  Scalable sparse LU factorization is critical for efficient numerical
simulation of circuits and electrical power grids. In this work, we present a
new scalable sparse direct solver called Basker. Basker introduces a new
algorithm to parallelize the Gilbert-Peierls algorithm for sparse LU
factorization. As architectures evolve, there exists a need for algorithms that
are hierarchical in nature to match the hierarchy in thread teams, individual
threads, and vector level parallelism. Basker is designed to map well to this
hierarchy in architectures. There is also a need for data layouts to match
multiple levels of hierarchy in memory. Basker uses a two-dimensional
hierarchical structure of sparse matrices that maps to the hierarchy in the
memory architectures and to the hierarchy in parallelism. We present
performance evaluations of Basker on the Intel SandyBridge and Xeon Phi
platforms using circuit and power grid matrices taken from the University of
Florida sparse matrix collection and from Xyce circuit simulations. Basker
achieves a geometric mean speedup of 5.91x on CPU (16 cores) and 7.4x on Xeon
Phi (32 cores) relative to KLU. Basker outperforms Intel MKL Pardiso (PMKL) by
as much as 53x on CPU (16 cores) and 13.3x on Xeon Phi (32 cores) for low
fill-in circuit matrices. Furthermore, Basker provides 5.4x speedup on a
challenging matrix sequence taken from an actual Xyce simulation.
