New Perspectives in Science Education

There are some areas of engineering and applied mathematics which computational methods are essential and benefit strongly from the enormous advances in computer technology. The finite element method (FEM) has become the most widely accepted general purpose technique for numerical simulations. More than 200 papers related to this subject had been published. Now, almost 30 years later, various aspects of finite element techniques remain a central area of engineering research and development. In the other hand splines play an important role in approximation and geometric modeling. They are used in data fitting, computer-aided design (CAD), automated manufacturing (CAM), and computer graphics. The early work of Schoenberg revealed that splines possess powerful approximation properties; many approximation schemes have been proposed. With geometric modeling and numerical simulation closely linked in engineering applications, the use of B-splines as finite element basis functions suggests itself. Utilizing a regular grid not only eliminates a difficult preprocessing step, but also permits very efficient implementations of algorithms. Moreover, the use of B-splines reduces the dimension of finite element systems, in particular when high accuracy is required. Regardless of the degree, there is only one parameter for each grid cell.

Keywords: technology, CAD, B-Splines;