TY - GEN

T1 - Solving initial value problems by the Picard-Chebyshev method with NVIDIA GPUS

AU - Bai, Xiaoli

AU - Junkins, John L.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Combining the Picard method with Chebyshev polynomials, we can solve a large number of initial value problems using parallel computation. We develop a matrixvector form of Picard-Chebyshev method and implement it using a NVIDIA graphics card. The algorithm is developed in the NVIDIA CUDA environment and utilize the CUBLAS toolbox. Compared with ODE45 (the Runge-Kutta 45 algorithm implemented in MATLAB), the speedup from using Picard-Chebyshev method for the exemplar problem is about a factor of 30 to 120. Compared with a CPU version of the Picard-Chebyshev algorithm implemented in MATLAB, the speedup from using one NVIDIA graphics card is about a factor of 2 to 3. These results show that even with the simplest utilization of graphical processing units presently available, the speedup with parallel implementations of the Picard-Chebyshev algorithm is up to two order of magnitude.

AB - Combining the Picard method with Chebyshev polynomials, we can solve a large number of initial value problems using parallel computation. We develop a matrixvector form of Picard-Chebyshev method and implement it using a NVIDIA graphics card. The algorithm is developed in the NVIDIA CUDA environment and utilize the CUBLAS toolbox. Compared with ODE45 (the Runge-Kutta 45 algorithm implemented in MATLAB), the speedup from using Picard-Chebyshev method for the exemplar problem is about a factor of 30 to 120. Compared with a CPU version of the Picard-Chebyshev algorithm implemented in MATLAB, the speedup from using one NVIDIA graphics card is about a factor of 2 to 3. These results show that even with the simplest utilization of graphical processing units presently available, the speedup with parallel implementations of the Picard-Chebyshev algorithm is up to two order of magnitude.

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M3 - Conference contribution

AN - SCOPUS:80053404829

SN - 9780877035602

T3 - Advances in the Astronautical Sciences

SP - 1459

EP - 1476

BT - Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences

T2 - AAS/AIAA Space Flight Mechanics Meeting

Y2 - 14 February 2010 through 17 February 2010

ER -