ν-SPLINE CURVES FOR BOUNDARY GEOMETRY MODELING IN TWO-DIMENSIONAL POTENTIAL BOUNDARY VALUE PROBLEMS WITH SINGULAR CORNER POINTS

Abstract

The paper presents a new modeling method of boundary geometry in boundary valueproblems by ν-spline curves. To define a smooth boundary geometry both B´ezier and B-spline curves are applied. At the segment join points B´ezier curves ensure continuity C¹, and B-spline curves allow us to maintain C² continuity. However, the curves hinder boundary modeling with corner points. In order to weaken the continuity at segment join points ν-spline curves are proposed. These curves are combined analytically with the Green formula, thus yielding the Parametric Integral Equation System (PIES). To solve the PIES a pseudospectral method is used. The results obtained for the domains with singular corner points are compared with the corresponding non-singular ones as defined by the ν spline curves.