| Research Abstract |
This research has achieved the following results on the two main targets of the project :
1. Algebraic Multigrid Preconditioner for Finite Element Methods
MGCG, the geometric multigrid preconditioned conjugate gradient method, which has been proposed and implemented by our group in 1992, is one of the most effective and scalable solvers for convection diffusion equations, but it has a drawback of slow convergence on anisotropic problems. This study proposed AMGCG, the algebraic multigrid preconditioned conjugate gradient method based on smoothed aggregation, which cancels the effect of geometric anisotropy, and implemented on a SPARC workstation cluster with 256 CPUs. Experiments up to 250^3 mesh points showed that the method achieves more than three times as fast convergence as ICCG, the conjugate gradient method with incomplete Cholesky factorization, for the largest size. Furthermore, using parallel direct solver on the coarsest grid, the method shows constant convergence time even on isotropic problems.
2. High Performance Computing on Distributed Shared Memory
Distributed shared memory architecture is one of the key technologies to make high performance computing on commodity shared memory machines scalable. We have built Linux environments on two Intel Processor based distributed shared memory computers, NEC's AzusA and IBM's xSeries 440. Our implementation of low level basic linear algebra routines and fast Fourier transform codes shows that we can achieve good scalability on such commodity DSM architectures, but careful tuning of the operation system is also required to get lair memory bandwidth.
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