Multi-grid reduced-order topology optimization

Xiao, Manyu; Lu, Dongcheng; Breitkopf, Piotr; Raghavan, Balaji; Zhang, Weihong; Dutta, Subhrajit

doi:10.1007/s00158-020-02570-y

Cited by 27 publications

(5 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are two types of AMG strategies: SA (Superior-Aggressive)/(Smooth Aggregation) and CF (Coarse-Fine). MG techniques use Gauss-Seidel, Jacobi, consecutive over or under relaxation techniques, which spread the corrective and residual vectors across various resolutions or levels utilizing prolongation and limitation operators to smooth out elevated errors and expedite convergence (Peetz and Elbanna, 2021;Xiao et al, 2020). The MG solver's computing effort grows proportionally to the number of Degrees of Freedom (DOF), and the convergence rate is irrespective of the resolution, thanks to three essential steps: coarse-grid correction, pre-smoothing and postsmoothing (Amir et al, 2014).…”

Section: Multi-grid Methodsmentioning

confidence: 99%

Section: Innovation In Optimization Phenomenonmentioning

confidence: 99%

See 1 more Smart Citation

A review on developing optimization techniques in civil engineering

Zaheer

Manzoor²,

Ahamad³

2023

View full text Add to dashboard Cite

PurposeThe purpose of this article is to analyze the optimization process in depth, elaborating on the components of the entire process and the techniques used. Researchers have been drawn to the expanding trend of optimization since the turn of the century. The rate of research can be used to measure the progress and increase of this optimization procedure. This study is phenomenal to understand the optimization process and different algorithms in addition to their application by keeping in mind the current computational power that has increased the implementation for several engineering applications.Design/methodology/approachTwo-dimensional analysis has been carried out for the optimization process and its approaches to addressing optimization problems, i.e. computational power has increased the implementation. The first section focuses on a thorough examination of the optimization process, its objectives and the development of processes. Second, techniques of the optimization process have been evaluated, as well as some new ones that have emerged to overcome the above-mentioned problems.FindingsThis paper provided detailed knowledge of optimization, several approaches and their applications in civil engineering, i.e. structural, geotechnical, hydraulic, transportation and many more. This research provided tremendous emerging techniques, where the lack of exploratory studies is to be approached soon.Originality/valueOptimization processes have been studied for a very long time, in engineering, but the current computational power has increased the implementation for several engineering applications. Besides that, different techniques and their prediction modes often require high computational strength, such parameters can be mitigated with the use of different techniques to reduce computational cost and increase accuracy.

show abstract

Section: Multi-grid Methodsmentioning

confidence: 99%

Section: Innovation In Optimization Phenomenonmentioning

confidence: 99%

A review on developing optimization techniques in civil engineering

Zaheer

Manzoor²,

Ahamad³

2023

View full text Add to dashboard Cite

show abstract

“…single-fidelity), which should be effectively computed in some way. So, based on the above mentioned method, [26] proposed an approach of multi-fidelity ROM construction using the multigrid method, where the original equilibrium equations are solved on grids of various resolutions, and then quickly obtain a multi-fidelity snapshot solution for constructing and updating the reduced basis.…”

Section: Multi-fidelity Rom Construction Using Multigridmentioning

confidence: 99%

“…and prolongation operators   1 + P can be seen in [26]. The smooth operators W use the PCG method.…”

Section: Multi-fidelity Rom Construction Using Multigridmentioning

confidence: 99%

“…In this work, we first apply two previously proposed ROM approaches to the stress-constrained topology optimization problem, the first being on-the-fly ROM using Principal Components Analysis (PCA) [25] and the other being multi-fidelity ROM using the multigrid method (MG) [26]. In addition, based on the proposed multi-fidelity ROM, we develop two improved strategies for further reductions in computational costs, the first one being the Adap-ROM where the residual threshold for the approximate solution of the equilibrium equations can be adaptively selected according to the relative error of the objective function value during the iteration; the second strategy being Bi-ROM where we simultaneously apply the ROM to both the equilibrium equations and adjoint equations (during the sensitivity analysis of the stress constraint).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stress-constrained topology optimization using approximate reanalysis with on-the-fly reduced order modeling

Xiao

et al. 2022

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

Most of the methods used today for handling local stress constraints in topology optimization, fail to directly address the non-self-adjointness of the stress-constrained topology optimization problem. This in turn could drastically raise the computational cost for an already large-scale problem. These problems involve both the equilibrium equations resulting from finite element analysis (FEA) in each iteration, as well as the adjoint equations from the sensitivity analysis of the stress constraints. In this work, we present a paradigm for large-scale stress-constrained topology optimization problems, where we build a multi-grid approach using an on-the-fly Reduced Order Model (ROM) and the p-norm aggregation function, in which the discrete reduced-order basis functions (modes) are adaptively constructed for adjoint problems. In addition to reducing the computational savings due to the ROM, we also address the computational cost of the ROM learning and updating phases. Both reduced-order bases are enriched according to the residual threshold of the corresponding linear systems, and the grid resolution is adaptively selected based on the relative error in approximating the objective function and constraint values during the iteration. The tests on 2D and 3D benchmark problems demonstrate improved performance with acceptable objective and constraint violation errors. Finally, we thoroughly investigate the influence of relevant stress constraint parameters such as the p norm factor, stress penalty factor, and the allowable stress value.

show abstract

Efficient stress‐constrained topology optimization using inexact design sensitivities

Amir

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

An efficient computational approach to stress‐constrained topology optimization is presented. Using a multigrid‐preconditioned Krylov solver for the state and adjoint problems, the number of Krylov iterations is reduced significantly by enforcing early termination of the iterative solves. The criterion for early termination is based on the convergence of the design sensitivities with respect to Krylov iterations. Consequently, the progress of optimization is not affected by the inexact resolution of the state and adjoint problems. The proposed approach is demonstrated on several design problems that possess different characteristics of the maximum stress. Optimization results obtained with early termination show very good agreement with those obtained with an accurate direct solver—in terms of objective value, constrained maximum stress and overall number of design cycles. Savings of 80% in the number of Krylov iterations are achieved, compared to the number of iterations required to satisfy the force residual convergence criterion to a common tolerance. The approach is directly applicable to high‐resolution problems that are solved on parallel computational environments. A MATLAB code for reproducing the results is freely available at https://github.com/odedamir/topopt-stress-inexact-sensitivities

show abstract

Multi-grid reduced-order topology optimization

Cited by 27 publications

References 41 publications

A review on developing optimization techniques in civil engineering

A review on developing optimization techniques in civil engineering

Stress-constrained topology optimization using approximate reanalysis with on-the-fly reduced order modeling

Efficient stress‐constrained topology optimization using inexact design sensitivities

Contact Info

Product

Resources

About