This publication deals an insider's view of ways commercial difficulties are translated into arithmetic and the way fixing the math ends up in convincing commercial options in addition. In 6 technical chapters, quite a lot of commercial difficulties is modeled, simulated, and optimized; four others describe the modeling, computing, optimization, and information research techniques shaping the paintings of the Fraunhofer ITWM. every one technical bankruptcy illustrates how the appropriate arithmetic has been tailored or prolonged for the explicit software and info the underlying functional challenge and ensuing software program. the ultimate bankruptcy exhibits how using mathematical modeling within the school room can switch just like this topic, making it intriguing and enjoyable.
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Additional resources for Currents in Industrial Mathematics: From Concepts to Research to Education
Example text
4 Avenues to Model Reduction How does one make a mathematical model? In the classroom, one starts perhaps with quite a simple model and then advances to more complex ones (see “The Training”). In practice, however, one usually starts with the complex models. Here, the natural laws are known and the materials can be described in detail. One therefore has to reduce the complexity to arrive at simpler models, since evaluating the complex ones is too expensive. ” Here, there are various approaches that can be used, initially, for genuine white box models.
Grützner, Fraunhofer ITWM, simulations: Fraunhofer ITWM, department SMS, photo: iStockphoto) This multi-scale modeling is closely related to the multi-grid methods of numerics. In “The Research—Modeling and Simulation of Filtration Processes,” up-scaling will be examined for the simulation of filters (which indeed exhibit a crucial microstructure), along with the interplay between multi-scale and multi-grid. Asymptotic analysis, perturbation theory, homonogenization, etc. are important analytical methods for the reduction of white box or grey box models.
This question also distinguishes between various groups offering “industrial mathematics” as a university or research institute topic. The “Study groups with industry” founded in Oxford some 45 years ago, for example, bear down for an entire week on industrial problems using mathematical methods and deliver interesting analyses, but rarely quantitative predictions. The Fraunhofer ITWM, in contrast, strives to ultimately provide the client with software for simulating, optimizing, or controlling the systems.