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Volume 34, Issue 1
Preconditioning for a Phase-Field Model with Application to Morphology Evolution in Organic Semiconductors

Kai Bergermann, Carsten Deibel, Roland Herzog, Roderick C. I. MacKenzie, Jan-Frederik Pietschmann & Martin Stoll

DOI: 10.4208/cicp.OA-2022-0115

Commun. Comput. Phys., 34 (2023), pp. 1-17.

Published online: 2023-08

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  • Abstract

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.

  • Keywords

Preconditioning, phase–field models, organic solar cells, Cahn–Hilliard, finite element analysis.

  • AMS Subject Headings

65F08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-1, author = {Bergermann , KaiDeibel , CarstenHerzog , RolandMacKenzie , Roderick C. I.Pietschmann , Jan-Frederik and Stoll , Martin}, title = {Preconditioning for a Phase-Field Model with Application to Morphology Evolution in Organic Semiconductors}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {1}, pages = {1--17}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/ 10.4208/cicp.OA-2022-0115}, url = {http://global-sci.org/intro/article_detail/cicp/21876.html} }
TY - JOUR T1 - Preconditioning for a Phase-Field Model with Application to Morphology Evolution in Organic Semiconductors AU - Bergermann , Kai AU - Deibel , Carsten AU - Herzog , Roland AU - MacKenzie , Roderick C. I. AU - Pietschmann , Jan-Frederik AU - Stoll , Martin JO - Communications in Computational Physics VL - 1 SP - 1 EP - 17 PY - 2023 DA - 2023/08 SN - 34 DO - http://doi.org/ 10.4208/cicp.OA-2022-0115 UR - https://global-sci.org/intro/article_detail/cicp/21876.html KW - Preconditioning, phase–field models, organic solar cells, Cahn–Hilliard, finite element analysis. AB -

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.

Bergermann , KaiDeibel , CarstenHerzog , RolandMacKenzie , Roderick C. I.Pietschmann , Jan-Frederik and Stoll , Martin. (2023). Preconditioning for a Phase-Field Model with Application to Morphology Evolution in Organic Semiconductors. Communications in Computational Physics. 34 (1). 1-17. doi: 10.4208/cicp.OA-2022-0115
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