报告题目：Extended r-Adaptive Isogeometric Analysis: From Prescribed to Image-Derived Interfaces

报 告 人：Jingyi Cao/曹静宜（Dalian University of Technology）

报告时间：2026年10月19日（星期一）17:00—17:30

报告地点：数学科学学院115（大报告厅）  

校内联系人：朱春钢 教授         联系方式：84708351-8618

报告摘要：Material interfaces in heterogeneous solids often lead to weak discontinuities: displacements remain continuous across an interface, while their gradients may jump. Extended isogeometric analysis (XIGA) captures these jumps through enrichment, but insufficient resolution near interfaces can still limit its accuracy. This talk presents an extended r-adaptive isogeometric framework and its development from prescribed material interfaces to interfaces extracted from images and scans.

The framework combines interface enrichment with control-point relocation, bringing together the ability to represent gradient jumps and the flexibility to redistribute resolution near material interfaces. A Gaussian monitor based on an aggregated level-set description guides the relocation of control points while preserving the CAD geometry, spline topology, and number of degrees of freedom. This allows the existing discretization to better resolve interface regions without mesh refinement. Numerical benchmarks show error reductions of up to 65.7% compared with XIGA without adaptivity, with less than 1% additional computational cost, demonstrating the benefit of coupling enrichment with adaptive parameterization.

Building on this work, we extend the approach to image-based models. Interface information extracted from images and scans guides the construction of an adapted NURBS parameterization before the elasticity solve, without requiring a preliminary solution or an a posteriori error estimate. The workflow connects image-derived interfaces with mesh redistribution and XIGA analysis, with suitable quadrature for interface-cut elements. Two- and three-dimensional examples examine the resulting meshes and solution accuracy in comparison with uniform-mesh XIGA.

报告人简介：Jingyi Cao is a PhD student in Computational Mathematics at Dalian University of Technology, China. Her research focuses on improving extended isogeometric analysis for weak-discontinuity problems through r-adaptive spline parameterization, with current work extending this approach to image-based models, including the development of suitable quadrature rules for interface-cut elements.