Intel ® Math Kernel Library PARDISO * for

The paper describes an efficient direct method to solve an equation Ax = b, where A is a sparse matrix, on the Intel ® Xeon PhiTM coprocessor. The main challenge for such a system is how to en-gage all available threads (about 240) and how to reduce OpenMP * synchronization overhead, which is very expensive for hundreds of threads. The method consists of decomposing A into a product of lower-triangular, diagonal, and upper triangular matrices followed by solves of the re-sulting three subsystems. The main idea is based on the hybrid parallel algorithm used in the In-tel ® Math Kernel Library Parallel Direct Sparse Solver for Clusters [1]. Our implementation ex-ploits a static scheduling algorithm during the factorization step to reduce OpenMP synchroniza-tion overhead. To effectively engage all available threads, a three-level approach of parallelization is used. Furthermore, we demonstrate that our implementation can perform up to 100 times bet-ter on factorization step and up to 65 times better in terms of overall performance on the 240 threads of the Intel ® Xeon PhiTM coprocessor