arXiv subjects

Jan-F. Pietschmann

Publications and source records attributed to Jan-F. Pietschmann.

9 recordsLinked to original sources

arXiv2026

Modeling and Simulation of Device Performance in Organic Photovoltaics

We present a pipeline to study the device performance of organic solar cells in silico. We introduce a mathematical model that includes the dynamics of excitons as well as their dissociation at bulk heterojunctions within the nanomorphology of the active layer. This is combined with realistic morphologies that we obtain from a detailed phase field model. To solve the coupled nonlinear system, we use a finite element discretization, robust linear solvers, and three numerical schemes, Newton, Gummel, and Semi--Newton--Gummel. This allows for an efficient simulation of the complete OPV device and results in current-voltage curves that can readily be compared to measured data.

math.NA↗

arXiv2025

Effective transmission through an interface with evolving microstructure

We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the channels and the thickness of the membrane are of order $\varepsilon \ll 1$, and the geometry evolves in time in an a priori known way. We consider nonlinear flux boundary conditions at the lateral boundaries of the channels and critical scaling of the diffusion inside the layer. Extending the method of homogenisation in domains with evolving microstructure to thin layers, we employ two-scale convergence and unfolding techniques in thin layers to derive an effective model in the limit $\varepsilon \to 0$, in which the membrane is reduced to a lower-dimensional interface. We obtain jump conditions for the solution and the total fluxes, which involve the solutions of local, space--time-dependent cell problems in the reference channel.

math.AP↗

arXiv2025

Visualizing the Link Between Nanomorphology and Energetic Disorder in 3D Organic Solar Cells

The performance of organic bulk heterojunction (BHJ) solar cells is highly sensitive to both nanomorphology and energetic disorder arising from microscopic molecular packing and structural defects. However, most models used to understand these devices are either one-dimensional effective medium approximations that neglect spatial and energetic disorder or three-dimensional Monte Carlo simulations that are computationally intensive. In this work, we present the results from a three-dimensional hybrid model capable of operating at both high carrier densities and incorporating the effects of energetic disorder. We first generate realistic morphologies using a phase-field approach that accounts for solvent evaporation during film formation. Using these example morphologies, we systematically study the interplay between energetic disorder and configurational disorder at carrier densities representative of real device operation. This enables us to separate and visualize the impact of the nanomorphology and energetic disorder on device performance. Our results reveal that, even when macroscopic percolation pathways remain intact, energetic disorder limits performance primarily through suppressed charge extraction in interconnected domains. This suggest that optimizing molecular packing at the nanoscale is as critical as controlling phase separation at the mesoscale, highlighting the need for multiscale design strategies in next-generation BHJ devices.

physics.app-ph↗

arXiv2025

Neural Network Acceleration of Iterative Methods for Nonlinear Schr\"odinger Eigenvalue Problems

We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional solvers often suffer from slow convergence in extreme parameter regimes, as exemplified by the rotating Bose- Einstein condensate (BEC) problem. Our method uses a neural network to predict and refine solution trajectories, leveraging knowledge from previous simulations to improve convergence speed and accuracy. Numerical experiments demonstrate significant speed-up over classical solvers, highlighting both the strengths and limitations of the approach.

math.NA↗

arXiv2025

Dynamic Optimal Transport with optimal star shaped graphs

We study an optimal transport problem in a compact convex set $\Omega\subset\mathbb{R}^d$ where bulk transport is coupled to dynamic optimal transport on a metric graph $ \mathsf{G} = (\mathsf{V},\mathsf{E})$ which is embedded in $\Omega$. We prove existence of solutions for fixed graphs. Next, we consider varying graphs, yet only for the case of star-shaped ones. Here, the action functional is augmented by an additional penalty that prevents the edges of the graph to overlap. This allows to preserve the graph topology and thus to rely on standard techniques in Calculus of Variations in order to show existence of minimizers.

math.AP↗

arXiv2025

Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport in biological cells to the motion of human crowds. While traditional numerical schemes require a large amount of tailoring, especially in the case of model design or parameter identification problems, physics informed deep operator networks (DeepONet) have emerged as a versatile tool for the solution of partial differential equations with the particular advantage that they easily incorporate parameter identification questions. We here present an approach where we first learn three DeepONet models for representative inflow, inner and outflow edges, resp., and then subsequently couple these models for the solution of the drift-diffusion metric graph problem by relying on an edge-based domain decomposition approach. We illustrate that our framework is applicable for the accurate evaluation of graph-coupled physics models and is well suited for solving optimization or inverse problems on these coupled networks.

cs.LG↗

arXiv2025

Dynamic Optimal Transport with Optimal Preferential Paths

We study a dynamic optimal transport type problem on a domain that consists of two parts: a compact set $\Omega \subset \mathbb{R}^d$ (bulk) and a non-intersecting and sufficiently regular curve $\Gamma \subset \Omega$. On each of them, a Benamou-Brenier type dynamic optimal transport problem is considered, yet with an additional mechanism that allows the exchange (at a cost) of mass between bulk and curve. In the respective actions, we also allow for non-linear mobilities. We first ensure the existence of minimizers by relying on the direct method of calculus of variations and we study the asymptotic properties of the minimizers under changes in the parameters regulating the dynamics in $\Omega$ and $\Gamma$. Then, we study the case when the curve $\Gamma$ is also allowed to change, being the main interest in this paper. To this end, the Tangent-Point energy is added to the action functional in order to preserve the regularity properties of the curve and prevent self-intersections. Also in this case, by relying on suitable compactness estimates both for the time-dependent measures and the curve $\Gamma$, the existence of optimizers is shown. We extend these analytical findings by numerical simulations based on a primal-dual approach that illustrate the behaviour of geodesics, for fixed and varying curves.

math.AP↗

arXiv2025

Preconditioning for a Cahn-Hilliard-Navier-Stokes model for morphology formation in organic solar cells

We present a model for the morphology evolution of printed organic solar cells which occurs during the drying of a mixture of polymer, the non-fullerene acceptor and the solvent. Our model uses a phase field approach coupled to a Navier-Stokes equation describing the macroscopic movement of the fluid. Additionally, we incorporate the evaporation process of the solvent using an Allen-Cahn equation. The model is discretized using a finite-element approach with a semi-implicit discretization in time. The resulting (non)linear systems are coupled and of large dimensionality. We present a preconditioned iterative scheme to solve them robustly with respect to changes in the discretization parameters. We illustrate that the preconditioned solver shows parameter-robust iteration numbers and that the model qualitatively captures the behavior of the film morphology during drying.

math.NA↗

arXiv2022

Data driven gradient flows

We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the most general case, we specialise to the space of probability measures endowed with the Wasserstein distance. This setting covers many non-linear partial differential equations (PDEs), such as the porous medium equation or general drift-diffusion-aggregation equations, which can be treated by our methods independent of their respective properties (such as finite speed of propagation or blow-up). We then focus on the numerical implementation of our approach using an primal-dual algorithm. The strength of our approach lies in the fact that by simply changing the driving functional, a wide range of PDEs can be treated without the need to adopt the numerical scheme. We conclude by presenting detailed numerical examples.

math.NA↗