libCEED: Fast algebra for high-order element-based discretizations

Brown, Jed; Abdelfattah, Ahmad; Barra, Valeria; Beams, Natalie; Camier, Jean-Sylvain; Dobrev, Veselin; Dudouit, Yohann; Ghaffari, Leila; Kolev, Tzanio; Medina, David; Pazner, Will; Ratnayaka, Thilina; Thompson, Jeremy; Tomov, Stanimire

doi:10.21105/joss.02945

Cited by 15 publications

(13 citation statements)

References 21 publications

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“…Systems of equations with the form ( 10) and ( 11) admit a natural implementation via libCEED [15], which provides fast algebra for element-based discretizations on CPUs and GPUs. Figure 1 illustrates the action of an arbitrary finite element operator,…”

Section: Libceed Abstractionmentioning

confidence: 99%

“…It is thus important that materials developers have a simple, debuggable environment for development and testing. libCEED [15] provides fast algebra for element-based computation on CPUs and GPUs, meant for easy embedding in existing applications and enabling high performance on multiple architectures (Figure 3 from a single source code, with run-time selection of the backend.…”

Section: Portability and Productivitymentioning

confidence: 99%

“…Meanwhile, algebraic multigrid (AMG) setup costs increase due to sparse matrix-matrix products, and the resulting solvers are observed to converge more slowly for highorder discretizations [10]- [12], even when using specialized methods [13]. A practical alternative to algebraic multigrid is p-multigrid [14], which is observed to be robust for finite element discretizations on unstructured meshes [11], [12] and pairs naturally with efficient matrix-free data structures [15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

Brown¹,

Barra²,

Beams³

et al. 2022

Preprint

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Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that highorder methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs. We demonstrate the reliability, efficiency, and scalability of matrix-free p-multigrid methods with algebraic multigrid coarse solvers through large deformation hyperelastic simulations of multiscale structures. We investigate accuracy, cost, and execution time on multi-node CPU and GPU systems for moderate to large models using AMD MI250X (OLCF Crusher), NVIDIA A100 (NERSC Perlmutter), and V100 (LLNL Lassen and OLCF Summit), resulting in order of magnitude efficiency improvements over a broad range of model properties and scales. We discuss efficient matrix-free representation of Jacobians and demonstrate how automatic differentiation enables rapid development of nonlinear material models without impacting debuggability and workflows targeting GPUs.

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Section: Libceed Abstractionmentioning

confidence: 99%

Section: Portability and Productivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

Brown¹,

Barra²,

Beams³

et al. 2022

Preprint

Self Cite

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“…libCEED [17,18] is a new library that offers a purely algebraic interface for matrix-free operator evaluation and supports run-time selection of implementations tuned for a variety of computational device types, including CPUs and GPUs. libCEED's purely algebraic interface can unobtrusively be integrated in new and legacy software to provide performance portable interfaces.…”

Section: Libceedmentioning

confidence: 99%

“…MFEM [12] is a general-purpose finite element library that since version 4.0 supports hardware accelerators, such as GPUs, as well as programming models and libraries, such as CUDA, HIP, OCCA [24], libCEED [17], RAJA [28] and OpenMP. The goal of the MFEM developments in CEED is to provide state-of-the-art optimized performance highorder kernels to applications in an ease of use, flexible form.…”

Section: Mfemmentioning

confidence: 99%

GPU Algorithms for Efficient Exascale Discretizations

Abdelfattah¹,

Barra²,

Beams³

et al. 2021

Preprint

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In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. We discuss the GPU developments in several components of the CEED software stack, including the libCEED, MAGMA, MFEM, libParanumal, and Nek projects. We report performance and capability improvements in several CEED-enabled applications on both NVIDIA and AMD GPU systems.

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Finite element methods for turbulence

Jansen¹,

Brown²

2023

Numerical Methods in Turbulence Simulation

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libCEED: Fast algebra for high-order element-based discretizations

Cited by 15 publications

References 21 publications

Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

GPU Algorithms for Efficient Exascale Discretizations

Finite element methods for turbulence

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