Representing PDE surfaces in terms of B-splines
type: Item
instance of: scholarly article
title: Representing PDE surfaces in terms of B-splines
zbMATH Open document ID: 0706.65006
DOI: 10.1016/0010-4485(90)90083-O
published in: CAD. Computer-Aided Design
publication date: 1990-01-01T00:00:00Z
review text: The paper discusses a technique for expressing PDE surfaces in terms of B-splines. The surface is obtained not as exact solution of the original boundary value problem but they have the virtue of being genuine tensor- product surfaces, which have B-splines as their basis functions. The collocation method for the solution of ordinary and partial differential equations is used: The approximate solution of the PDE \((\frac{\partial^ 2}{\partial u^ 2}+a^ 2\frac{\partial}{\partial v^ 2})X=0\) over the region \(\Omega =(0,1)\times (0,1)\) is searched in the following form, allowing local control: \(\tilde X=\sum^{N+2}_{i=-2}\sum^{M+2}_{j=-2}a_{ij}B_ i(u)B_ j(v)\) where, \(a_{ij}\) are the ``smoothing vectors''. To illustrate the principles of the method the authors concentrate their attention to the particularly simple surfaces with constrained boundary conditions.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 4159948
zbMATH Keywords: surface approximation
zbMATH Keywords: design systems
zbMATH Keywords: PDE surfaces
zbMATH Keywords: B-splines
zbMATH Keywords: tensor- product surfaces
zbMATH Keywords: collocation method
author: Malcolm I. G. Bloor
author: Michael J. Wilson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4159948