A5024767834- Model Reduction and Neural Networks
- Advanced Numerical Methods in Computational Mathematics
- Numerical methods for differential equations
- Real-time simulation and control systems
- Advanced Mathematical Modeling in Engineering
- Electromagnetic Simulation and Numerical Methods
- Advanced Battery Technologies Research
- Probabilistic and Robust Engineering Design
- Scientific Computing and Data Management
- Numerical methods in engineering
- Composite Material Mechanics
- Modeling and Simulation Systems
- Parallel Computing and Optimization Techniques
- Geological and Geophysical Studies
- Seismic Imaging and Inversion Techniques
- Research Data Management Practices
- Fuel Cells and Related Materials
- Electromagnetic Scattering and Analysis
- Numerical Methods and Algorithms
- Advanced Electron Microscopy Techniques and Applications
- Geological formations and processes
- Computer Graphics and Visualization Techniques
- Computability, Logic, AI Algorithms
- Nuclear Engineering Thermal-Hydraulics
- Data Quality and Management
University of Münster
2013-2023
Virginia Tech
2022
Max Planck Institute for Dynamics of Complex Technical Systems
2018-2022
FH Münster
2016-2022
Applied Mathematics (United States)
2018-2021
Eindhoven University of Technology
2020
University of Twente
2020
University of Stuttgart
2020
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable models of parametrized partial differential equation problems. With speedups that reach several orders magnitude, enable high fidelity real-time simulations complex systems and dramatically reduce the computational costs in many-query applications. In this contribution we analyze methodology, mainly focussing on theoretical aspects approach. particular discuss what is known...
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing amount data vectors, however, computing POD often becomes prohibitively expensive. This work presents generic, easy-to-implement approach to compute approximate based on arbitrary tree hierarchies worker nodes, where each computes only small vectors. The hierarchy can be freely adapted...
Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss design pyMOR, a freely available software library algorithms, in particular reduced methods, implemented with Python programming language. As its main feature, all algorithms pyMOR generically via operations on well-defined vector array, operator, and discretization interface classes. This...
<ns3:p>Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements embeds knowledge, constitutes an essential product itself. Research must be sustainable order to understand, replicate, reproduce, build upon or conduct effectively. In other words, available, discoverable, usable, adaptable needs, both now the future. therefore requires environment that supports sustainability.</ns3:p><ns3:p> </ns3:p><ns3:p> Hence,...
Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements embeds knowledge, constitutes an essential product itself. must be sustainable order to understand, replicate, reproduce, build upon or conduct effectively. In other words, available, discoverable, usable, adaptable needs, both now the future. therefore requires environment that supports sustainability. Hence, change is needed way development maintenance are...
The Reduced Basis (RB) method is a well established for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement application RB schemes availability an posteriori error estimator to reliably estimate introduced by process. However, straightforward implementations standard residual based estimators show poor numerical stability, rendering them unusable if high accuracy required. In this work we propose new algorithm on...
Engineers manually optimizing a structure using finite element based simulation software often employ an iterative approach where in each iteration they change the slightly and resimulate. Standard is usually not well suited for this workflow, as it restarts iteration, even tiny changes. In settings with complex local microstructure, fine mesh required to capture geometric detail, localized model reduction can improve workflow. To end, we introduce ArbiLoMod, method which allows fast...
We are concerned with employing Model Order Reduction (MOR) to efficiently solve parameterized multiscale problems using the Localized Orthogonal Decomposition (LOD) method. Like many methods, LOD follows idea of separating problem into localized fine-scale subproblems and an effective coarse-scale system derived from solutions local problems. While Reduced Basis (RB) method has already been used speed up solution problems, resulting coarse remained untouched, thus limiting achievable up. In...
Scientific software projects evolve rapidly in their initial development phase, yet at the end of a funding period, completion research project, thesis, or publication, further engagement project may slow down cease completely. To retain invested effort for sciences, this needs to be preserved handed over succeeding developer team, such as next generation (PhD) students. Comparable guides provide top-down recommendations leads. This paper intends bottom-up approach sustainable hand-over...
Abstract The cross Gramian matrix encodes the input‐output coherence of linear control systems and is used in projection‐based model reduction. empirical a data‐driven variant which also extends to nonlinear systems. A drawback for large‐scale its full order dense structure; yet, it may be computed column‐wise. Using hierarchical approximate proper orthogonal decomposition (HAPOD), this partial computability can exploited obtain truncated projection reduction without assembling Gramian. (©...
The Parareal algorithm was invented in 2001 order to parallelize the solution of evolution problems time direction. It is based on parallel fine propagators called F and sequential coarse G, which alternatingly solve problem iteratively converge solution. propagator G a very important component Parareal, as one sees convergence analyses. We present here for first without propagator, explain why this can work well parabolic problems. give new proof approximating space, contrast more classical...