-Stokes Equations
• Numerical Optimization
• A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case
• Finite Element Analysis of the Landau--de Gennes Minimization Problem for Liquid Crystals
• A stabilized finite element method for the Stokes problem based on polynomial pressure projections
• Mixed Finite Element Methods and Applications
• A Preconditioned Nullspace Method for Liquid Crystal Director Modeling
• Numerical Investigation of Tumbling Phenomena Based on a Macroscopic Model for Hydrodynamic Nematic Liquid Crystals
• Numerical Simulations of Hydrodynamics of Nematic Liquid Crystals: Effects of Kinematic Transports
• Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations

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