Higher‐order multi‐resolution topology optimization using the finite cell method

Groen, Jeroen; Langelaar, Matthijs; Sigmund, Ole; Ruess, Martin

doi:10.1002/nme.5432

Cited by 77 publications

(80 citation statements)

References 49 publications

(58 reference statements)

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“…If not, different designs may show similar performance, resulting in non-unique optima and unexpected convergence behavior. Numerical results related to a similar aspect have been reported in [10], where it is shown that varying the density resolution beyond a certain threshold can lead to unacceptable solutions. Moreover, introducing more design freedom than can be observed from the model only adds to the computational burden.…”

Section: Introductionsupporting

confidence: 59%

“…The approach of increasing the polynomial interpolation order to represent more complex material descriptions is also found in the finite cell method. For more numerical examples on finite cell method-based TO that illustrate the interplay between design and analysis resolutions, see [10]. From the numerical cases studied earlier, it can be understood that the proper choice of the number of design points depends on the chosen FEM scheme.…”

Section: Numerical Examplementioning

confidence: 99%

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Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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SUMMARYTopology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing nonuniqueness.

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Section: Introductionsupporting

confidence: 59%

Section: Numerical Examplementioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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“…On the other hand, there are some studies that choose to increase the resolution of the design variable mesh and maintain a coarser finite element mesh. Based on the work of Nguyen (2010), the high-order finite elements were used to improve the accuracy and efficiency of the algorithm (Groen et al 2017). An adaptive refinement/coarsening criterion was used to further accelerate the multi-resolution topology optimization method (Gupta et al 2018).…”

Section: Method Moving Morphablementioning

confidence: 99%

An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

Liu¹,

Liu²,

Wen³

et al. 2019

Preprint

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Topology optimization is a pioneering design method that can provide various candidates with high mechanical properties. However, the high-resolution for the optimum structures is highly desired, normally in turn leading to computationally intractable puzzle, especially for the famous Solid Isotropic Material with Penalization (SIMP) method. In this paper, we introduce the Super-Resolution Convolutional Neural Network (SRCNN) technique into topology optimization framework to improve the resolution of topology solutions with extremely high computational efficiency. Additionally, a pooling strategy is established to balance the number of finite element analysis (FEA) and the output mesh in optimization process. Considering the high training cost of 3D neural networks, several 2D neural networks are combined to deal with 3D topology optimization design problems. The combined treatment method used in 3D topology optimization design eliminates the expense of retraining 3D convolutional neural network and guarantees the quality of 3D design. Some typical examples justify that the high-resolution topology optimization method adopting SRCNN has excellent applicability and high efficiency.

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“…Immersed finite element techniques, such as the finite cell method [1][2][3], Cut-FEM [4,5] and immersogeometric analysis [6,7], have been successfully applied to a broad range of problems. Noteworthy applications include isogeometric analysis on trimmed CAD objects, e.g., [8][9][10][11][12][13], fluid-structure interaction with large displacements, e.g., [14][15][16][17][18][19][20][21], scan based analysis [22][23][24][25][26][27] and topology optimization, e.g., [28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

et al. 2019

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Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system matrix, which generally degrades efficiency and robustness of iterative solvers. In this contribution we investigate the spectral properties of immersed finite element systems treated by Schwarz-type methods, to establish the suitability of these as smoothers in a multigrid method. Based on this investigation we develop a geometric multigrid preconditioner for immersed finite element methods, which provides mesh-independent and cut-element-independent convergence rates. This preconditioning technique is applicable to higher-order discretizations, and enables solving large-scale immersed systems in parallel, at a computational cost that scales linearly with the number of degrees of freedom. The performance of the preconditioner is demonstrated for conventional Lagrange basis functions and for isogeometric discretizations with both uniform B-splines and locally refined approximations based on truncated hierarchical B-splines.

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Higher‐order multi‐resolution topology optimization using the finite cell method

Cited by 77 publications

References 49 publications

Bounds for decoupled design and analysis discretizations in topology optimization

Bounds for decoupled design and analysis discretizations in topology optimization

An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

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