I'm Xinyun Li, a master student of Medical Engineering in Erlangen university, Gemrnay. It's great honor for me to have the chance to contribute to DUNE as a GSoC student. DUNE is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. This summer, I'm going to work on spline geometries for isogeometric analysis.
Project description
Isogeometric analysis is a finite element technique that allows to solve partial differential equations defined on spline surfaces. This is useful because a lot of geometries used in engineering are directly available in this format, and the grid generation step can be skipped. However, no Dune grid implementation is currently able to represent spline geometries. The goal of this project is to develop such a grid manager for the special case of spline surfaces representable as a single tensor-product patch.
Project milestones and timelines:
1.Implement the complete Geometry interface in the B-spline prototype(4 weeks)
Here is a documentation of Dund geometry interface. I am supposed to implement all members listed there.
2.Generalize the geometry interface from B-splines to NURBS(4 weeks)
2.Add iterator access and index sets to the above two grids to help ascess the gird elements more easily. (3 weeks)
Due to my personal schedules, I'm not able to work full time in July. So I would like to strat earlier and end earlier. I started working from mid April and have have already got some outcomes.
Difficulties:
Among all the interface functions, the inverse mapping is the most challenging one. Because the forward mapping is a recursive process. So I think it's analytically impossible. We need to find other ways to get the solution.
Besides, all functions require integration over the physical space is non-triveil. A linear solver may be needed.
