skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on November 1, 2020

Title: A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling

Abstract

A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the approximation error and significantly improves efficiency. Moreover, the deferred-compression technique introduces minimal overhead and does not affect parallelism. As a result, the new solver achieves linear computational complexity under mild assumptions and excellent parallel scalability. To demonstrate the performance of the new solver, we focus on applying it to solve sparse linear systems arising from ice sheet modeling. The strong anisotropic phenomena associated with the thin structure of ice sheets creates serious challenges for existing solvers. To address the anisotropy, we additionally developed a customized partitioning scheme for the solver, which captures the strong-coupling direction accurately. In general, the partitioning can be computed algebraically with existing software packages, and thus the new solver is generalizable for solving other sparse linear systems. Our results show that ice sheet problems of about 300 million degrees of freedom have been solved in just a few minutes using a thousand processors.

Authors:
 [1];  [1];  [2];  [2];  [2];  [1]
  1. Stanford Univ., CA (United States)
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Laboratories, Livermore, CA
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1559514
Alternate Identifier(s):
OSTI ID: 1547944
Report Number(s):
SAND2019-9481J
Journal ID: ISSN 0021-9991; 678447
Grant/Contract Number:  
AC04-94AL85000; NA0002373-1; NA-0003525
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 396; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Chen, Chao, Cambier, Leopold, Boman, Erik Gunnar, Rajamanickam, Sivasankaran, Tuminaro, Raymond S., and Darve, Eric. A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling. United States: N. p., 2019. Web. doi:10.1016/j.jcp.2019.07.024.
Chen, Chao, Cambier, Leopold, Boman, Erik Gunnar, Rajamanickam, Sivasankaran, Tuminaro, Raymond S., & Darve, Eric. A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling. United States. doi:10.1016/j.jcp.2019.07.024.
Chen, Chao, Cambier, Leopold, Boman, Erik Gunnar, Rajamanickam, Sivasankaran, Tuminaro, Raymond S., and Darve, Eric. Fri . "A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling". United States. doi:10.1016/j.jcp.2019.07.024.
@article{osti_1559514,
title = {A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling},
author = {Chen, Chao and Cambier, Leopold and Boman, Erik Gunnar and Rajamanickam, Sivasankaran and Tuminaro, Raymond S. and Darve, Eric},
abstractNote = {A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the approximation error and significantly improves efficiency. Moreover, the deferred-compression technique introduces minimal overhead and does not affect parallelism. As a result, the new solver achieves linear computational complexity under mild assumptions and excellent parallel scalability. To demonstrate the performance of the new solver, we focus on applying it to solve sparse linear systems arising from ice sheet modeling. The strong anisotropic phenomena associated with the thin structure of ice sheets creates serious challenges for existing solvers. To address the anisotropy, we additionally developed a customized partitioning scheme for the solver, which captures the strong-coupling direction accurately. In general, the partitioning can be computed algebraically with existing software packages, and thus the new solver is generalizable for solving other sparse linear systems. Our results show that ice sheet problems of about 300 million degrees of freedom have been solved in just a few minutes using a thousand processors.},
doi = {10.1016/j.jcp.2019.07.024},
journal = {Journal of Computational Physics},
number = C,
volume = 396,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 1, 2020
Publisher's Version of Record

Save / Share: