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Section: Highlights of the Year

Highlights of the Year

We have presented two approaches using a Block Low-Rank (BLR) compression technique to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver PaStiX. Thanks to this compression technique, we have been able to solve a 1 billion unknown system (a 3D Laplacian matrix $100\times 100\times 100.000$) on a single node with 3Tb of memory. The factorization time for this system was less than 6 hours using 96 cores, and the precision achieved at the first solve was ${10}^{-5}$. With 10 additional iterative refinement steps, we reached easily ${10}^{-8}$ in double precision. The cost of one solve was limited to 280 seconds. We were able to save 9Tb over the 11Tb that would be requested by the direct solver. The last release of the software (PaStiX 6.0) includes these implementations and the description of the parameters are documented in solverstack/pastix.

2017 has been the last year of the FASTLA associate team that has been for 6 years the framework of fruitful and intense research collaborations with Lawrence Berkeley National Laboratory and Stanford University on data sparse numerical algorithms; the joint research addressed especially fast multipole techniques and low rank calculation in sparse linear algebra. This successful collaboration has been concluded by the participation of E. Ng, head of Applied Mathematics Department at Berkeley, to the two HDR juries of A. Guermouche andP. Ramet that have been defended on the same day, November 27th.