Four sides PDE surfaces generation method based on Pseudo-spectral method

FAN Zhi-hua1，ZHANG Jing-lei2
（1. School of Mechanical Engineering， Hangzhou Dianzi University， Hangzhou 310018， China；
2. School of Computer Science and Technology， Hangzhou Dianzi University， Hangzhou 310018， China）

Abstract： In order to solve the problems of generate the surface quickly，efficiently and accurately，the partial differential equation（PDE）was applied to the surface generation. The power of the PDE method lies in its ability to represent smooth surfaces in terms of a relatively small set of design parameters. Based on PDE analytical method，a four sided PDE surface patch based on pseudo-spectral method for rapidly calculating an analytic approximation was investigated. Different from separation of variables，the generated approximate solution was consisted of three parts：an eigenfunction solution and a polynomial solution，both of which satisfied the generating partial differential equation exactly，and a remainder function ensured the boundary conditions were satisfied exactly. The method of separation of variables and analytic pseudo-spectral to generate surface were tested in the same boundary conditions. The experimental results show that the method based on pseudo-spectral has high accurate and more smooth compared with the separation of variables.
Key words： pseudo-spectral method；partial differential equation（PDE） surface；four sided suface；boundary