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Articles | Volume 11, issue 6
Articles | Volume 11, issue 6
https://doi.org/10.5194/se-11-2031-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-11-2031-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 11, issue 6
Method article
 | 
10 Nov 2020
Method article |  | 10 Nov 2020

Pragmatic solvers for 3D Stokes and elasticity problems with heterogeneous coefficients: evaluating modern incomplete LDLT preconditioners

Patrick Sanan, Dave A. May, Matthias Bollhöfer, and Olaf Schenk

Supplement

https://doi.org/10.5194/se-11-2031-2020-supplement

Model code and software

exSaddle Dave A. May and Patrick Sanan https://doi.org/10.5281/zenodo.4040667

Algebraic Multilevel Pre-conditioner for the Helmholtz Equation in Heterogeneous Media M. Bollhöfer, M. Grote, and o. Schenk https://doi.org/10.1137/080725702

A Sur- vey of Direct Methods for Sparse Linear Systems T. A. Davis, S. Rajamanickam, and W. M. Sid-Lakhdar https://doi.org/10.1017/S0962492916000076

PETSc S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, A. Dener, V. Eijkhout,W. D. Gropp, D. Karpeyev, D. Kaushik, M. G. Knepley, D. A. May, L. C. McInnes, R. T. Mills, T. Munson, K. Rupp, P. Sanan, B. F. Smith, S. Zampini, H. Zhang, and H. Zhang https://www.mcs.anl.gov/petsc

PCILUPACK P. Sanan https://github.com/psanan/pcilupack

PARDISO-PETSc wrapper P. Sanan, and R. Janalik https://bitbucket.org/psanan/petsc/branch/psanan/pardiso-3.12.4

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Short summary
Mantle and lithospheric dynamics, elasticity, subsurface flow, and other fields involve solving indefinite linear systems. Tools include direct solvers (robust, easy to use, expensive) and advanced iterative solvers (complex, problem-sensitive). We show that a third option, ILDL preconditioners, requires less memory than direct solvers but is easy to use, as applied to 3D problems with parameter jumps. With included software, we hope to allow researchers to solve previously infeasible problems.
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