SIAM Journal on Scientific Computing
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
14.9 TFLOPS three-dimensional fluid simulation for fusion science with HPF on the Earth Simulator
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
A 15.2 TFlops Simulation of Geodynamo on the Earth Simulator
Proceedings of the 2004 ACM/IEEE conference on Supercomputing
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Proceedings of the 2006 ACM/IEEE conference on Supercomputing
High Performance Computing for Computational Science - VECPAR 2008
PDCN '08 Proceedings of the IASTED International Conference on Parallel and Distributed Computing and Networks
International Journal of High Performance Computing Applications
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
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In order to study a possibility of superfluidity in trapped atomic Fermi gases loaded on optical lattices, we implement an exact diagonalization code for the trapped Hubbard model on the Earth Simulator. Comparing two diagonalization algorithms, we find that the performance of the preconditioned conjugate gradient (PCG) method is 1.5 times superior to the conventional Lanczos one since the PCG method can conceal the communication overhead much more efficiently. Consequently, the PCG method shows 16.447 TFlops (50.2% of the peak) on 512 nodes. On the other hand, we succeed in solving a 159-billion-dimensional matrix by using the conventional Lanczos method. To our knowledge, this dimension is a world-record. Numerical results reveal that an unconventional type of superfluidity specific to the confined system develops under repulsive interaction.