Adaptive Optimization Approach of Computational Domain Based on Local Error Indicator for Iso-geometric Analysis

The iso-geometric analysis method provides a new way to realize the seamless integration of geometric data representation in CAD/CAE.However, its accuracy and efficiency strongly depend on the parameterization of the computational domain.In order to improve its optimization efficiency, a local refinement method is proposed in this paper.In our method, the local position optimization of interior partial control points is used to improve the simulation accuracy.Firstly the local error indicator is obtained on each sub-patch by applying a residual-based approach.Then the set of subpatches to be refined are obtained by a mean-value marking method to determine the set of inner control points to be optimized.Finally the optimal distribution of inner control points is obtained by minimizing the sum of local error indicators using a nonlinear optimization method.A local h-rrefinement is also proposed by combining local r-refinement with h-refinement method based on knot insertion.Several examples for two-dimensional Poisson equation solving are presented to show the efficiency of the proposed local optimization method in iso-geometric analysis.