8 research outputs found
Preconditioning for a Phase-Field Model with Application to Morphology Evolution in Organic Semiconductors
The Cahn--Hilliard equations are a versatile model for describing the
evolution of complex morphologies. In this paper we present a computational
pipeline for the numerical solution of a ternary phase-field model for
describing the nanomorphology of donor--acceptor semiconductor blends used in
organic photovoltaic devices. The model consists of two coupled fourth-order
partial differential equations that are discretized using a finite element
approach. In order to solve the resulting large-scale linear systems
efficiently, we propose a preconditioning strategy that is based on efficient
approximations of the Schur-complement of a saddle point system. We show that
this approach performs robustly with respect to variations in the
discretization parameters. Finally, we outline that the computed morphologies
can be used for the computation of charge generation, recombination, and
transport in organic solar cells
Modeling the morphology evolution of organic solar cells
Organic solar cells present a promising alternative for the generation of solar energy at lower material and production costs compared to widely used silicon-based solar cells. The major drawback of organic solar cells currently is a lower rate of energy conversion. Thus many research projects aim to improve the achievable efficiency. In this work a phase field model is used to mathematically describe the morphology evolution of the active layer composed of polymer as electron-donor and fullerene as electron-acceptor. The derivation of a chemical potential term and a surface energy term for the polymer-fullerene solution using the Flory-Huggins theory forms the basis to employ the Cahn-Hilliard equation. After including several specifics of the application in this non-linear partial differential equation of fourth order, an implementation of the model using the FEM solver software FEniCS provides some simulation results that qualitatively match results from the literature
Simulation of thin film flows with a moving mesh mixed finite element method
We present an efficient mixed finite element method to solve the fourth-order
thin film flow equations using moving mesh refinement. The moving mesh strategy
is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170
(2001), pp. 562-588, and 177 (2002), pp. 365-393]. To achieve a high quality
mesh, we adopt an adaptive monitor function and smooth it based on a diffusive
mechanism. A variety of numerical tests are performed to demonstrate the
accuracy and efficiency of the method. The moving mesh refinement accurately
resolves the overshoot and downshoot structures and reduces the computational
cost in comparison to numerical simulations using a fixed mesh.Comment: 18 pages, 10 figure
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Emerging Developments in Interfaces and Free Boundaries
The field of the mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a well established and flourishing area of research. This workshop focused on recent developments and emerging new themes. By bringing together experts in these fields we achieved progress in open questions and developed novel research directions in mathematics related to interfaces and free boundaries. This interdisciplinary workshop brought together researchers from distinct mathematical fields such as analysis, computation, optimisation and modelling to discuss emerging challenges
Fast iterative solvers for Cahn-Hilliard problems
Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016von M. Sc. Jessica BoschLiteraturverzeichnis: Seite [247]-25