## On the scalability of the *Albany/FELIX* first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets

## Abstract

We examine the scalability of the recently developed *Albany/FELIX* finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditioner results in faster linear solve times but the ILU preconditioner exhibits better scalability. In addition, a weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. We show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than onmore »

- Authors:

- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1201743

- Alternate Identifier(s):
- OSTI ID: 1214669; OSTI ID: 1214670

- Grant/Contract Number:
- AC04-94AL85000; AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Procedia Computer Science

- Additional Journal Information:
- Journal Volume: 51; Journal Issue: C; Journal ID: ISSN 1877-0509

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; 97 MATHEMATICS AND COMPUTING; ice sheet model; first-order Stokes approximation; finite element method; scalability; ILU preconditioner; algebraic multigrid (AMG) preconditioner; semi-coarsening; Greenland; Antarctica; Algebraic multigrid (AMG) preconditioner

### Citation Formats

```
Tezaur, Irina K., Tuminaro, Raymond S., Perego, Mauro, Salinger, Andrew G., and Price, Stephen F. On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets. United States: N. p., 2015.
Web. doi:10.1016/j.procs.2015.05.467.
```

```
Tezaur, Irina K., Tuminaro, Raymond S., Perego, Mauro, Salinger, Andrew G., & Price, Stephen F. On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets. United States. doi:10.1016/j.procs.2015.05.467.
```

```
Tezaur, Irina K., Tuminaro, Raymond S., Perego, Mauro, Salinger, Andrew G., and Price, Stephen F. Thu .
"On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets". United States. doi:10.1016/j.procs.2015.05.467. https://www.osti.gov/servlets/purl/1201743.
```

```
@article{osti_1201743,
```

title = {On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets},

author = {Tezaur, Irina K. and Tuminaro, Raymond S. and Perego, Mauro and Salinger, Andrew G. and Price, Stephen F.},

abstractNote = {We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditioner results in faster linear solve times but the ILU preconditioner exhibits better scalability. In addition, a weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. We show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than on the AMG preconditioner.},

doi = {10.1016/j.procs.2015.05.467},

journal = {Procedia Computer Science},

number = C,

volume = 51,

place = {United States},

year = {2015},

month = {1}

}

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