{"title":"A family of C1 Clough–Tocher spline spaces on C0 piecewise quadratic domain partitions","authors":"Jan Grošelj, Marjeta Knez","doi":"10.1016/j.matcom.2025.03.006","DOIUrl":null,"url":null,"abstract":"<div><div>The paper addresses the construction of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> splines on a curved domain that is parametrized by a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> piecewise geometry mapping composed of quadratic Bézier triangles. The <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> splines are assembled from polynomials of a chosen total degree greater than or equal to four, and their construction is based on the Clough–Tocher splitting technique that ensures locality. In particular, the splines are locally characterized by an interpolation problem described by Hermite data, which resembles the standard macro-element concepts developed for <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> splines on triangulations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 368-389"},"PeriodicalIF":4.4000,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378475425000813","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper addresses the construction of splines on a curved domain that is parametrized by a piecewise geometry mapping composed of quadratic Bézier triangles. The splines are assembled from polynomials of a chosen total degree greater than or equal to four, and their construction is based on the Clough–Tocher splitting technique that ensures locality. In particular, the splines are locally characterized by an interpolation problem described by Hermite data, which resembles the standard macro-element concepts developed for splines on triangulations.
期刊介绍：
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
Topics covered by the journal include mathematical tools in:
•The foundations of systems modelling
•Numerical analysis and the development of algorithms for simulation
They also include considerations about computer hardware for simulation and about special software and compilers.
The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research.
The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
