Projection Operators and Error Analysis of Complex Physical Domains in Isogeometric Analysis

For solving partial differential equations(PDEs) on complex physical regions in isogeometric analysis(IGA), a method of bicubic spline projection mapping on multi-parameter domains is presented. Firstly, a projection mapping is constructed for complex physical domains based on multi-patch parameterization. Secondly, the approximation error of the projection mapping is discussed for the smooth functions defined over the physical domain, and the theoretical analysis shows that the projection mapping can reach the optimal approximation order.Finally, an IGA-suitable spline space is provided for solving the second order elliptic PDEs on the complex physical domain in IGA based on the idea of projection mapping. Numerical results show that the method based on projection operator reaches optimal approximation order.