A mesh adaptivity scheme on the Landau–de Gennes functional minimization case in 3D, and its driving efficiency

Bajc, Iztok; Hecht, Frédéric; Žumer, S.

doi:10.1016/j.jcp.2016.02.072

Cited by 20 publications

(21 citation statements)

References 32 publications

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“…Experimental work on high-aspect ratio colloidal particle shapes observes both hedgehogs and disclination loops, but numerical modeling has been limited to the line defect case [35, 38-43, 64, 65]. Adaptive mesh refinement in finite-element simulations can help to avoid computational and memory expense in regions not near defects [66] but typically does not remove the need to scale down.…”

Section: Introductionmentioning

confidence: 99%

Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

Sussman

Beller

2019

Front. Phys.

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Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single-or multiplecore configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.

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Section: Introductionmentioning

confidence: 99%

Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

Sussman

Beller

2019

Front. Phys.

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“…By replacing L by L d in Eqs. (8) and (9), and using Prop. 3.1.1. in the Bertsekas textbook [14], we get the equivalent discrete optimization problem:…”

Section: B Discretized Optimization Problemmentioning

confidence: 99%

“…The minimization is usually done with an Euler relaxation scheme [1,4], which is formally equivalent to a gradient descent algorithm. Alternatively, Bajc et al [8] recently proposed a hybrid method that uses either the Newton method or the gradient descent method when the convergence is difficult.…”

Section: Introductionmentioning

confidence: 99%

Role of anchoring energy on the texture of cholesteric droplets: Finite-element simulations and experiments

2017

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We present a numerical method to compute defect-free textures inside cholesteric domains of arbitrary shape. This method has two interesting properties, namely a robust and fast quadratic convergence to a local minimum of the Frank free energy, thanks to a trust region strategy. We apply this algorithm to study the texture of cholesteric droplets in coexistence with their isotropic liquid in two cases: when the anchoring is planar and when it is tilted. In the first case, we show how to determine the anchoring energy at the cholesteric-isotropic interface from a study of the optical properties of droplets of different sizes oriented with an electric field. This method is applied to the case of the liquid crystal CCN-37. In the second case, we come back to the issue of the textural transition as a function of the droplet radius between the double-twist droplets and the banded droplets, observed for instance in cyanobiphenyl liquid crystals. We show that, even if this transition is dominated by the saddle-splay Gauss constant K_{4}, as was recently recognized by Yoshioka et al. [Soft Matter 12, 2400 (2016)1744-683X10.1039/C5SM02838H], the anchoring energy does also play an important role that cannot be neglected.

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“…The energy landscape of an NLC system, in which the equilibrium states are located, is determined by the properties of the LC material as well as the environment, such as temperature, size and shape of the confining space, and the external field. Tremendous experimental and theoretical studies have been undertaken to investigate defect patterns in NLCs (Muševič et al 2006, Lubensky, Pettey, Currier and Stark 1998, Onsager 1949, Bajc, Hecht and Žumer 2016.…”

Section: Introductionmentioning

confidence: 99%

Modelling and computation of liquid crystals

Wang¹,

Zhang

2021

Acta Numerica

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Liquid crystals are a type of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the past four decades, which is of great importance for fundamental scientific research and has widespread applications in industry. In this paper we review the mathematical models and their connections to liquid crystals, and survey the developments of numerical methods for finding rich configurations of liquid crystals.

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A mesh adaptivity scheme on the Landau–de Gennes functional minimization case in 3D, and its driving efficiency

Cited by 20 publications

References 32 publications

Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

Role of anchoring energy on the texture of cholesteric droplets: Finite-element simulations and experiments

Modelling and computation of liquid crystals

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