Toric Parameterization Based Isogeometric Collocation Method for Planar Multi-Sided Physical Domains

作     者：ZHOU Pei ZHU Chungang 

作者机构：School of Mathematical Sciences Dalian University of Technology Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.12071057 and 11671068 the Fundamental Research Funds for the Central Universities under Grant No.DUT23LAB302 

摘      要：Isogeometric collocation method(IGC) shows high computational efficiency compared with isogeometric Galerkin method(IGG) when solving partial differential equations(PDEs). However, few studies about IGC have focused on multi-sided physical domains. In this paper, the authors propose a new IGC method based on toric parameterization(IGCT) for the multi-sided planar physical *** to the high order continuity of toric basis functions, the IGCT method shows more accurate numerical approximation. Moreover, the authors generalize the adaptive w-refinement method into IGCT(IGCT-w), in which the weights of basis functions in physical domains are optimized independently for geometry representation. The numerical accuracy of IGCT-w is significantly improved by an order of magnitude in comparison with IGCT method. To save the computational cost of IGCT-w, the authors devise a selection of weights scheme according to relative residuals. Finally, several numerical examples demonstrate the effectiveness and robustness of the proposed method.