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Regarding content of the manuscript there are many dilemmas regarding some topics in Numerical Methods and Computational support of given methods, like:

1.      Programming of methods in classical languages (FORTRAN, PASCAL, C, Basic) or object oriented languages or language extensions (Java, C++, Pascal 6.0, etc.), having in mind that more of 90% of numerical software is written in classical, i.e. procedural languages. Numerical methods are usually easy to explain in algorithmic way, but object oriented approach involves new association relations that could lead to new “macaroni” programming.

2.      Error estimation differs in theoretical, usually stabile computations, and practical applications like in big FEM computations. There are a-priory and a-posteriori approaches  in estimation of error in FEM computations. In addition, if even possible, the error is much easier to trace by using algorithmic software design, and very difficult in object-oriented programming, with enormous consumption of computation time. Anyway, it is very challenging field for student research by case-study assignments.

3.      New introduced Chapter “Mathematical Modeling” (Appendix B) in engineering design is mostly modeling for partial differential equations, followed by mesh generation and some appropriate numerical methods. It includes for practical applications geometrical modeling (and differential geometry as a mathematical tool), but also very tricky field known as Artificial Intelligence (for example, for mesh generation). It includes techniques for optimization (mesh and grid generation in FEM), what usually depends on stated problem. Good field for case-study but not for clear theoretical explanation.

Benchmarking of available numerical and engineering software is special field of interest of this course. In addition to specialized numerical packages (SSP, LinPack, EisPack, IMSL Library, etc.), systems like Mathematica, Matlab, and MatCAD will be used for numerical programming and benchmarking purpose.

 

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Last updated: 01/16/07.