Research On Construction And Optimization Method For Isogeometric-analysis-suitable Parameterization Of Complex Planar Region

Isogeometric analysis is a new method for physical simulation and analysis based on the exact geometry representation of CAD models directly,which provides a new idea for overcoming the gap between CAD and CAE.In isogeometric analysis,the parameterization of the computational domain has a great effect on the final analysis results.In this paper,the construction and optimzation method for isogeometric-analysis-suitable parameterization of complex planar region are studied in depth,including the following two aspects:(1)For the parameterization of planar region with high genus and more complex boundary curves,we propose a general framework for constructing IGA-suitable planar parameterization by domain partition and global/local optimization.Firstly,some pre-processing operations including Bézier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization;then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments.After the topology information generation of quadrilateral decomposition,the optimal placement of interior Bézier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality.Finally,after the imposition of C~1/G~1-continuity constraints on the interface of neighboring Bézier patches with respect to each quad in the quadrangulation,the high-quality Bézier patch parameterization is obtained by a local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches.The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach.(2)Based on the good properties of the moving mesh method and harmonic mapping in isogeometric analysis,this paper presents a new method to optimize the computational domain in isogeometric analysis.A new monitor function based on the absolute curvature metric of isogeometric solution surface is proposed according to the feature of isogeometric analysis.With the proposed r-adaptive framework,the inner control points can be re-distributed to the regions with large solution features with the curvature-based monitor function or the regions with large errors with the error-based monitor function.Comparing with the previous direct optimization method,the resulting locations of inner control points are obtained by solving PDEs with isogeometric collocation method,hence it is more efficient for large-scale simulation problems;on the other hand,the resulting r-adaptive parameterization of computational domain is valid for isogeometric analysis due to the property of harmonic mapping,and can be used as optimal initial grid for subsequent h-refinement.Several examples are tested on two-dimensional heat conduction problems to show the effectiveness of the proposed method.