B-spline parametrization of finite element models for optimal design of electromagnetic devices

This paper presents B-spline parametrization method for the optimal shape design of electromagnetic devices. As an optimal design technique, the design sensitivity method based on the finite element method is used. Since the design variables of one-to-one correspondence with node points of finite element model can cause saw-tooth shape and serious accuracy problem, the design interface is parameterized into smooth curves using geometrical relation of design variables and node points of finite element model. B-spline technique used widely in computer graphics is capable of representing smooth curves and surfaces and can generate a wide variety of shapes. In addition, its geometry data can be easily connected to many commercial CAD tools. To show validity of the presented technique, we test two numerical examples: a magnet shape design problem for uniform magnetic field and a electrode shape design problem for uniform electric field.