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Content
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.
