Achieving linear complexity is crucial for demonstrating optimal convergence rates in adaptive refinement.It has been shown that the existing linear complexity local refinement algorithm for T-splines generally produc...Achieving linear complexity is crucial for demonstrating optimal convergence rates in adaptive refinement.It has been shown that the existing linear complexity local refinement algorithm for T-splines generally produces more degrees of freedom than the existing greedy refinement,which lacks linear complexity.This paper introduces a novel greedy local refinement algorithm for analysis-suitable T-splines,which achieves linear complexity and requires fewer control points than existing algorithms with linear complexity.Our approach is based on the observation that confining refinements around each T-junction to a preestablished feasible region ensures the algorithm’s linear complexity.Building on this constraint,we propose a greedy optimization local refinement algorithm that upholds linear complexity while significantly reducing the degrees of freedom relative to previous linear complexity local refinement methods.展开更多
Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aid...Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aided Geom Design 29:63-76,2012;Scott et al.Comput Methods Appl Mech Eng 213-216,2012).The paper independently derives a class of bi-degree(d_(1),d_(2))T-splines for which no perpendicular T-junction extensions intersect,and provides a new proof for the linearly independence of the blending functions.We also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation.展开更多
Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric ana...Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis （IGA） oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines.展开更多
The present paper conjectures a topological condition which classifies a T-spline into standard,semi-standard and non-standard.We also provide the basic framework to prove the conjecture on the classification of semi-...The present paper conjectures a topological condition which classifies a T-spline into standard,semi-standard and non-standard.We also provide the basic framework to prove the conjecture on the classification of semi-standard T-splines and give the proof for the semi-standard of bi-degree(1,d)and(d,1)T-splines.展开更多
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB0640000)the Key Grant Project of the NSF of China(Grant No.12494552)the NSF of China(Grant No.12471360).
文摘Achieving linear complexity is crucial for demonstrating optimal convergence rates in adaptive refinement.It has been shown that the existing linear complexity local refinement algorithm for T-splines generally produces more degrees of freedom than the existing greedy refinement,which lacks linear complexity.This paper introduces a novel greedy local refinement algorithm for analysis-suitable T-splines,which achieves linear complexity and requires fewer control points than existing algorithms with linear complexity.Our approach is based on the observation that confining refinements around each T-junction to a preestablished feasible region ensures the algorithm’s linear complexity.Building on this constraint,we propose a greedy optimization local refinement algorithm that upholds linear complexity while significantly reducing the degrees of freedom relative to previous linear complexity local refinement methods.
基金This work was supported by the NSF of China(No.11031007,No.60903148)the Chinese Universities Scientific Fund,SRF for ROCS SE,the CAS Startup Scientific Research Foundation and NBRPC 2011CB302400.
文摘Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aided Geom Design 29:63-76,2012;Scott et al.Comput Methods Appl Mech Eng 213-216,2012).The paper independently derives a class of bi-degree(d_(1),d_(2))T-splines for which no perpendicular T-junction extensions intersect,and provides a new proof for the linearly independence of the blending functions.We also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation.
文摘Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis （IGA） oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines.
基金supported by the NSF of China(No.61872328)NKBR-PC(2011CB302400)+1 种基金SRF for ROCS SEthe Youth Innovation Promotion Association CAS.
文摘The present paper conjectures a topological condition which classifies a T-spline into standard,semi-standard and non-standard.We also provide the basic framework to prove the conjecture on the classification of semi-standard T-splines and give the proof for the semi-standard of bi-degree(1,d)and(d,1)T-splines.
