FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica
Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are...
Published in: | SIAM Journal on Scientific Computing |
---|---|
Main Authors: | , , |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
2022
|
Subjects: | |
Online Access: | http://resolver.tudelft.nl/uuid:b19efdbc-73f0-46f4-8599-98d4d05458b6 https://doi.org/10.1137/21M1395260 |
id |
fttudelft:oai:tudelft.nl:uuid:b19efdbc-73f0-46f4-8599-98d4d05458b6 |
---|---|
record_format |
openpolar |
spelling |
fttudelft:oai:tudelft.nl:uuid:b19efdbc-73f0-46f4-8599-98d4d05458b6 2024-04-28T07:58:35+00:00 FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica Heinlein, A. (author) Perego, Mauro (author) Rajamanickam, Sivasankaran (author) 2022 http://resolver.tudelft.nl/uuid:b19efdbc-73f0-46f4-8599-98d4d05458b6 https://doi.org/10.1137/21M1395260 en eng http://www.scopus.com/inward/record.url?scp=85128982962&partnerID=8YFLogxK SIAM Journal on Scientific Computing--1064-8275--30797d97-251f-4ed3-b419-69e3a5957f0b http://resolver.tudelft.nl/uuid:b19efdbc-73f0-46f4-8599-98d4d05458b6 https://doi.org/10.1137/21M1395260 © 2022 A. Heinlein, Mauro Perego, Sivasankaran Rajamanickam domain decomposition methods GDSW coarse spaces monolithic Schwarz preconditioners multiphysics simulations parallel computing journal article 2022 fttudelft https://doi.org/10.1137/21M1395260 2024-04-10T00:15:27Z Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level generalized Dryja-Smith-Widlund (GDSW)-type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)- parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32 K processor cores (8 K MPI ranks and ... Article in Journal/Newspaper Antarc* Antarctic Antarctica Greenland Ice Sheet Delft University of Technology: Institutional Repository SIAM Journal on Scientific Computing 44 2 B339 B367 |
institution |
Open Polar |
collection |
Delft University of Technology: Institutional Repository |
op_collection_id |
fttudelft |
language |
English |
topic |
domain decomposition methods GDSW coarse spaces monolithic Schwarz preconditioners multiphysics simulations parallel computing |
spellingShingle |
domain decomposition methods GDSW coarse spaces monolithic Schwarz preconditioners multiphysics simulations parallel computing Heinlein, A. (author) Perego, Mauro (author) Rajamanickam, Sivasankaran (author) FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica |
topic_facet |
domain decomposition methods GDSW coarse spaces monolithic Schwarz preconditioners multiphysics simulations parallel computing |
description |
Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level generalized Dryja-Smith-Widlund (GDSW)-type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)- parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32 K processor cores (8 K MPI ranks and ... |
format |
Article in Journal/Newspaper |
author |
Heinlein, A. (author) Perego, Mauro (author) Rajamanickam, Sivasankaran (author) |
author_facet |
Heinlein, A. (author) Perego, Mauro (author) Rajamanickam, Sivasankaran (author) |
author_sort |
Heinlein, A. (author) |
title |
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica |
title_short |
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica |
title_full |
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica |
title_fullStr |
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica |
title_full_unstemmed |
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica |
title_sort |
frosch preconditioners for land ice simulations of greenland and antarctica |
publishDate |
2022 |
url |
http://resolver.tudelft.nl/uuid:b19efdbc-73f0-46f4-8599-98d4d05458b6 https://doi.org/10.1137/21M1395260 |
genre |
Antarc* Antarctic Antarctica Greenland Ice Sheet |
genre_facet |
Antarc* Antarctic Antarctica Greenland Ice Sheet |
op_relation |
http://www.scopus.com/inward/record.url?scp=85128982962&partnerID=8YFLogxK SIAM Journal on Scientific Computing--1064-8275--30797d97-251f-4ed3-b419-69e3a5957f0b http://resolver.tudelft.nl/uuid:b19efdbc-73f0-46f4-8599-98d4d05458b6 https://doi.org/10.1137/21M1395260 |
op_rights |
© 2022 A. Heinlein, Mauro Perego, Sivasankaran Rajamanickam |
op_doi |
https://doi.org/10.1137/21M1395260 |
container_title |
SIAM Journal on Scientific Computing |
container_volume |
44 |
container_issue |
2 |
container_start_page |
B339 |
op_container_end_page |
B367 |
_version_ |
1797570448514351104 |