48 research outputs found
Parametric Model Order Reduction using pyMOR
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 the available methods and
experimentally compare them for the parametric instationary thermal-block
benchmark defined in arXiv:2003.00846.Comment: 9 pages, 6 figure
A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries
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 scale on current hardware. Model
order reduction strategies are therefore necessary to reduce the computational
complexity while retaining the features of the model. The application of such
strategies to specialized high performance solvers asks for new software
designs allowing flexible control of the solvers by the reduction algorithms.
In this contribution we discuss the reduction of microscale battery models with
the reduced basis method and report on our new software approach on integrating
the model order reduction software pyMOR with third-party solvers. Finally, we
present numerical results for the reduction of a 3D microscale battery model
with porous electrode geometry.Comment: 7 pages, 2 figures, 2 table
Model Reduction for Multiscale Lithium-Ion Battery Simulation
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-Volmer kinetics. Empirical
operator interpolation is used to efficiently deal with this issue.
Furthermore, we present the localized reduced basis multiscale method for
parabolic problems applied to a thermal model of batteries with resolved porous
electrodes. Numerical experiments are given that demonstrate the reduction
capabilities of the presented approaches for these real world applications
Low-Rank Alternating Direction Implicit Iteration in pyMOR
The low-rank alternating direction implicit (LR-ADI) iteration is an effective method for solving large-scale Lyapunov equations. In the software library pyMOR, solutions to Lyapunov equations play an important role when reducing a model using the balanced truncation method. In this article we introduce the LR-ADI iteration as well as pyMOR, while focusing on its features which are relevant for integrating the iteration into the library. We compare the run time of the iteration's pure pyMOR implementation with those achieved by external libraries available within the pyMOR framework