计算域与物理场样条空间相异的广义等几何配点法  

Generalized Isogeometric Collocation Method with Different Spline Space for Computational Domain and Physical Field

作　　者：马佳玲 徐岗[1] 许金兰[1] 吴卿[1] MA Jialing;XU Gang;XU Jinlan;WU Qing(Key Laboratory of Complex Systems Modeling and Simulation, Department of Computer Science, Hangzhou Dianzi University, Hangzhou 310018)

机构地区：[1]杭州电子科技大学计算机学院,复杂系统建模与仿真教育部重点实验室,杭州310018

出　　处：《系统科学与数学》2018年第12期1393-1406,共14页Journal of Systems Science and Mathematical Sciences

基　　金：浙江省自然科学基金(LR16F020003);国家自然科学基金(61761136010,61772163,61472111,61602138)资助课题.

摘　　要：提出了一种计算域与物理场样条空间相异的广义等几何配点方法.在该框架中,表示计算域与物理场的样条空间可以互不相同.该方法在保持传统等几何配点法的求解精度以及与CAD系统无缝集成特点的同时,使得物理场样条空间的选择可以更加灵活,从而可以获得更加精确的数值结果.文章通过一些数值实例验证了该方法的有效性.In this paper, we propose a generalized isogeometric collocation framework by geometry-independent field approximation method. In the proposed framework, the spline spaces can be chosen and adapted independently for geometry and the field variables. The proposed method not only can preserve geometric exactness and tight CAD integration as traditional isogeometric collocation approach, but also can achieve a much more accurate numerical results because of the flexible choice of spline space of solution field. Several numerical examples are presented to show the effectiveness of the proposed generalized isogeometric collocation method.

关 键 词：等几何分析 配点法 样条空间 计算域 

分 类 号：O241.82[理学—计算数学] TP391.72[理学—数学]