Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts

Journal Article · · Parallel Computing
 [1];  [2];  [2];  [2]
  1. Bucknell Univ., Lewisburg, PA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Transient simulation in circuit simulation tools, such as SPICE and Xyce, depend on scalable and robust sparse LU factorizations for efficient numerical simulation of circuits and power grids. As the need for simulations of very large circuits grow, the prevalence of multicore architectures enable us to use shared memory parallel algorithms for such simulations. A parallel factorization is a critical component of such shared memory parallel simulations. We develop a parallel sparse factorization algorithm that can solve problems from circuit simulations efficiently, and map well to architectural features. This new factorization algorithm exposes hierarchical parallelism to accommodate irregular structure that arise in our target problems. It also uses a hierarchical two-dimensional data layout which reduces synchronization costs and maps to memory hierarchy found in multicore processors. We present an OpenMP based implementation of the parallel algorithm in a new multithreaded solver called Basker in the Trilinos framework. Here, 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 simulation. Basker achieves a geometric mean speedup of 5.91× on CPU (16 cores) and 7.4× on Xeon Phi (32 cores) relative to state-of-the-art solver KLU. Basker outperforms Intel MKL Pardiso solver (PMKL) by as much as 30× on CPU (16 cores) and 7.5× on Xeon Phi (32 cores) for low fill-in circuit matrices. Furthermore, Basker provides 5.4× speedup on a challenging matrix sequence taken from an actual Xyce simulation.

Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1499033
Alternate ID(s):
OSTI ID: 1550153
Report Number(s):
SAND--2019-2046J; 672871
Journal Information:
Parallel Computing, Journal Name: Parallel Computing Journal Issue: C Vol. 68; ISSN 0167-8191
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (18)

An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination journal January 1999
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix journal January 2001
Algorithmic Aspects of Vertex Elimination on Graphs journal June 1976
An Approximate Minimum Degree Ordering Algorithm journal October 1996
Sparse Partial Pivoting in Time Proportional to Arithmetic Operations journal September 1988
The university of Florida sparse matrix collection journal November 2011
Algorithmic Aspects of Vertex Elimination on Directed Graphs journal January 1978
Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout report January 2016
A Supernodal Approach to Sparse Partial Pivoting journal January 1999
Kokkos: Enabling manycore performance portability through polymorphic memory access patterns journal December 2014
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems journal June 2003
Algorithm 907: KLU, A Direct Sparse Solver for Circuit Simulation Problems journal September 2010
The Theory of Elimination Trees for Sparse Unsymmetric Matrices journal January 2005
A survey of direct methods for sparse linear systems journal May 2016
PARDISO: a high-performance serial and parallel sparse linear solver in semiconductor device simulation journal September 2001
PaStiX: a high-performance parallel direct solver for sparse symmetric positive definite systems journal February 2002
The Role of Elimination Trees in Sparse Factorization journal January 1990
Computing the block triangular form of a sparse matrix journal December 1990

Cited By (1)

Preparing sparse solvers for exascale computing
  • Anzt, Hartwig; Boman, Erik; Falgout, Rob
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2166 https://doi.org/10.1098/rsta.2019.0053
journal January 2020