Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts
Abstract
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 (32more »
- Authors:
-
- Bucknell Univ., Lewisburg, PA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1499033
- Alternate Identifier(s):
- OSTI ID: 1550153
- Report Number(s):
- SAND-2019-2046J
Journal ID: ISSN 0167-8191; 672871
- Grant/Contract Number:
- AC04-94AL85000; NA-0003525
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Parallel Computing
- Additional Journal Information:
- Journal Volume: 68; Journal Issue: C; Journal ID: ISSN 0167-8191
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Parallel LU factorization; Multithreaded solvers; Circuit simulation; Solvers on Intel Xeon Phi
Citation Formats
Booth, Joshua Dennis, Ellingwood, Nathan David, Thornquist, Heidi K., and Rajamanickam, Sivasankaran. Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts. United States: N. p., 2017.
Web. doi:10.1016/j.parco.2017.06.003.
Booth, Joshua Dennis, Ellingwood, Nathan David, Thornquist, Heidi K., & Rajamanickam, Sivasankaran. Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts. United States. https://doi.org/10.1016/j.parco.2017.06.003
Booth, Joshua Dennis, Ellingwood, Nathan David, Thornquist, Heidi K., and Rajamanickam, Sivasankaran. Sat .
"Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts". United States. https://doi.org/10.1016/j.parco.2017.06.003. https://www.osti.gov/servlets/purl/1499033.
@article{osti_1499033,
title = {Basker: Parallel sparse LU factorization utilizing hierarchical parallelism and data layouts},
author = {Booth, Joshua Dennis and Ellingwood, Nathan David and Thornquist, Heidi K. and Rajamanickam, Sivasankaran},
abstractNote = {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.},
doi = {10.1016/j.parco.2017.06.003},
journal = {Parallel Computing},
number = C,
volume = 68,
place = {United States},
year = {Sat Jun 03 00:00:00 EDT 2017},
month = {Sat Jun 03 00:00:00 EDT 2017}
}
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Works referencing / citing this record:
Preparing sparse solvers for exascale computing
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