A parallel geometric multigrid method for adaptive topology optimization

This work presents an efficient parallel geometric multigrid (GMG) implementation for preconditioning Krylov subspace methods solving differential equations using non-conforming meshes for discretization. The approach does not constrain such meshes to the typical multiscale grids used by Cartesian h...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization Vol. 66; no. 10; p. 225
Main Authors: Herrero-Pérez, David, Picó-Vicente, Sebastián Ginés
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023
Springer Nature B.V
Subjects:
Cartesian coordinates
Computational Mathematics and Numerical Analysis
Differential equations
Engineering
Engineering Design
Finite element method
Interpolation
Multigrid methods
Octrees
Operators (mathematics)
Optimization
Preconditioning
Research Paper
Subspace methods
Theoretical and Applied Mechanics
Topology optimization
Topology optimization
Adaptivity
Parallel computing
Geometric multigrid
ISSN:1615-147X, 1615-1488
Online Access:Get full text
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Summary:This work presents an efficient parallel geometric multigrid (GMG) implementation for preconditioning Krylov subspace methods solving differential equations using non-conforming meshes for discretization. The approach does not constrain such meshes to the typical multiscale grids used by Cartesian hierarchical grid methods, such as octree-based approaches. It calculates the restriction and interpolation operators for grid transferring between the non-conforming hierarchical meshes of the cycle scheme. Using non-Cartesian grids in topology optimization, we reduce the mesh size discretizing only the design domain and keeping the geometry of boundaries in the final design. We validate the GMG method operating on non-conforming meshes using an adaptive density-based topology optimization method, which coarsens the finite elements dynamically following a weak material estimation criterion. The GMG method requires the generation of the hierarchical non-conforming meshes dynamically from the one used by the adaptive topology optimization to analyze to the one coarsening all the mesh elements until the coarsest level of the mesh hierarchy. We evaluate the performance of the adaptive topology optimization using the GMG preconditioner operating on non-conforming meshes using topology optimization on a fine-conforming mesh as the reference. We also test the strong and weak scaling of the parallel GMG preconditioner with two three-dimensional topology optimization problems using adaptivity, showing the computational advantages of the proposed method.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-023-03675-w