Computationally efficient solution to the Cahn–Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem

Wodo, Olga; Ganapathysubramanian, Baskar

doi:10.1016/j.jcp.2011.04.012

Cited by 132 publications

(113 citation statements)

References 51 publications

(110 reference statements)

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“…Their difference can then be employed as an estimate for the temporal error and as a guide to decrease or increase the time-step size. For phase-field models such techniques have been employed in, e.g., (Ceniceros and Roma, 2007;Cueto-Felgueroso and Peraire, 2008;Gomez et al, 2008;Wodo and Ganapathysubramanian, 2011).…”

Section: Adaptive Mesh and Time-step Refinementmentioning

confidence: 99%

Computational Phase‐Field Modeling

Gómez

Zee

2017

Encyclopedia of Computational Mechanics Second Edition

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Phase-field modeling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domain motions are also unknowns. The computational treatment of these problems requires moving meshes and is very difficult when the moving domains undergo topological changes. Phase-field modeling may be understood as a methodology to reformulate interface problems as equations posed on fixed domains. In some cases, the phase-field model may be shown to converge to the moving-boundary problem as a regularization parameter tends to zero, which shows the mathematical soundness of the approach. However, this is only part of the story because phase-field models do not need to have a moving-boundary problem associated and can be rigorously derived from classical thermomechanics. In this context, the distinguishing feature is that constitutive models depend on the variational derivative of the free energy. In all, phase-field models open the opportunity for the efficient treatment of outstanding problems in computational mechanics, such as, the interaction of a large number of cracks in three dimensions, cavitation, film and nucleate boiling, tumor growth or fully three-dimensional air-water flows with surface tension. In addition, phase-field models bring a new set of challenges for numerical discretization that will excite the computational mechanics community.

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Section: Adaptive Mesh and Time-step Refinementmentioning

confidence: 99%

Computational Phase‐Field Modeling

Gómez

Zee

2017

Encyclopedia of Computational Mechanics Second Edition

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“…Figure 8 depicts six representative morphologies for each type. These morphologies are obtained by solving the Cahn-Hilliard equation (for more details refer to [47]). We utilize a graph-based framework to quantify the differences between two morphologies, thus, validating this intuitive hypothesis.…”

Section: Analysis Of the Fabrication Processmentioning

confidence: 99%

A graph-based formulation for computational characterization of bulk heterojunction morphology

Wodo

Tirthapura

Chaudhary

et al. 2012

Organic Electronics

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Organic solar cells (OSC) have the potential for widespread usage, due to their promise of low cost, roll-to-roll manufacturability, and mechanical flexibility. However, ubiquitous deployment is impeded by their relatively low power conversion efficiencies (PCE). The last decade has seen significant progress in enhancing the PCE of these devices through various strategies. One such approach is based on morphology control. This is because morphology affects all phenomena involved in solar conversion: (1) light absorption and electron-hole pair (exciton) generation; (2) exciton diffusion and dissociation into free charges; and (3) transport of charges to the electrodes.Progress in experimental characterization and computational modeling now allow reconstruction and imaging of thin film morphology. This opens up the possibility of rationally linking fabrication processes with morphology, as well as morphology with performance. In this context, a comprehensive set of computational tools to rapidly quantify and classify the 2D/3D heterogeneous internal structure of thin films will be invaluable in linking process, structure, and property.We present a novel graph-based framework to efficiently compute a broad suite of physically meaningful morphology descriptors. These morphology descriptors are further classified according to the physical subprocesses within OSCs -photon absorption, exciton diffusion, charge separation, and charge transport. This approach is motivated by the equivalence between a discretized 2D/3D morphology and a labeled, weighted, undirected graph. We utilize this approach to pose six key questions related to structure characterization. We subsequently construct estimates and rigorous upper bounds of various efficiencies. The approach is showcased by characterizing the effect of thermal annealing on time-evolution of a thin film morphology. We conclude by formulating natural extensions of our framework to characterize crystallinity and anisotropy of the morphology using the framework.

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“…The same model, which stems from that considered in [35], has been used in the two-dimensional study of Mata et al [26] and the current work is a follow-up report on our findings for the corresponding three-dimensional system. Similar phase field models have been used extensively in phase separation [14,25,19,4,1,2,21,22,5,35,37,36,3,38,13,39,12,30,17,33].…”

Section: Introductionmentioning

confidence: 99%