Doktorandenseminar des WIAS
FG3: Numerische Mathematik und Wissenschaftliches
Rechnen /
RG3: Numerical Mathematics
and Scientific Computing/
LG5: Numerik für innovative
Halbleiter-Bauteile
LG5: Numerics for
innovative semiconductor devices
Seminar Numerische Mathematik / Numerical mathematics seminars
aktuelles Programm / current program
Archiv
Hybrid-/Online-Vorträge finden über ''Zoom'' statt. Der Zoom-Link wird jeweils ca. 15 Minuten vor Beginn des Gesprächs versendet. / The zoom link will be send about 15 minutes before the start of the talk. People who are not members of the research group 3 and who are interested in participating should contact christian.merdon@wias-berlin.de to obtain the zoom login details.
Donnerstag, 06. 06. 2024, 14:00 Uhr (WIAS-ESH)
Steffen Maass & Tim Siebert (WIAS/TU Berlin)
... tbd ...... tbd ...
Dienstag, 04. 06. 2024, 13:30 Uhr (WIAS-ESH)
Jürgen Fuhrmann (WIAS)
... tbd ...... tbd ...
Dienstag, 28. 05. 2024, 13:30 Uhr (WIAS-406)
Sarah Katz & Francesco Romor (WIAS)
... tbd ...... tbd ...
Donnerstag, 23. 05. 2024, 14:00 Uhr (WIAS-ESH)
Alfonso Caiazzo (WIAS)
... tbd ...... tbd ...
Dienstag, 21. 05. 2024, 13:30 Uhr (WIAS-ESH)
Christian Merdon (WIAS)
... tbd ...... tbd ...
Donnerstag, 16.05.2024, 14:00 Uhr (WIAS-ESH)
Medine Demir & Daniel Runge (WIAS)
... tbd ...... tbd ...
Dienstag, 14. 05. 2024, 13:30 Uhr (WIAS-ESH)
Cristian Cárcamo (WIAS)
Equal-order finite element methods for coupled and multiphysics problemsWe discuss the well-posedness and error analysis of the Coupled Navier-Stokes-Darcy equations and Biot’s Poroelastic equations in this talk. To demonstrate the solvability of the poroelastic continuous issue, we first use the well-known Fredholm Alternative. In order to improve computational efficiency and address the issues raised by the discrete inf-sup condition, we present a novel and stable stabilized numerical system that is tuned for equal polynomial order. Analogous aspects of the Coupled Navier-Stokes Equations are examined. We also perform a numerical analysis to determine the stability of solutions and offer an a priori analysis of them. Lastly, we provide a few numerical illustrations. These examples offer strong proof of the usefulness and effectiveness of the suggested numerical framework.
Dienstag, 14. 05. 2024, 14:00 Uhr (WIAS-ESH)
Marwa Zainelabdeen (WIAS)
... tbd ...... tbd ...
Dienstag, 07. 05. 2024, 13:30 Uhr (WIAS-ESH)
Dilara Abdel (WIAS)
Modeling and simulation of vacancy-assisted charge transport in innovative semiconductor devicesIn response to the climate crisis, there is a need for technological innovations to reduce the escalating CO$_2$ emissions. Two promising semiconductor technologies in this regard, perovskite-based solar cells and memristive devices based on two-dimensional layered transition metal dichalcogenide (TMDC), can potentially contribute to the expansion of renewable energy sources and the development of energy-efficient computing hardware. Within perovskite and TMDC materials, ions dislocate from their ideal position in the semiconductor crystal and leave void spaces. So far, the precise influence of these vacancies and their dynamics on device performance remain underexplored.
Therefore, this talk is dedicated to comprehensively examining the impact of vacancy-assisted charge transport in innovative semiconductor devices through a theoretical approach by modeling and simulating systems of partial differential equations. We start by deriving drift-diffusion equations using thermodynamic principles. Furthermore, we formulate drift-diffusion models to describe charge transport in perovskite solar cells and TMDC memristors. We discretize the transport equations via the finite volume method and establish the existence of discrete solutions. Our study concludes with simulations conducted with an open source software tool developed in the programming language Julia. These simulations explore the influence of volume exclusion effects on charge transport in perovskite solar cells and compare our simulation results with experimental measurements found in literature for TMDC-based memristive devices.
Dienstag, 07. 05. 2024, 14:00 Uhr (WIAS-ESH)
Timo Streckenbach (WIAS)
tbdtbd
Donnerstag, 02. 05. 2024, 14:00 Uhr (WIAS-ESH)
Baptiste Moreau (WIAS)
... tbd ...... tbd ...
