Graph Grammar Based Multi-Frontal Solver for Isogeometric FEM Simulations On GPU

Abstract

We present a multi-frontal direct solver for two dimensional isogeometric finite element method simulations with NVIDIA CUDA and perform numerical experiments for linear, quadratic and cubic B-splines. We compare the computational cost O(Np2) for 2D parallel shared memory implementation with the corresponding estimate O(N1.5p3) for a standard 2D sequential implementation. We conclude the presentation with observa- tion that computational cost of the shared memory direct solver scales like p2 when we increase the global continuity of the isogeometric solution, which is an adventage with respect to sequential isogeometric solver scalability of the order of p3.