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Towards Scalable Topology Optimization, Classical or Quantum?
Towards Scalable Topology Optimization, Classical or Quantum?
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103533
- ISBN
- 9798314888391
- DDC
- 530
- 저자명
- Ye, Zisheng.
- 서명/저자
- Towards Scalable Topology Optimization, Classical or Quantum?
- 발행사항
- [Sl] : The University of Wisconsin - Madison, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 187 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
- 주기사항
- Advisor: Pan, Wenxiao.
- 학위논문주기
- Thesis (Ph.D.)--The University of Wisconsin - Madison, 2025.
- 초록/해제
- 요약Continuum 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.
- 일반주제명
- Computational physics
- 일반주제명
- Statistics
- 일반주제명
- Applied mathematics
- 키워드
- Meshless method
- 기타저자
- The University of Wisconsin - Madison Mechanical Engineering
- 기본자료저록
- Dissertations Abstracts International. 86-11B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798314888391
■035 ▼a(MiAaPQ)AAI32040162
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aYe, Zisheng.
■24510▼aTowards Scalable Topology Optimization, Classical or Quantum?
■260 ▼a[Sl]▼bThe University of Wisconsin - Madison▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a187 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-11, Section: B.
■500 ▼aAdvisor: Pan, Wenxiao.
■5021 ▼aThesis (Ph.D.)--The University of Wisconsin - Madison, 2025.
■520 ▼aContinuum 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.
■590 ▼aSchool code: 0262.
■650 4▼aComputational physics
■650 4▼aStatistics
■650 4▼aApplied mathematics
■653 ▼aMeshless method
■653 ▼aMixed-integer nonlinear programming
■653 ▼aMultigrid preconditioner
■653 ▼aQuadratic unconstrained binary optimization
■653 ▼aQuantum computing
■653 ▼aTopology optimization
■690 ▼a0216
■690 ▼a0463
■690 ▼a0364
■71020▼aThe University of Wisconsin - Madison▼bMechanical Engineering.
■7730 ▼tDissertations Abstracts International▼g86-11B.
■790 ▼a0262
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357585▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
