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Spectral Element Poisson Preconditioners for Heterogeneous Architectures
Spectral Element Poisson Preconditioners for Heterogeneous Architectures
Detailed Information
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260209102932
- ISBN
- 9798291562604
- DDC
- 004
- 서명/저자
- Spectral Element Poisson Preconditioners for Heterogeneous Architectures
- 발행사항
- [Sl] : University of Illinois at Urbana-Champaign, 2023
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2023
- 형태사항
- 213 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-03, Section: B.
- 주기사항
- Advisor: Fischer, Paul.
- 학위논문주기
- Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2023.
- 초록/해제
- 요약The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. Two classes of preconditioners prove most effective: geometric p-multigrid and low-order refined methods. Low-order refined preconditioners, moreover, require the use of algebraic multigrid to approximate the inverse of the operator. The communication associated with the multigrid coarse-grid solve hinders the parallel scalability of both classes of preconditioners, especially on heterogeneous architectures. To mitigate the coarse-grid solve cost, novel smoothing strategies are considered. The fourth-kind Chebyshev polynomial smoothing proposed by James Lottes is utilized to accelerate additive Schwarz-based smoothers in a geometric p-multigrid preconditioner. Through these techniques, we develop geometric p-multigrid preconditioners capable of achieving up to an 81% speedup over the state-ofthe-art p-multigrid preconditioners on the Summit supercomputer. A p-multigrid approach with an additive coarse-grid solve specifically designed for heterogeneous architectures is considered. We also propose a hybrid p-multigrid and low-order refined preconditioner that improve the time-to-solution by as much as 86% compared to the low-order preconditioner. We demonstrate the effectiveness of these novel approaches on a variety of problems arising from the spectral element discretization of the incompressible Navier-Stokes equations on GPU architectures spanning to P ≥ 1024 NVIDIA V100 GPUs on Summit.
- 일반주제명
- Computer science
- 일반주제명
- Computer engineering
- 일반주제명
- Applied mathematics
- 키워드
- Preconditioning
- 키워드
- Multigrid
- 키워드
- Poisson equation
- 기타저자
- University of Illinois at Urbana-Champaign Computer Science
- 기본자료저록
- Dissertations Abstracts International. 87-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■1001 ▼aPhillips, Malachi.
■24510▼aSpectral Element Poisson Preconditioners for Heterogeneous Architectures
■260 ▼a[Sl]▼bUniversity of Illinois at Urbana-Champaign▼c2023
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2023
■300 ▼a213 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-03, Section: B.
■500 ▼aAdvisor: Fischer, Paul.
■5021 ▼aThesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2023.
■520 ▼aThe solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. Two classes of preconditioners prove most effective: geometric p-multigrid and low-order refined methods. Low-order refined preconditioners, moreover, require the use of algebraic multigrid to approximate the inverse of the operator. The communication associated with the multigrid coarse-grid solve hinders the parallel scalability of both classes of preconditioners, especially on heterogeneous architectures. To mitigate the coarse-grid solve cost, novel smoothing strategies are considered. The fourth-kind Chebyshev polynomial smoothing proposed by James Lottes is utilized to accelerate additive Schwarz-based smoothers in a geometric p-multigrid preconditioner. Through these techniques, we develop geometric p-multigrid preconditioners capable of achieving up to an 81% speedup over the state-ofthe-art p-multigrid preconditioners on the Summit supercomputer. A p-multigrid approach with an additive coarse-grid solve specifically designed for heterogeneous architectures is considered. We also propose a hybrid p-multigrid and low-order refined preconditioner that improve the time-to-solution by as much as 86% compared to the low-order preconditioner. We demonstrate the effectiveness of these novel approaches on a variety of problems arising from the spectral element discretization of the incompressible Navier-Stokes equations on GPU architectures spanning to P ≥ 1024 NVIDIA V100 GPUs on Summit.
■590 ▼aSchool code: 0090.
■650 4▼aComputer science
■650 4▼aComputer engineering
■650 4▼aApplied mathematics
■653 ▼aPreconditioning
■653 ▼aMultigrid
■653 ▼aPoisson equation
■653 ▼aNavier-Stokes equations
■653 ▼aSpectral element method
■653 ▼aHeterogeneous computing
■653 ▼aHigh-performance computing
■690 ▼a0984
■690 ▼a0464
■690 ▼a0364
■71020▼aUniversity of Illinois at Urbana-Champaign▼bComputer Science.
■7730 ▼tDissertations Abstracts International▼g87-03B.
■790 ▼a0090
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17366036▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
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