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

Chen, Chao; Cambier, Leopold; Boman, Erik Gunnar; Rajamanickam, Sivasankaran; Tuminaro, Raymond S.; Darve, Eric

doi:10.1016/j.jcp.2019.07.024

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

Journal Article · Fri Nov 01 00:00:00 EDT 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.07.024· OSTI ID:1559514

Chen, Chao ^[1]; Cambier, Leopold ^[1]; Boman, Erik Gunnar ^[2]; Rajamanickam, Sivasankaran ^[2]; Tuminaro, Raymond S. ^[2]; Darve, Eric ^[1]

Stanford Univ., CA (United States)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)

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.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1559514

Alternate ID(s):: OSTI ID: 1547944

Report Number(s):: SAND2019-9481J; 678447; TRN: US2000355

Journal Information:: Journal of Computational Physics, Vol. 396, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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