Andreas Buhr

Andreas Buhr
The Qt Company

Dr. rer. nat.

About

12
Publications
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103
Citations

Publications

Publications (12)
Article
Full-text available
We provide first the functional analysis background required for reducedorder modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions, offline-online decomposition, and error estimation are introduced. Several tools for geometry parameterizations such a...
Chapter
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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...
Preprint
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Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering workflows require multiple simulations with small, non parametric changes in between. The use of localized model...
Preprint
Full-text available
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...
Article
Full-text available
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation (PDE) with random boundary conditions, yield an approximation that converges provably at a nearly optimal rate,...
Article
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Online enrichment is the extension of a reduced solution space based on the solution of the reduced model. Procedures for online enrichment were published for many localized model order reduction techniques. We show that residual based online enrichment on overlapping domains converges exponentially. Furthermore, we present an optimal enrichment st...
Chapter
Full-text available
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...
Article
Full-text available
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...
Article
An interactive simulation tool should allow its user to change the geometry of the simulation and present an updated solution within a very short time span. To achieve this, the Reduced Basis Method can be used. For problems described by parametrized partial differential equations, it allows for very fast recomputation of the solution after paramet...
Article
Full-text available
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...
Article
Full-text available
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...

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Project (1)
Project
Model reduction approaches for parameterized problems have seen tremendous development in recent years. A particular instance of projection based model reduction is the reduced basis (RB) method, which is based on the construction of low-dimensional approximation spaces from snapshot computations, i.e. solutions of the underlying parameterized problem for suitably chosen parameter values. In this project we are concerned with developing and analyzing localized model order reduction methods that are particularly well suited to treat large scale or heterogeneous multiscale scale problems. We derive suitable localized a posteriori error estimates, also with respect to the underlying true solution of the parameterized problem and demonstrated how this error estimator can be used to overcome classical so called offline/online splitting though the newly developed concept of online enrichment. We even go a step further and introduce a model reduction concept that is suitable for arbitrary local modifications and therefore applicable for non-parameterized variations.