Donnerstag, 02. 05. 2024, 14:30 Uhr (WIAS-ESH)
Ondřej Pártl (WIAS)
Optimization of geothermal energy production from fracture-controlled reservoirs via 3D numerical modeling and simulationWe develop a computation framework from scratch that allows us to conduct 3D numerical simulations of groundwater flow and heat transport in hot fractured-controlled reservoirs to find optimal placements of injection and production wells that sustainably optimize geothermal energy production.
We model the reservoirs as geologically consistent randomly generated discrete fracture networks (DFN) in which the fractures are 2D manifolds with polygonal boundary embedded in a 3D porous medium. The wells are modeled as line sources and sinks. The flow and heat transport in the DFN-matrix system are modeled by solving the balance equations for mass, momentum, and energy. The fully developed computational framework combines the finite element method with semi-implicit time-stepping and algebraic flux correction. To perform the optimization, we use various gradient-free algorithms.
I will present our latest results for several geologically and physically realistic scenarios.
Dienstag, 30. 04. 2024, 13:30 Uhr (WIAS-ESH)
Patricio Farrell (WIAS)
Numerical methods for innovative semiconductor devicesThe 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, memristors, 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.
Donnerstag, 25. 04. 2024, 14:00 Uhr (WIAS-ESH)
Holger Stephan & trainees (WIAS)
... tbd ...... tbd ...
Dienstag, 23. 04. 2024, 13:30 Uhr (WIAS-ESH)
Zeina Amer (WIAS)
Numerical methods for coupled drift-diffusion and Helmholtz models for laser applicationsSemiconductor lasers are pivotal components in modern technologies, spanning medical procedures, manufacturing, and autonomous systems like LiDARs. Understanding their operation and developing simulation tools are paramount for advancing such technologies. In this talk, we present a mathematical PDE model for an edge-emitting laser, combining charge transport and light propagation. The charge transport will be described by a drift-diffusion model and the light propagation by the Helmholtz equation. We discuss a coupling strategy for both models and showcase initial numerical simulations.
Dienstag, 23. 04. 2024, 14:00 Uhr (WIAS-ESH)
Yiannis Hadjimichael (WIAS)
An energy-based finite-strain model for 3D heterostructured materialsThis talk presents a mathematical model that accurately describes the intrinsic strain response of 3D heterostructures arising from lattice mismatch. Combining materials with different lattice constants induces strain, leading to the bending of such heterostructures. To validate our model, we apply it to bimetallic beams and hexagonal hetero-nanowires and perform numerical simulations using finite element methods (FEM). In order to assess the fidelity of the model and the accuracy of simulations, we compare the calculated curvature with analytically derived formulations. The outcomes of our study yield valuable insights into the behavior of strained bent heterostructures. We compare the strain profiles of wurtzite and zincblende crystal structures, shedding light on their distinct characteristics. This is particularly significant as the strain has the potential to influence piezoelectricity, the electronic band structure, and the dynamics of charge carriers.
Donnerstag, 18. 04. 2024, 14:00 Uhr (WIAS-ESH)
Volker John (WIAS/FU Berlin)
Finite element methods respecting the discrete maximum principle for convection-diffusion equationsConvection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the solution. That the same bounds are respected by numerical approximations of the solution is often of utmost importance in practice. The mathematical formulation of this property, which contributes to the physical consistency of a method, is called Discrete Maximum Principle (DMP). In many applications, convection dominates diffusion by several orders of magnitude. It is well known that standard discretizations typically do not satisfy the DMP in this convection-dominated regime. In fact, in this case, it turns out to be a challenging problem to construct discretizations that, on the one hand, respect the DMP and, on the other hand, compute accurate solutions. This paper presents a survey on finite element methods, with a main focus on the convection-dominated regime, that satisfy a local or a global DMP. The concepts of the underlying numerical analysis are discussed. The survey reveals that for the steady-state problem there are only a few discretizations, all of them nonlinear, that at the same time satisfy the DMP and compute reasonably accurate solutions, e.g., algebraically stabilized schemes. Moreover, most of these discretizations have been developed in recent years, showing the enormous progress that has been achieved lately. Methods based on algebraic stabilization, nonlinear and linear ones, are currently as well the only finite element methods that combine the satisfaction of the global DMP and accurate numerical results for the evolutionary equations in the convection-dominated situation.