Modelling and effective modification of smooth boundary geometry in boundary problems using B-spline curves
To create curves in computer graphics, we use, among others, B-splines since they make it possible to effectively produce curves in a continuous way using a small number of de Boors control points. The properties of these curves have also been used to define and create boundary geometry in boundary problems solving using parametric integral equations system (PIES). PIES was applied for resolution 2D boundary-value problems described by Laplaces equation. In this PIES, boundary geometry is theoretically defined in its mathematical formalism, hence the numerical solution of the PIES requires no boundary discretization (such as in BEM) and is simply reduced to the approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained were compared with both exact and numerical solutions.
b-spline curve parametric integral equations system boundary integral equation potential problem