Adaptive layered Cartesian cut cell method is presented to solve the difficulty of the tmstructured hexahedral anisotropic Cartesian grids generation from the complex CAD model. ＂Vertex merging algorithm based on rel...Adaptive layered Cartesian cut cell method is presented to solve the difficulty of the tmstructured hexahedral anisotropic Cartesian grids generation from the complex CAD model. ＂Vertex merging algorithm based on relaxed AVL tree is investigated to construct topological structure for stereo lithography （STL） files, and a topology-based self-adaptive layered slicing algorithm with special features control strategy is brought forward. With the help of convex hull, a new points-in-polygon method is employed to improve the Cartesian cut cell method. By integrating the self-adaptive layered slicing algorithm and the improved Cartesian cut cell method, the adaptive layered Cartesian cut cell method gains the volume data of the complex CAD model in STL file and generates the unstructured hexahedral anisotropic Cartesian grids.展开更多
To efficiently estimate the central subspace in sufficient dimension reduction,response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied.Howe...To efficiently estimate the central subspace in sufficient dimension reduction,response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied.However,existing slicing schemes are almost all ad hoc and not widely accepted.Thus,how to define datadriven schemes with certain optimal properties is a longstanding problem in this field.The research described here is then twofold.First,we introduce a likelihood-ratio-based framework for dimension reduction,subsuming the popularly used methods including the sliced inverse regression,the sliced average variance estimation and the likelihood acquired direction.Second,we propose a regularized log likelihood-ratio criterion to obtain a data-driven slicing scheme and derive the asymptotic properties of the estimators.A simulation study is carried out to examine the performance of the proposed method and that of existing methods.A data set concerning concrete compressive strength is also analyzed for illustration and comparison.展开更多
基金This project is supported by National Natural Science Foundation of China (No. 60375020, No. 50305033)Provincial Natural Science Foundation of Zhejiang, China (No. Y105430).
文摘Adaptive layered Cartesian cut cell method is presented to solve the difficulty of the tmstructured hexahedral anisotropic Cartesian grids generation from the complex CAD model. ＂Vertex merging algorithm based on relaxed AVL tree is investigated to construct topological structure for stereo lithography （STL） files, and a topology-based self-adaptive layered slicing algorithm with special features control strategy is brought forward. With the help of convex hull, a new points-in-polygon method is employed to improve the Cartesian cut cell method. By integrating the self-adaptive layered slicing algorithm and the improved Cartesian cut cell method, the adaptive layered Cartesian cut cell method gains the volume data of the complex CAD model in STL file and generates the unstructured hexahedral anisotropic Cartesian grids.
基金supported by National Natural Science Foundation of China(Grant Nos.11971017 and 11971018)Shanghai Rising-Star Program(Grant No.20QA1407500)+1 种基金Multidisciplinary Cross Research Foundation of Shanghai Jiao Tong University(Grant Nos.YG2019QNA26,YG2019QNA37 and YG2021QN06)Neil Shen's SJTU Medical Research Fund of Shanghai Jiao Tong University。
文摘To efficiently estimate the central subspace in sufficient dimension reduction,response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied.However,existing slicing schemes are almost all ad hoc and not widely accepted.Thus,how to define datadriven schemes with certain optimal properties is a longstanding problem in this field.The research described here is then twofold.First,we introduce a likelihood-ratio-based framework for dimension reduction,subsuming the popularly used methods including the sliced inverse regression,the sliced average variance estimation and the likelihood acquired direction.Second,we propose a regularized log likelihood-ratio criterion to obtain a data-driven slicing scheme and derive the asymptotic properties of the estimators.A simulation study is carried out to examine the performance of the proposed method and that of existing methods.A data set concerning concrete compressive strength is also analyzed for illustration and comparison.
