By Helmut Neunzert, Dieter Prätzel-Wolters, William Uber
This publication deals an insider's view of ways business 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 innovations shaping the paintings of the Fraunhofer ITWM. every one technical bankruptcy illustrates how the appropriate arithmetic has been tailored or prolonged for the explicit program and information the underlying useful challenge and ensuing software program. the ultimate bankruptcy exhibits how using mathematical modeling within the school room can swap a dead ringer for this topic, making it fascinating and enjoyable.
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Extra resources for Currents in Industrial Mathematics: From Concepts to Research to Education
Gerda de Vries  has one more argument: “Experimental scientists are very good at taking apart the real world and studying small components. Since the real world is nonlinear, fitting the components together is a much harder puzzle. ” Modeling and simulating is problem solving. We are always doing this, wherever we may find ourselves—though we are not always doing it consciously. However, this fact should be made conscious at an early age, while we are still in school. The models don’t have to be differential equations; counting and adding can suffice for model evaluation purposes.
Granted, a problem may be transferred to the department that has the appropriate method for it. To be perfectly honest, however, departments usually attract the problems that suit them, which makes such problems transferals relatively rare. Even when the modeler’s methodological competence is not the determining factor, the model of choice is not unambiguous. Again, we see varying degrees of complexity. One begins with the “full physics” (models of first principles)—for example, the full compressible Navier Stokes equations—and, since these are not utilizable for the given parameters, ends with Prandtl boundary layer equations or with simpler turbulence models.
In structural mechanics, where FEM dominates, grid generation is unavoidable.