A Complete Particle Finite Element Method Pipeline On The GPU
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The α-shape of a point set generalizes the notion of convex hull and is used at every iteration of the Particle Finite Element Method (PFEM) to approximate the boundaries of the computational domain. In the case of incompressible flows the α-shape is used to retrieve the free-surface. Until now, PFEM implementations computed the α-shape by removing triangles with a large circumradius from the Delaunay Triangulation and subsequently assembled the linear system on CPU. The system is then solved either on CPU (e.g. Pardiso, PETSc) which can be slow for large systems, or GPU (e.g. cuDSS) which requires to transfer the system to the GPU memory. Earlier this year, the authors developed a GPU algorithm able to compute the α-shape of a million 2D point set in 50 milliseconds, more than an order of magnitude faster than previously possible. Computing the mesh on the GPU yields a performance improvement as we are now able to assemble and solve the system directly on GPU. This means that besides the initial transfer of the point cloud to the GPU, this implementation does not require any additional memory transfers between the CPU and GPU! In this work, we use our implementation of the α-shape to propose what we believe to be the first PFEM pipeline completely running on the GPU.