TY - JOUR
T1 - On the use of multigrid preconditioners for topology optimization
AU - Peetz, Darin
AU - Elbanna, Ahmed
N1 - Funding Information:
This work received financial support from the National Science Foundation through awards 1435920 and 1753249. Acknowledgments
PY - 2020
Y1 - 2020
N2 - Topology optimization for large-scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the finite element analysis (FEA). However, the preconditioners used in these works vary, and in many cases are notably suboptimal. A handful of works have already demonstrated the effectiveness of geometric multigrid (GMG) preconditioners in topology optimization. We provide a direct comparison of GMG preconditioners with algebraic multigrid (AMG) preconditioners. We demonstrate that AMG preconditioners offer improved robustness over GMG preconditioners as topologies evolve, albeit with a higher overhead cost. In 2D the gain from increased robustness more than offsets the overhead cost. However, in 3D the overhead becomes prohibitively large. We thus demonstrate the benefits of mixing geometric and algebraic methods to limit overhead cost while improving robustness, particularly in 3D.
AB - Topology optimization for large-scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the finite element analysis (FEA). However, the preconditioners used in these works vary, and in many cases are notably suboptimal. A handful of works have already demonstrated the effectiveness of geometric multigrid (GMG) preconditioners in topology optimization. We provide a direct comparison of GMG preconditioners with algebraic multigrid (AMG) preconditioners. We demonstrate that AMG preconditioners offer improved robustness over GMG preconditioners as topologies evolve, albeit with a higher overhead cost. In 2D the gain from increased robustness more than offsets the overhead cost. However, in 3D the overhead becomes prohibitively large. We thus demonstrate the benefits of mixing geometric and algebraic methods to limit overhead cost while improving robustness, particularly in 3D.
KW - Multigrid
KW - Topology optimization
UR - http://www.scopus.com/inward/record.url?scp=85094634041&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85094634041&partnerID=8YFLogxK
U2 - 10.1007/s00158-020-02750-w
DO - 10.1007/s00158-020-02750-w
M3 - Article
AN - SCOPUS:85094634041
JO - Structural and Multidisciplinary Optimization
JF - Structural and Multidisciplinary Optimization
SN - 1615-147X
ER -