TY - JOUR A1 - Fenske, Markus A1 - Schultz, Christof A1 - Dagar, Janardan A1 - Kosasih, Felix Utama A1 - Zeiser, Andreas A1 - Junghans, Cornelia A1 - Bartelt, Andreas A1 - Ducati, Caterina A1 - Schlatmann, Rutger A1 - Unger, Eva A1 - Stegemann, Bert T1 - Improved Electrical Performance of Perovskite Photovoltaic Mini‐Modules through Controlled PbI2 Formation Using Nanosecond Laser Pulses for P3 Patterning JF - Energy Technology N2 - The upscaling of perovskite solar cells to modules requires the patterning of the layer stack in individual cells that are monolithically interconnected in series. This interconnection scheme is composed of three lines, P1–P3, which are scribed using a pulsed laser beam. The P3 scribe is intended to isolate the back contact layer of neighboring cells, but is often affected by undesired effects such as back contact delamination, flaking, and poor electrical isolation. Herein, the influence of the laser pulse duration on the electrical and compositional properties of P3 scribe lines is investigated. The results show that both nanosecond and picosecond laser pulses are suitable for P3 patterning, with the nanosecond pulses leading to a higher open circuit voltage, a higher fill factor, and a higher power conversion efficiency. It is found that the longer pulse duration resultes in a larger amount of PbI2 formed within the P3 line and a thin Br‐rich interfacial layer which both effectively passivate defects at the scribe line edges and block charge carrier in its vicinity. Thus, nanosecond laser pulses are preferable for P3 patterning as they promote the formation of beneficial chemical phases, resulting in an improved photovoltaic performance. KW - Laserablation KW - ablation KW - laser KW - perovskites KW - photovoltaics KW - series interconnections KW - solar modules KW - thin films KW - Laser KW - Perowskit KW - Fotovoltaik Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:523-15841 VL - 9 IS - 4 SP - 1 EP - 8 ER - TY - JOUR A1 - Zeiser, Andreas T1 - Sparse grid time-discontinuous Galerkin method with streamline diffusion for transport equations JF - Partial Differential Equations and Applications N2 - High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the transport equation in moderately complex geometrical domains using a Galerkin method stabilized by streamline diffusion. The ansatz spaces are a tensor product of a sparse grid in space and discontinuous piecewise polynomials in time. Here, the sparse grid is constructed upon nested multilevel finite element spaces to provide geometric flexibility. This results in an implicit time-stepping scheme which we prove to be stable and convergent. If the solution has additional mixed regularity, the convergence of a 2 d -dimensional problem equals that of a d -dimensional one up to logarithmic factors. For the implementation, we rely on the representation of sparse grids as a sum of anisotropic full grid spaces. This enables us to store the functions and to carry out the computations on a sequence regular full grids exploiting the tensor product structure of the ansatz spaces. In this way existing finite element libraries and GPU acceleration can be used. The combination technique is used as a preconditioner for an iterative scheme to solve the transport equation on the sequence of time strips. Numerical tests show that the method works well for problems in up to six dimensions. Finally, the method is also used as a building block to solve nonlinear Vlasov-Poisson equations. KW - Sparse grid KW - Sparse grid KW - High-dimensional transport equations KW - Streamline diffusion KW - Combination technique KW - Vlasov-Poisson equations KW - 65M60 KW - 65M12 KW - Mathematical Sciences Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:523-19095 SN - 2662-2963 SN - 2662-2971 VL - 4 PB - Springer International Publishing ER - TY - JOUR A1 - Uschmajew, André A1 - Zeiser, Andreas T1 - Dynamical low-rank approximation of the Vlasov–Poisson equation with piecewise linear spatial boundary JF - BIT Numerical Mathematics N2 - Dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov–Poisson equations is based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. In this work, a variational formulation of the projector splitting is proposed which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach. KW - Dynamical low-rank approximation KW - Boundary condition KW - Projector-splitting integrator KW - Friedrichs’ system KW - 15A69 KW - 65M60 KW - 82D10 Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:523-19786 SN - 0006-3835 SN - 1572-9125 VL - 64 IS - 2 PB - Springer Nature CY - Dordrecht ER - TY - JOUR A1 - Uschmajew, André A1 - Zeiser, Andreas T1 - Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov–Poisson equation JF - BIT Numerical Mathematics N2 - A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov–Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs’ systems in a continuous setting, it combines recently proposed conservative DLRA methods with a discontinuous Galerkin discretization. The resulting scheme is shown to ensure mass and momentum conservation at the discrete level. In addition, a new formulation of the conservative integrator is proposed based on its interpretation as a tangent space projector splitting scheme. Numerical experiments validate our approach in one- and two-dimensional simulations of Landau damping. As a demonstration of feasibility, it is also shown that the rank-adaptive unconventional integrator can be combined with mesh adaptivity. KW - - KW - Dynamical low-rank approximation KW - Discontinuous Galerkin method KW - Friedrichs’ system KW - Mass and momentum conservation KW - 15A69 KW - 65M60 KW - 82D10 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:523-21753 SN - 0006-3835 SN - 1572-9125 VL - 65 IS - 4 PB - Springer Nature CY - Dordrecht ER - TY - JOUR A1 - Uschmajew, André A1 - Zeiser, Andreas T1 - Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov–Poisson equation JF - BIT Numerical Mathematics N2 - A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov–Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs’ systems in a continuous setting, it combines recently proposed conservative DLRA methods with a discontinuous Galerkin discretization. The resulting scheme is shown to ensure mass and momentum conservation at the discrete level. In addition, a new formulation of the conservative integrator is proposed based on its interpretation as a tangent space projector splitting scheme. Numerical experiments validate our approach in one- and two-dimensional simulations of Landau damping. As a demonstration of feasibility, it is also shown that the rank-adaptive unconventional integrator can be combined with mesh adaptivity. KW - Dynamical low-rank approximation KW - Discontinuous Galerkin method KW - Friedrichs’ system KW - Mass and momentum conservation KW - 15A69 KW - 65M60 KW - 82D10 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:523-21983 SN - 0006-3835 SN - 1572-9125 VL - 65 IS - 4 PB - Springer CY - Dordrecht ER -