Isogeometric Analysis

For my PhD thesis, I developed Mixed-Galerkin and Least-Squares formulations for the simulation of compressible and nearly incompressible hyperelastic as well as elasto-plastic material models, and incompressible Navier-Stokes using NURBS-based Isogeometric analysis ( Link1, Link2, Link3 ).

Subdivision stabilisation for NURBS

In the Taylor-Hood elements popularly used in mixed formulations, the pressure space is one order lower than that used for the displacement field. We have demonstrated that extending the Taylor-Hood element concept to NURBS does not yield inf-sup stable combinations. When it comes to NURBS, it is the subdivision that provides inf-sup stable combinations rather than the degree of basis functions.

Check our paper (Link2) for more details.