Isogeometric Analysis for the Scattering of NURBS Surfaces with Coinciding Knots

This paper first introduces and addresses the discontinuity problem in isogeometric analysis (IGA) for nonuniform rational B-spline (NURBS) surfaces. Herein, we focus on solving the scattering problem of the perfect electric conductor (PEC) based on the electric field integral equation (EFIE). This discontinuity problem arises from the coinciding knots in the knot vectors of NURBS surfaces, where the NURBS basis functions have a reduced differentiable continuity. The basis functions with reduced continuity may dissatisfy the div-conforming requirements in the EFIE and finally lead to the wrong simulation. To address this problem, this work split the surfaces at the coinciding knots by inserting the knots repeatedly and making the one-to-one correspondence for the two sets of basis functions at the splitting interface. Numerical results demonstrate the validity and accuracy of the proposed method.