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MOR Wiki

Welcome to the MOR Wiki

Introduction

The purpose of the Model-Order-Reduction-Wiki is to bring together experts in the area of model reduction along with researchers from related application areas, with the goal of providing a platform for exchanging ideas and benchmark examples.

Modeling and numerical simulation are unavoidable in many application and research areas such as reaction processes, micro-electro-mechanical systems (MEMS) design, and control design. Such processes or devices can be modeled by partial differential equations (PDEs). To simulate these models, spatial discretization via, for example, finite element discretization is necessary, which results in a system of ordinary differential equations (ODEs), or differential algebraic equations (DAEs).

After spatial discretization, the number of degrees of freedom (DoFs) is usually very high. Simulating such large-scale systems of ODEs or DAEs can therefore become incredibly time-consuming. Developed from well established mathematical theory and robust numerical algorithms, Model Order Reduction (MOR) or Model Reduction has been recognized as very efficient for reducing the simulation time of large-scale systems; see the page Projection based MOR for a basic overview. Through model order reduction, a small system with a reduced number of equations (i.e., the reduced model) is derived. The reduced model is simulated instead, and the solution of the original PDEs or ODEs can then be recovered from the solution of the reduced model. As a result, the simulation time of the original large-scale system can be shortened by several orders of magnitude. The reduced model as a whole can also replace the original system and be reused repeatedly during the design process, which can lead to further time or energy savings.

Parametric model order reduction (PMOR) methods are designed for model order reduction of parametrized systems, where the parameters of the system play an important role in practical applications such as Integrated Circuit (IC) design, MEMS design, and chemical engineering. The parameters could be the variables describing geometrical measurements, material properties, the damping of the system or the component flow-rate. Reduced models are constructed such that all the parameters can be preserved with acceptable accuracy.

How to use the MOR Wiki

The MOR Wiki comprises pages providing benchmarks of parametric or non-parametric models and pages explaining applicable (P)MOR methods as well as available software implementations. We (the editors) are actively improving documentation at the moment, so check back often for updates!

Following the Submission rules, it is also possible to submit new benchmarks, methods, or software packages, along with pages describing the contribution.

Consult the User's Guide for information on using Wiki software and the Wiki markup language we use here.

See the Glossary for definitions and abbreviations.

Find current model reduction conferences, workshops and minisymposia, a list of books and lectures on model reduction and links to the model reduction community.

MORB: Model Order Reduction Benchmarker

A new benchmarking tool for model order reduction is currently under development. It is a demonstrator of the generic benchmark framework developed for Task Area 2 of the Mathematical Research Data Initiative (MaRDI). MORB will serve as an example of how to fairly compare different implementations of algorithms across a standardized benchmark set for scientific computing. Visit the MORB page for updates.

Citations

To cite the MOR Wiki itself, please use the following

The MORwiki Community. MORwiki - Model Order Reduction Wiki. http://modelreduction.org

 @misc{morwiki,
   author =       {{The MORwiki Community}},
   title =        {{MORwiki} - {M}odel {O}rder {R}eduction {W}iki},
   howpublished = {\url{http://modelreduction.org}},
   key =          {morwiki}
 }
 

A BibTeX file which contains a list of references related to model order reduction can be found and downloaded here: mor.bib.

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