A New Basis for Hierarchical B-splines
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Hierarchical B-splines constructed from B-splines over nested domains, present an extension of traditional tensor product B-splines with local refinement property. This unique characteristic renders hierarchical B-splines well suited for both geometric modeling and isogeometric analysis. In this paper, we introduce a new construction of the basis functions of hierarchical B-splines that have smaller supports and have the completeness property. Through various examples of surface fitting and numerical solutions of PDEs, we demonstrate the superiority of the modified hierarchical B-splines over existing counterparts. Numerical results reveal that the new basis functions exhibit reduced condition numbers in solving PDEs, thereby ensuring enhanced numerical stability and superior performance in practical applications.