Articles | Volume 11, issue 6
https://doi.org/10.5194/se-11-2031-2020
https://doi.org/10.5194/se-11-2031-2020
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

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Cited articles

Aliaga, J. I., Bollhöfer, M., Dufrechou, E., Ezzatti, P., and Quintana-Ortí, E. S.: Leveraging Data-Parallelism in ILUPACK using Graphics Processors, in: 2014 IEEE 13th International Symposium on Parallel and Distributed Computing, 119–126, https://doi.org/10.1109/ISPDC.2014.19, 2014. a
Aliaga, J. I., Badia, R. M., Barreda, M., Bollhöfer, M., Dufrechou, E., Ezzatti, P., and Quintana-Ortí, E. S.: Exploiting Task and Data Parallelism in ILUPACK's Preconditioned CG Solver on NUMA Architectures and Many-Core Accelerators, Parallel Computing, 54, 97–107, 2016a. a
Aliaga, J. I., Bollhöfer, M., Dufrechou, E., Ezzatti, P., and Quintana-Ortí, E. S.: A Data-Parallel ILUPACK for Sparse General and Symmetric Indefinite Linear Systems, in: European Conference on Parallel Processing, Springer, 121–133, 2016b. a
Aliaga, J. I., Barreda, M., Flegar, G., Bollhöfer, M., and Quintana-Ortí, E. S.: Communication in Task-Parallel ILU-Preconditioned CG Solvers using MPI+OmpSs, Concurr. Comput.-Pract. E., 29, e4280, https://doi.org/10.1002/cpe.4280, 2017. a
Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. D., Karpeyev, D., Kaushik, D., Knepley, M. G., May, D. A., McInnes, L. C., Mills, R. T., Munson, T., Rupp, K., Sanan, P., Smith, B. F., Zampini, S., Zhang, H., and Zhang, H.: PETSc Web page, available at: https://www.mcs.anl.gov/petsc (last access: 27 October 2020), 2019a. a, b, c
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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.