Abstract
By allowing split-in-half in mesh refinement, MPHT-splines (modified polynomial splines over hierarchical T-meshes) were recently introduced to increase the flexibility of PHT-splines. However, some basis functions of MPHT-splines may severely decay as the basis functions of PHT-splines during the process of certain refinement of hierarchical T-meshes. This decay phenomenon may cause the isogeometric analysis matrices assembled by these basis functions to be ill-conditioned. To overcome this defect, we present a method to modify the basis functions of MPHT-splines when the supports of the original truncated basis functions are rectangular domains. Hence, the truncation operations are less used, which alleviates the decay phenomenon of MPHT-splines. In addition, the modified basis functions preserve the good properties of the original MPHT-spline basis functions, e.g., the partition of unity, local support and linear independence. Numerical examples show that the condition numbers of isogeometric analysis matrices significantly decrease when new basis functions are applied.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.