This booklet bargains an insider's view of the way business difficulties are translated into arithmetic and the way fixing the math ends up in convincing business ideas to boot. In 6 technical chapters, a variety of business difficulties is modeled, simulated, and optimized; four others describe the modeling, computing, optimization, and knowledge research suggestions shaping the paintings of the Fraunhofer ITWM. every one technical bankruptcy illustrates how the correct arithmetic has been tailored or prolonged for the explicit program and info the underlying useful challenge and ensuing software program. the ultimate bankruptcy exhibits how using mathematical modeling within the school room can swap similar to this topic, making it fascinating and enjoyable.

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Extra info for Currents in Industrial Mathematics: From Concepts to Research to Education

Example text

Finally, we reflect a bit upon the topic “validation” of models and algorithms. 1 The Fundamentals Most of the models discussed in this book use partial differential equations (PDE). Ordinary differential equations (ODE), differential algebraic equations (DAE), and integrodifferential equations also occur, albeit less frequently. These models describe deterministic systems. For stochastic cases, of course, stochastic ordinary or partial differential equations (SDE and SPDE) must also be analyzed and solved.

Naturally, the developers at this software firm keep very close track of these cases and, after a certain period of time, release a new version that redresses these deficiencies. 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.

There has been a dramatic paradigm change with regard to generating the highest computational performance for industrial applications. PC clusters, multi-core systems, and cloud computing are replacing super computers. Parallel computing systems, which just a few years ago were found only in a few meteorological research centers, have now made their way into industrial settings. Adapting numerical algorithms to these rapid changes in hardware configuration is still a troublesome bottleneck in the complete realization of the performance potential of these new computing systems.

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