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Towards Scalable Topology Optimizati...

Ye, Zisheng,

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Towards Scalable Topology Optimization, Classical or Quantum? /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Towards Scalable Topology Optimization, Classical or Quantum? // Zisheng Ye.
Author:	Ye, Zisheng,
Description:	1 electronic resource (187 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
Contained By:	Dissertations Abstracts International86-11B.
Subject:	Computational physics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32040162
ISBN:	9798314888391

Towards Scalable Topology Optimization, Classical or Quantum? /
Ye, Zisheng,

Towards Scalable Topology Optimization, Classical or Quantum? /Zisheng Ye. - 1 electronic resource (187 pages)

Source: Dissertations Abstracts International, Volume: 86-11, Section: B.

Continuum topology optimization (TO), originated from structural mechanics, aims to find optimal distributions of materials to improve the performance of designs under governing physical equations described with partial differential equations (PDEs). Discrete variable topology optimization (DVTO) employs binary design variables to represent optimal topologies with sharp and clear boundaries, eliminating the need for post-processing. However, achieving high-fidelity designs requires fine discretization, leading to large-scale mixed-integer nonlinear programming (MINLP) problems. This thesis proposes a new scalable framework for solving the large-scale TO problems, with implementations for both classical and quantum computing. It discusses the proposed framework in the integration of classical and quantum computing for solving the large-scale TO problems.The proposed framework in this thesis can tremendously reduce the number of iteration steps required to achieve optimality, compared to the conventional continuous relaxation based methods like the solid isotropic material with penalization (SIMP) method. A series of mixed integer linear programming (MILP) problems are constructed to the MINLP formulation under the proposed framework. A new optimizer based on Dantzig-Wolfe (DW) decomposition is proposed to solve the MINLP formulation, which leverages the block-angular structure of TO problems. The proposed optimizer enables a parallel implementation of the optimization process, which can take advantage of the computational resources available in the scalable computation environment used for solving the large-scale PDEs. The new proposed formulation based on DW decomposition also enables a simple implementation of a quadratic unconstrained binary optimization (QUBO) problem, which can be embedded on near-term quantum computers for further acceleration of the optimization process. The proposed framework is validated through a series of numerical experiments, ranging from the single-material minimum compliance problem to the multi-material compliant mechanism design problem. The results demonstrates the effectiveness of the proposed framework in solving large-scale TO problems, including the design of complex structures with multiple candidate materials.A geometric multi-grid (GMG) preconditioner, as a classically scalable approach, based on the generalized moving least square (GMLS) method is presented to implement a scalable PDE solver with moving boundaries in fluid-solid interaction problems. Due to the lack of large enough mature quantum computers and the ill-conditioning of the linear systems arising from the discretization of PDEs, this thesis only investigates and discusses the commonly used quantum computing algorithms for solving the linear systems and the potential approach to develop the quantum algorithms for solving the linear systems arising from TO problems.

English

ISBN: 9798314888391Subjects--Topical Terms:

3343998
Computational physics.
Subjects--Index Terms:

Meshless method

Towards Scalable Topology Optimization, Classical or Quantum? /
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245 1 0 $a Towards Scalable Topology Optimization, Classical or Quantum? / $c Zisheng Ye.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (187 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
500 $a Advisors: Pan, Wenxiao Committee members: Qian, Xiaoping; Negrut, Dan; Wu, Jinlong; Wang, Bu; Hu, Xiaozhe.
502 $b Ph.D. $c The University of Wisconsin - Madison $d 2025.
520 $a Continuum topology optimization (TO), originated from structural mechanics, aims to find optimal distributions of materials to improve the performance of designs under governing physical equations described with partial differential equations (PDEs). Discrete variable topology optimization (DVTO) employs binary design variables to represent optimal topologies with sharp and clear boundaries, eliminating the need for post-processing. However, achieving high-fidelity designs requires fine discretization, leading to large-scale mixed-integer nonlinear programming (MINLP) problems. This thesis proposes a new scalable framework for solving the large-scale TO problems, with implementations for both classical and quantum computing. It discusses the proposed framework in the integration of classical and quantum computing for solving the large-scale TO problems.The proposed framework in this thesis can tremendously reduce the number of iteration steps required to achieve optimality, compared to the conventional continuous relaxation based methods like the solid isotropic material with penalization (SIMP) method. A series of mixed integer linear programming (MILP) problems are constructed to the MINLP formulation under the proposed framework. A new optimizer based on Dantzig-Wolfe (DW) decomposition is proposed to solve the MINLP formulation, which leverages the block-angular structure of TO problems. The proposed optimizer enables a parallel implementation of the optimization process, which can take advantage of the computational resources available in the scalable computation environment used for solving the large-scale PDEs. The new proposed formulation based on DW decomposition also enables a simple implementation of a quadratic unconstrained binary optimization (QUBO) problem, which can be embedded on near-term quantum computers for further acceleration of the optimization process. The proposed framework is validated through a series of numerical experiments, ranging from the single-material minimum compliance problem to the multi-material compliant mechanism design problem. The results demonstrates the effectiveness of the proposed framework in solving large-scale TO problems, including the design of complex structures with multiple candidate materials.A geometric multi-grid (GMG) preconditioner, as a classically scalable approach, based on the generalized moving least square (GMLS) method is presented to implement a scalable PDE solver with moving boundaries in fluid-solid interaction problems. Due to the lack of large enough mature quantum computers and the ill-conditioning of the linear systems arising from the discretization of PDEs, this thesis only investigates and discusses the commonly used quantum computing algorithms for solving the linear systems and the potential approach to develop the quantum algorithms for solving the linear systems arising from TO problems.
546 $a English
590 $a School code: 0262
650 4 $a Computational physics. $3 3343998
650 4 $a Statistics. $3 517247
650 4 $a Applied mathematics. $3 2122814
653 $a Meshless method
653 $a Mixed-integer nonlinear programming
653 $a Multigrid preconditioner
653 $a Quadratic unconstrained binary optimization
653 $a Quantum computing
653 $a Topology optimization
690 $a 0216
690 $a 0463
690 $a 0364
710 2 $a The University of Wisconsin - Madison. $b Mechanical Engineering. $e degree granting institution. $3 3823165
720 1 $a Pan, Wenxiao $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-11B.
790 $a 0262
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32040162