Space-Time Mixed System Formulation of Phase-Field Fracture Optimal Control Problems

In this work, space-time formulations and Galerkin discretizations for phase-field fracture optimal control problems are considered. The fracture irreversibility constraint is formulated on the time-continuous level and is regularized by means of penalization. The optimization scheme is formulated in terms of the reduced approach and then solved with a Newton method. To this end, the state, adjoint, tangent, and adjoint Hessian equations are derived. The key focus is on the design of appropriate function spaces and the rigorous justification of all Fréchet derivatives that require fourth-order regularizations. Therein, a second-order time derivative on the phase-field variable appears, which is reformulated as a mixed first-order-in-time system. These derivations are carefully established for all four equations. Finally, the corresponding time-stepping schemes are derived by employing a dG(r) discretization in time

Space-time fluid-structure interaction: formulation and dG(0) time discretization

This contribution is related to the key-note lecture `Space-time fluid-structure interaction with adjoint-based methods for error estimation and optimization' given in the Minisymposium `Innovative Methods for Fluid-Structure Interaction'. The main objective is twofold. First, we design function spaces and a space-time variational-monolithic formulation of fluid-structure interaction in arbitrary Lagrangian-Eulerian coordinates. Second, we apply a Galerkin-time discretization using discontinuous finite elements of degree r = 0. Therein, the main emphasis is on the correct derivation of the jump terms and the integration of nonlinear time derivatives, as the latter arise due to the arbitrary Lagrangian-Eulerian transformation

Modeling, Discretization, Optimization, and Simulation of Phase-Field Fracture Problems

This course is devoted to phase-field fracture methods. Four different sessions are centered around modeling, discretizations, solvers, adaptivity, optimization, simulations and current developments. The key focus is on research work and teaching materials concerned with the accurate, efficient and robust numerical modeling. These include relationships of model, discretization, and material parameters and their influence on discretizations and the nonlinear (Newton-type methods) and linear numerical solution. One application of such high-fidelity forward models is in optimal control, where a cost functional is minimized by controlling Neumann boundary conditions. Therein, as a side-project (which is itself novel), space-time phase-field fracture models have been developed and rigorously mathematically proved. Emphasis in the entire course is on a fruitful mixture of theory, algorithmic concepts and exercises. Besides these lecture notes, further materials are available, such as for instance the open-source libraries pfm-cracks and DOpElib. The prerequisites are lectures in continuum mechanics, introduction to numerical methods, finite elements, and numerical methods for ODEs and PDEs. In addition, functional analysis (FA) and theory of PDEs is helpful, but for most parts not necessarily mandatory. Discussions with many colleagues in our research work and funding from the German Research Foundation within the Priority Program 1962 (DFG SPP 1962) within the subproject Optimizing Fracture Propagation using a Phase-Field Approach with the project number 314067056 (D. Khimin, T. Wick), and support of the French-German University (V. Kosin) through the French-German Doctoral college ``Sophisticated Numerical and Testing Approaches" (CDFA-DFDK 19-04) is gratefully acknowledged

"Flora of Russia" on iNaturalist: a dataset

The "Flora of Russia" project on iNaturalist brought together professional scientists and amateur naturalists from all over the country. Over 10,000 people are involved in the data collection.Within 20 months the participants accumulated over 750,000 photo observations of 6,853 species of the Russian flora. This constitutes the largest dataset of open spatial data on the country’s biodiversity and a leading source of data on the current state of the national flora. About 85% of all project data are available under free licenses (CC0, CC-BY, CC-BY-NC) and can be freely used in scientific, educational and environmental activities

"Flora of Russia" on iNaturalist: a dataset

The "Flora of Russia" project on iNaturalist brought together professional scientists and amateur naturalists from all over the country. Over 10,000 people are involved in the data collection.Within 20 months the participants accumulated over 750,000 photo observations of 6,853 species of the Russian flora. This constitutes the largest dataset of open spatial data on the country’s biodiversity and a leading source of data on the current state of the national flora. About 85% of all project data are available under free licenses (CC0, CC-BY, CC-BY-NC) and can be freely used in scientific, educational and environmental activities

"Flora of Russia" on iNaturalist: a dataset

The "Flora of Russia" project on iNaturalist brought together professional scientists and amateur naturalists from all over the country. Over 10,000 people are involved in the data collection.Within 20 months the participants accumulated over 750,000 photo observations of 6,853 species of the Russian flora. This constitutes the largest dataset of open spatial data on the country’s biodiversity and a leading source of data on the current state of the national flora. About 85% of all project data are available under free licenses (CC0, CC-BY, CC-BY-NC) and can be freely used in scientific, educational and environmental activities