Categorical approach to modelling and to coupling of models. (23rd June 2016)

• Record Type: Journal Article
• Authors: Gürlebeck, Klaus; Hofmann, Dirk; Legatiuk, Dmitrii
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 3(2017)
• Page Start: 523
• Page End: 534
• Publication Date: 2016-06-23
• Subjects: category theory -- modelling -- engineering -- coupling -- abstract approach -- mathematical concept; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3978
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Solution of any engineering problem starts with a modelling process, which typically involves a choice among different kinds of models. To create a realistic model, one has to think carefully about the modelling process. Particularly in the case of coupled problems when several models are coupled together to represent a given physical phenomenon. This paper presents an approach based on the category theory that allows to describe this modelling process on a more abstract level. Using the advantages of abstract level, one can describe the coupling process in a concise way and introduce certain criteria to check consistency of a coupled model. The main idea of the proposed approach is to introduce a structure in the modelling process, which allows to see how different models interact without a precise look into them. Copyright © 2016 John Wiley & Sons, Ltd.