Cloth simulation with various methods such as implicit integration with stiff springs or continuum style approach (Baraff & Witkins). Also I implemented constraint-based inextensible cloth based on this paper. The fast project method in that paper uses a direct solver (PARDISO) but I implemented a new iterative approach for a better performance and convergence. I am currently working on writing it.
Cloth simulation uses continuous collision detection using qubic equation solver and proximity based impulses based on this paper.
For real-time, I am implementing GPGPU cloth simulation using OpenCL. It is using constraints for stretch links and batch processes for parallel processing. Entire simulation is in the GPU. It is a part of Bullet and under active development for two-way interaction with rigid-body simulation in OpenCL.
I made a 3DS Max plugin to test my cloth simulation as below. It can simulate cloth and closed body as below. If the object can be a tetrahedral mesh, it is possible to use it as a input mesh too.
Below is a screenshot of my 2D cloth simulator. I use 2D version to experiments various things i.e. multiple simultaneous collision handling and integration methods. It handles stacking robustly and maintains the thickness of cloth very well.