Quadratic splines on unstructured meshes for fourth-order problems

Deepesh Toshniwal (TU Delft)

Abstract. Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from Computer-Aided Design models, which is in general a non-trivial and time-consuming task. This talk will present an overview of new piecewise-quadratic spline constructions [1-3] that enable model reconstruction, as well as simulation of high-order PDEs on the reconstructed models. In particular, we will discuss splines on unstructured meshes in both two and three dimensions.
[1] Toshniwal, D. (2022). Quadratic splines on quad-tri meshes: Construction and an application to simulations on watertight reconstructions of trimmed surfaces. Computer Methods in Applied Mechanics and Engineering, 388, 114174.
[2] Koh, K. J., Toshniwal, D., & Cirak, F. (2021). An optimally convergent smooth blended B-spline construction for unstructured quadrilateral and hexahedral meshes. arXiv preprint arXiv:2111.04401.
[3] Takacs, T., & Toshniwal, D. (2022). Almost-$C^1$ splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems. arXiv preprint arXiv:2201.11491.