Extended r-adaptive isogeometric analysis for weak-discontinuous problems
Jingyi Cao (Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian University of Technology)
Ye Ji (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Matthias Möller (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Chungang Zhu (Dalian University of Technology, Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province)
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Abstract
This paper proposes an extended r-adaptive isogeometric analysis framework for problems exhibiting weak discontinuities in solution derivatives, where discretization errors are often dominated by insufficient resolution of material interfaces. The method combines enrichment functions with a control-point relocation strategy guided by a Gaussian monitor constructed from an aggregated level-set representation of the interfaces. Rather than refining the mesh, resolution is redistributed according to interface geometry, enabling sharp representation of gradient jumps while preserving exact CAD geometry, spline topology, and a fixed number of degrees of freedom. Benchmark examples indicate up to 65.7% error reduction relative to enrichment-only formulations, and even larger improvements compared with standard IGA, while introducing less than 1% additional computational cost. The results demonstrate that redistributing geometric resolution provides an efficient alternative to conventional refinement-based adaptive strategies for weak-discontinuous problems.
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