International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428613000676

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

Maciej Paszyński^1,a, Krzysztof Kuźnik^1,b, Victor Manuel Calo² and David Pardo^{3 1}AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunication, Department of Computer Science al. A. Mickiewicza 30, 30-059, Krakow, Poland. ^akmkuznik@gmail.com ^bkmkuznik@gmail.com ²King Abdullah University of Science and Technology, Applied Mathematics & Computational Science, Earth Science & Engineering Center for Numerical Porous Media,
4700 King Abdullah University of Science and Technology, al-Khawarizmi Bldg (Bldg 1), Office # 4110, Thuwal 23955-6900, Kingdom of Saudi Arabia. vmcalo@gmail.com ³The University of The Basque Country, Department of Applied Mathematics, Statistics and Operational Research, 00100 University of the Basque Country, Barrio Sarriena S/N,
Campus de Leioa, 48940 Leioa (Vizcaya), Spain. dzubiaur@gmail.com

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(N^1.5p³) 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.

Keywords: Multi-frontal direct solver, Isogeometric finite element method, Computational cost, Shared memory machine.

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