Extended isogeometric analysis for material interface problems. (English) Zbl 1331.74166
Summary: We propose an approach to extend the isogeometric analysis (IGA) method to solve material interface problems. The development is carried out through incorporating the advantages of the extended finite element method into the standard IGA approach for solving problems with discontinuities. By applying both the XIGA and IGA methods to solve Poisson’s equation problem containing weak discontinuities, we demonstrate that the XIGA achieves the optimal convergence rate, whereas the IGA only converges suboptimally. The proposed method is then successfully applied to solve bimaterial and curved material interface problems.
MSC:
74S05 | Finite element methods applied to problems in solid mechanics |
65D07 | Numerical computation using splines |
74A50 | Structured surfaces and interfaces, coexistent phases |
65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
65D17 | Computer-aided design (modeling of curves and surfaces) |