Stephan Rave

• University of Münster

In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from polymerization and depolymerization of cytoskeletal components. In detail, we propose a nonlinear continuum approach to m...

pyMOR is a free software library for model order reduction that includes both reduced basis and system-theoretic methods. All methods are implemented in terms of abstract vector and operator interfaces, which allows a direct integration of pyMOR’s algorithms with a wide array of external PDE solvers. In this contribution, we give a brief overview o...

In this contribution, we aim to satisfy the demand for a publicly available benchmark for parametric model order reduction that is scalable both in degrees of freedom as well as parameter dimension.

Scientific software projects evolve rapidly in their initial development phase, yet at the end of a funding period, the completion of a research project, thesis, or publication, further engagement in the project may slow down or cease completely. To retain the invested effort for the sciences, this software needs to be preserved or handed over to a...

pyMOR is a free software library for model order reduction that includes both reduced basis and system-theoretic methods. All methods are implemented in terms of abstract vector and operator interfaces, which allows direct integration of pyMOR's algorithms with a wide array of external PDE solvers. In this contribution, we give a brief overview of...

In this contribution we aim to satisfy the demand for a publicly available benchmark for parametric model order reduction that is scalable both in degrees of freedom as well as parameter dimension.

We consider model order reduction for a free boundary problem of an osmotic cell that is parameterized by material parameters as well as the initial shape of the cell. Our approach is based on an Arbitrary-Lagrangian-Eulerian description of the model that is discretized by a mass-conservative finite element scheme. Using reduced basis techniques an...

This paper shows recent developments in pyMOR, in particular the addition of system‐theoretic methods. All methods are implemented using pyMOR's abstract interfaces, which allows the application to partial differential equation (PDE) models implemented with third‐party libraries. We demonstrate this by applying balanced truncation to a PDE model di...

In the context of model order reduction of parametric elliptic problems, we present a methodology to reconstruct a conforming flux from a given a reduced solution, that is locally conservative with respect to the underlying finite element grid. All components of the procedure depend separably on the parameter and allow for further use in offline/on...

Scientific software projects evolve rapidly in their initial development phase, yet at the end of a funding period, the completion of a research project, thesis, or publication, further engagement in the project may slow down or cease completely. To retain the invested effort for the sciences, this software needs to be preserved or handed over to a...

Scientific software projects evolve rapidly in their initial development phase, yet at the end of a funding period, the completion of a research project, thesis, or publication, further engagement in the project may slow down or cease completely. To retain the invested effort for the sciences, this software needs to be preserved or handed over to a...

In the context of model order reduction of parametric elliptic problems, we present a methodology to reconstruct a conforming flux from a given reduced solution, that is locally conservative with respect to the underlying finite element grid. All components of the procedure depend separably on the parameter and allow for further use in offline/onli...

In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that have only support on part of the domain and compute a global approximation by a suitable coupling of the local...

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 number of input data vectors, however, computing the POD often becomes prohibitively expensive. This work presents a general, easy-to-implement...

We consider model order reduction for a free boundary problem of an osmotic cell that is parameterized by material parameters as well as the initial shape of the cell. Our approach is based on an Arbitrary-Lagrangian-Eulerian description of the model that is discretized by a mass-conservative finite element scheme. Using reduced basis techniques an...

Proper Orthogonal Decomposition (POD) is a widely used technique for constructing low-order approximation spaces from high-dimensional input data. Apart from numerous applications in the data sciences, POD is also a fundamental tool for the basis generation in projection-based reduced order modelling methods. For large-scale applications with an i...

The cross Gramian matrix encodes the input-output coherence of linear control systems and is used in projection-based model reduction. The empirical cross Gramian is a data-driven variant of the cross Gramian which also extends to nonlinear systems. A drawback of the empirical cross Gramian for large-scale systems is its full order and dense struct...

The simulation method ArbiLoMod (Buhr et al., SIAM J. Sci. Comput. 2017, accepted) has the goal of providing users of Finite Element based simulation software with quick re-simulation after localized changes to the model under consideration. It generates a Reduced Order Model (ROM) for the full model without ever solving the full model. To this end...

In this contribution we present first results towards localized model order reduction for spatially resolved, three-dimensional lithium-ion batterymodels. We introduce a localized reduced basis scheme based on non-conforming local approximation spaces stemming from a finite volume discretization of the analytical model and localized empirical opera...

We present an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations, based on elliptic reconstruction techniques (Makridakis and Nochetto, SIAM J. Numer. Anal. 41(4):1585–1594, 2003. doi:10.1137/S0036142902406314; Lakkis and Makridakis, Math. Comput. 75(256):1627–1658, 2006. doi:10.1090/S002...

We present a simulation workflow for efficient investigations of the interplay between 3D lithium-ion electrode microstructures and electrochemical performance, with emphasis on lithium plating. Our approach addresses several challenges. First, the 3D microstructures of porous electrodes are generated by a parametric stochastic model, in order to s...

We present a simulation workflow for efficient investigations of the interplay between 3D lithium-ion electrode microstructures and electrochemical performance, with emphasis on lithium plating. Our approach addresses several challenges. First, the 3D microstructures of porous electrodes are generated by a parametric stochastic model, in order to s...

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 of input data vectors, however, computing the POD often becomes prohibitively expensive. This work presents a generic, easy to implement...

The main contribution of this article is an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations and its application for true error estimation of the localized reduced basis method. To this end we combine the abstract framework with true error a posteriori estimation of the localized reduce...

The simulation method ArbiLoMod has the goal to provide users of Finite Element based simulation software with quick re-simulation after localized changes to the model under consideration. It generates a Reduced Order Model (ROM) for the full model without ever solving the full model. To this end, a localized variant of the Reduced Basis method is...

In this contribution we present first results towards localized model order reduction for spatially resolved, three-dimensional lithium-ionbattery models. We introduce a localized reduced basis scheme based on non-conforming local approximation spaces stemming from a finite volume discretizationof the analytical model and localized empirical operat...

In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis method to the resulting instationary 3D battery model that involves strong non-linearities due to Buttler-Volme...

In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis method to the resulting instationary 3D battery model that involves strong non-linearities due to Buttler-Volme...

Finite Element based simulation software is often used in engineering workflows to design structures whose behavior can be modeled by partial differential equations. Engineers manually optimizing a structure using simulation software often employ an iterative approach where in each iteration they change the structure slightly and resimulate. Standa...

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of magnitude, reduced basis methods enable high fidelity real-time simulations of complex systems and dramatical...

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 the design of pyMOR, a freely available software library of model order reduction algorithms, in particular reduced basis methods, implemented w...

The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial di?erential equations. One crucial requirement for the application of RB schemes is the availability of an a posteriori error estimator to reliably estimate the error introduced by the reduction process. However, s...

In order to achieve a better understanding of degradation processes in lithium-ion batteries, the modelling of cell dynamics at the mircometer scale is an important focus of current mathematical research. These models lead to large-dimensional, highly nonlinear finite volume discretizations which, due to their complexity, cannot be solved at cell s...

We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the solution space, the original problem is reformulated as a partial differential algebraic equation system by decomposi...

We define the finitely summable K-homology K fin * for the category of topological *-algebras in terms of homotopy classes of finitely summable Fredholm modules and study various properties of this theory: We show that K fin * is invariant under stabilization with the algebras of Schatten class operators, but that it is not additive with respect to...