Incomplete LU (ILU) methods are widely used in petroleum reservoir simulation and many other applications. However high complexity oftenmakes them the hotspot in the whole simulation due to high complexity when problem size is large. ILU's inherent serial nature also makes them difficult to take full advantage of computing power of multi-core and many-core devices. In this paper, a greedy graph coloringmethod is applied to the ILU(k) factorization and triangular solution phases. This method increases degree of parallelism and improves load balance.Ablock-wise storage format is employed in our ILU implementation in order to take advantage of hierarchical memory structures.Moreover, a dual intensive parallelmodel is proposed to further improve the performance of ILU(k) on GPUs. We test the performance of the proposed parallel ILU(k) with a set of Jacobian systems arising from petroleum reservoir simulation. Numerical results suggest that the proposed parallel ILU(k) method is effective and robust on multi-core and many-core architectures. On an Intel Xeon E5 multi-core CPU, the speedup compared with the serial execution time is 5.6× and 5.4× for factorization and triangular solution, respectively; on an Nvidia K40c GPU card, the speedup can reach 8.6× and 12.7× for factorization and triangular solution, respectively.
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