A creative solution for rapid and inexpensive model-making in product design processes

Innovative Developments in Virtual and Physical Prototyping

A creative solution for rapid and inexpensive model-making in product design processes

Rapid prototyping (RP) is an approach for automatically building a physical object through solid freeform fabrication. Nowadays, RP has become a vital aspect of most product development processes, due to the significant competitive advantages it offers compared to traditional manual model making. Even in academic environments, it is important to be able to quickly create accurate physical representations of concept solutions. Some of these can be used for simple visual validation, while others can be employed for ergonomic assessment by potential users or even for physical testing. However, the cost of traditional RP methods prevents their use in most academic environments on a regular basis, and even for very preliminary prototypes in many small companies. That results in delaying the first physical prototypes to later stages, or creating very rough mock-ups which are not as useful as they could be. In this paper we propose an approach for rapid and inexpensive model-making, which was developed in an academic context, and which can be employed for a variety of objects.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.