Currents in Industrial Mathematics: From Concepts to by Helmut Neunzert, Dieter Prätzel-Wolters, William Uber

By Helmut Neunzert, Dieter Prätzel-Wolters, William Uber

This e-book deals an insider's view of the way commercial difficulties are translated into arithmetic and the way fixing the maths ends up in convincing commercial suggestions besides. In 6 technical chapters, quite a lot of business difficulties is modeled, simulated, and optimized; four others describe the modeling, computing, optimization, and knowledge research techniques shaping the paintings of the Fraunhofer ITWM. every one technical bankruptcy illustrates how the suitable arithmetic has been tailored or prolonged for the categorical program and info the underlying sensible challenge and ensuing software program. the ultimate bankruptcy indicates how using mathematical modeling within the lecture room can swap a twin of this topic, making it intriguing and enjoyable.

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And we do indeed take this software right up to the limits of its capabilities. However, if it cannot provide a usable answer—and this is not so seldom an occurrence— then we develop new software ourselves. The pros and cons of commercial software are well known. We would like to briefly address the counter arguments. Comsol, for example, is outstanding for training purposes. It also claims to be able to quickly solve every industrial problem. Experience has shown us, however, that this is only true when the same or very similar problems have already been solved in the past using Comsol, and are therefore contained in the library.

One thus obtains models that only capture large-scale effects, but still maintain a memory of the micro-scales. One therefore speaks of up-scaling, which can also be attained–granted, in a somewhat “more robust” manner— by means of averaging in numerical methods (numerical up-scaling) (Fig. 8). 46 H. Neunzert Fig. 8 Filter simulation at various scales (Graphic: S. Grützner, Fraunhofer ITWM, simulations: Fraunhofer ITWM, department SMS, photo: iStockphoto) This multi-scale modeling is closely related to the multi-grid methods of numerics.

Unfortunately, we can rarely wait, and therefore need our own developments. The situation is similar with Open Source software tools, which, on top of the aforementioned problem, offer even less support. The developers of FLUENT take great pains to ensure that their software is as robust as possible. One sometimes pays a price for this robustness, however, in terms of precision. Our own software development has many facets. The algorithms are often implemented in MATLAB for quick testing or the quick computation of a solution.

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