TY - CONF
T1 - Evaluation of convergence rate in extraordinary regions for isogeometric analysis of models with arbitrary topology
AU - MA, Weiyin
AU - YUAN, Xiaoyun
AU - MA, Yue
AU - MAHMUD, Md Asif
PY - 2015/6/1
Y1 - 2015/6/1
N2 - In the literature, one may find results in isogeometric analysis (IGA) for models defined by a control mesh of arbitrary topology, such as using subdivision methods, mapped B-spline basis functions and unstructured T-splines. It is generally understood that the convergence of analysis at extraordinary regions is usually lower than that in regular regions. There is however no systematic study about the convergence properties in such extraordinary regions. In the first part of this talk, we present a numerical method for convergence rate evaluation in isogeometric analysis, named L2-STF [1]. The method is based on L2 projection [2-4], a set of standard geometry stencils and a class of scaled target functions. In case of regular meshes using cubic B-splines, mapped B-splines or unstructured T-splines, the method produces standard convergence rate of commonly known in the literature. In cases of unstructured meshes using mapped B-splines or unstructured T-splines of degree 3, it produces reliable convergence rate in extraordinary regions. The method can be applied for convergence evaluation in IGA using any basis functions. In the second part of this talk, we present some consolidated computation results [1] on convergence rate evaluation for two known schemes of isogeometric analysis using mapped B-spline basis functions [5] and unstructured T-splines [6]. The results are systematically computed for a set of standard geometry stencils representing physical domains against a class of scaled target functions representing underlying field solutions. The results reconfirm the above mentioned rates and that the local convergence rate in an extraordinary region is dependent to the corresponding valence, i.e., number of edges meeting at an extraordinary vertex.
AB - In the literature, one may find results in isogeometric analysis (IGA) for models defined by a control mesh of arbitrary topology, such as using subdivision methods, mapped B-spline basis functions and unstructured T-splines. It is generally understood that the convergence of analysis at extraordinary regions is usually lower than that in regular regions. There is however no systematic study about the convergence properties in such extraordinary regions. In the first part of this talk, we present a numerical method for convergence rate evaluation in isogeometric analysis, named L2-STF [1]. The method is based on L2 projection [2-4], a set of standard geometry stencils and a class of scaled target functions. In case of regular meshes using cubic B-splines, mapped B-splines or unstructured T-splines, the method produces standard convergence rate of commonly known in the literature. In cases of unstructured meshes using mapped B-splines or unstructured T-splines of degree 3, it produces reliable convergence rate in extraordinary regions. The method can be applied for convergence evaluation in IGA using any basis functions. In the second part of this talk, we present some consolidated computation results [1] on convergence rate evaluation for two known schemes of isogeometric analysis using mapped B-spline basis functions [5] and unstructured T-splines [6]. The results are systematically computed for a set of standard geometry stencils representing physical domains against a class of scaled target functions representing underlying field solutions. The results reconfirm the above mentioned rates and that the local convergence rate in an extraordinary region is dependent to the corresponding valence, i.e., number of edges meeting at an extraordinary vertex.
M3 - 33_Other conference paper
T2 - IGA 2015 - The Third International Conference on Isogeometric Analysis
Y2 - 1 June 2015 through 3 June 2015
ER -