Graph Grammar Based Multi-Frontal Solver for Isogeometric FEM Simulations On GPU
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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.
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Wozniak, M.; Kuznik, K.; Paszynski, M.; Calo, Victor; Pardo, D. (2014)In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) ...
Garcia, D.; Pardo, D.; Dalcin, L.; Calo, Victor (2018)Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C 0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the ...
Kuznik, K.; Paszynski, M.; Calo, Victor (2013)In this paper, we present a multi-frontal direct solver for one-dimensional iso-geometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the ...