Patricio Farrell
Coworkers:
Dilara Abdel, Zeina Amer, Daniel Fritsch, Yiannis Hadjimichael
Secretary:
Imke Weitkamp

Overview
The Leibniz group NUMSEMIC develops and numerically solves nonlinear PDE models. These models are often inspired by charge transport in innovative semiconductor devices. In particular, applications include perovskite solar cells, nanowires, quantum wells, lasers as well as doping reconstruction. To translate these applications into mathematical models, we rely on nonlinear drift-diffusion, hyperelastic material models, inverse PDE problems, localized landscape theory and atomistic coupling. Our methodologies include physics-preserving finite volume methods, data-driven techniques as well as meshfree methods.
Mathematical research topics
- Modeling with and numerical solution of nonlinear systems of partial differential equations
- Nonlinear drift-diffusion models, hyperelastastic materials, inverse PDE problems, localized landscape theory and atomistic coupling
- Physics preserving finite volume methods on Voronoi meshes
- Charge transport in semiconductors
- Preconditioners and anisotropic meshing strategies
- High dimensional meshfree approximation
- Data-driven techniques for ill-posed inverse problems
Applications
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Source: Pang Kakit (CC BY-SA 3.0) -
Highlights
- Daniel Fritsch presented at the Annual Meeting of DPG in Dresden.
- At the SIAM Conference on Computational Science and Engineering 2023 in Amsterdam, Dilara Abdel presented a poster, Yiannis Hadjimichael a talk and Patricio Farrell organized a minisymposium.
- In January 2023, Patricio Farrell completed his Habilitation.
- In September 2022, Dilara Abdel and Yiannis Hadjimichael presented talks at the online conference NUSOD 2022 conference. An additional submission together with Julien Moatti, Inria Lille, was voted among the top 10 contributions.
- In summer 2022, Julien Moatti from Inria Lille visited the group for three months.
- In spring 2022, Stefano Piani from SISSA visited the group twice.
- In June 2022, Yiannis Hadjimichael was invited to present a talk the SDIDE 2022 workshop.
- In April 2022, a MATH+ incubator project (Identifying and Efficiently Computing Band-Edge Energies for Charge Transport Simulations in Strained Materials) together with Costanza Manganelli and Christian Merdon will tackle band edge computations in strained semiconductors.
- In December 2021, Patricio Farrell was as GNCS visiting professor at SISSA, Italy
- Patricio Farrell was invited to be a plenary speaker at the ABPDE4 and Dilara Abdel presents a poster.
- During October/November 2021, Patricio Farrell was a CEMPI invited researcher at Inria, Lille and the University of Lille
- Dilara Abdel won a stipend (€1,500) by the science department of the French embassy ("Procope") to visit Inria Lille in October/November 2021
- Dilara Abdel and Yiannis Hadjimichael presented two separate posters at the AMaSiS 2021
- MATH+ AA2-10 project Electro-mechanical coupling for semiconductor devices together with Annegret Glitzky, Matthias Liero and Barbara Zwicknagl
- The Leibniz group is organizing a mini symposium at the SIAM Conference on Mathematical Aspects of Materials Science 2021 with the title Modelling and simulation of charge transport in perovskites. Dilara Abdel won a SIAM MS student travel award for attending the conference to give a talk.
- The Leibniz group presents two posters at the SIAM Conference on Computational Science and Engineering 2021. Dilara Abdel won a SIAM CSE student travel award for attending the conference to present a poster.
- Poster presented at the German Conference on Crystal Growth, Munich
- Two abstracts have been accepted to the NUSOD 2020 conference. One of them was voted among the top 10 contributions.
- MATH+ IP-TB-3 project Understanding doping variations in silicon crystals together with Nella Rotundo

Flexible Research Platform
- Modeling, Analysis, and Scaling Limits for Bulk-Interface Processes
- Data-driven Optimization and Control
- Numerical Methods for Innovative Semiconductor Devices
- Probabilistic Methods for Dynamic Communication Networks
- Quantitative Analysis of Stochastic and Rough Systems
- Simulation of Semiconductor Devices for Quantum Technologies
- Former Groups
