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Scalable sparse LU factorization is critical for efficient numericalsimulation of circuits and electrical power grids. In this work, we present anew scalable sparse direct solver called Basker. Basker introduces a newalgorithm to parallelize the Gilbert-Peierls algorithm for sparse LUfactorization. As architectures evolve, there exists a need for algorithms thatare hierarchical in nature to match the hierarchy in thread teams, individualthreads, and vector level parallelism. Basker is designed to map well to thishierarchy in architectures. There is also a need for data layouts to matchmultiple levels of hierarchy in memory. Basker uses a two-dimensionalhierarchical structure of sparse matrices that maps to the hierarchy in thememory architectures and to the hierarchy in parallelism. We presentperformance evaluations of Basker on the Intel SandyBridge and Xeon Phiplatforms using circuit and power grid matrices taken from the University ofFlorida sparse matrix collection and from Xyce circuit simulations. Baskerachieves a geometric mean speedup of 5.91x on CPU (16 cores) and 7.4x on XeonPhi (32 cores) relative to KLU. Basker outperforms Intel MKL Pardiso (PMKL) byas much as 53x on CPU (16 cores) and 13.3x on Xeon Phi (32 cores) for lowfill-in circuit matrices. Furthermore, Basker provides 5.4x speedup on achallenging matrix sequence taken from an actual Xyce simulation.

Basker: A Threaded Sparse LU Factorization Utilizing Hierarchical Parallelism and Data Layouts