The <i>HyTeG</i> finite-element software framework for scalable multigrid solvers

Kohl, Nils; Thönnes, Dominik; Drzisga, Daniel; Bartuschat, Dominik; Rüde, Ulrich

doi:10.1080/17445760.2018.1506453

Cited by 23 publications

(18 citation statements)

References 29 publications

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“…We employ a lexicographic Gauss-Seidel smoother for the linear discretizations and a multi-color ordering for the quadratic test cases that is tied to the orientation of the edges and the corresponding, constant stencils. See [29] for more details. The execution is performed MPI-parallel, without OpenMP on a single node.…”

Section: Runtime Resultsmentioning

confidence: 99%

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Code generation approaches for parallel geometric multigrid solvers

Köstler¹,

Heisig²,

Kohl³

et al. 2020

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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Software development for applications in computational science and engineering has become complex in recent years. This is mainly due to the increasing parallelism and heterogeneity in modern computer architectures and to the more realistic physical and mathematical models that have to be processed. One idea to address this issue is to use code generation techniques. In contrast to manual implementations in a general-purpose computing language, they allow to integrate automatic code transforms to produce efficient code for different models and platforms. As an example the numerical solution of an elliptic partial differential equation via generated geometric multigrid solvers is considered. We present three code generation approaches for it and discuss their advantages and disadvantages with respect to performance, portability, and productivity.

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Section: Runtime Resultsmentioning

confidence: 99%

“…General concept HyTeG (Hybrid Tetrahedral Grids) [29] is a massively parallel finite element framework with a strong focus on matrix-free geometric multigrid solvers on block-structured tetrahedral grids. It is built around the concept of hierarchical hybrid grids as introduced in the early 2000s [6,7].…”

Section: Hytegmentioning

confidence: 99%

Code generation approaches for parallel geometric multigrid solvers

Köstler¹,

Heisig²,

Kohl³

et al. 2020

Analele Universitatii "Ovidius" Constanta - Seria Matematica

Self Cite

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“…One software package that already utilized concepts and functionalities of waLBerla is the Hybrid Tetrahedral Grids (HyTeG) framework [131] which aims at extreme scale simulations of Earth mantle convection. It uses the concept of strict separation between data structures and actual compute data and transfers this to unstructured triangle and tetrahedral meshes.…”

Section: Hytegmentioning

confidence: 99%

waLBerla: A block-structured high-performance framework for multiphysics simulations

Bauer

Eibl

Godenschwager

et al. 2021

Computers & Mathematics with Applications

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Programming current supercomputers efficiently is a challenging task. Multiple levels of parallelism on the core, on the compute node, and between nodes need to be exploited to make full use of the system. Heterogeneous hardware architectures with accelerators further complicate the development process. waLBerla addresses these challenges by providing the user with highly efficient building blocks for developing simulations on block-structured grids. The block-structured domain partitioning is flexible enough to handle complex geometries, while the structured grid within each block allows for highly efficient implementations of stencil-based algorithms. We present several example applications realized with waLBerla, ranging from lattice Boltzmann methods to rigid particle simulations. Most importantly, these methods can be coupled together, enabling multiphysics simulations. The framework uses meta-programming techniques to generate highly efficient code for CPUs and GPUs from a symbolic method formulation. To ensure software quality and performance portability, a continuous integration toolchain automatically runs an extensive test suite encompassing multiple compilers, hardware architectures, and software configurations.

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“…Therefore, in this section, we highlight the important features of ours. We use the HyTeG finite-element software framework [29] as the core framework for all the numerical experiments in Section 9. It offers efficient distributed data structures for simplicial meshes in 2D and 3D, which serve as a basis for the implementation of massively parallel fast iterative solvers.…”

Section: 3mentioning

confidence: 99%

“…These studies used the HHG software framework [11,12,13] in their experiments. Here, the finite-element software framework HyTeG [29] is used.…”

mentioning

confidence: 99%

The Surrogate Matrix Methodology: A Priori Error Estimation

Drzisga¹,

Keith²,

Wohlmuth³

2019

SIAM J. Sci. Comput.

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We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is based on the piece-wise smooth approximation of the matrices involved in a standard finite element discretization. In particular, it relies on the projection of smooth so-called stencil functions onto high-order polynomial subspaces. The performance advantage of the surrogate matrix methodology is seen in constructions where each stencil function uniquely determines the values of a significant collection of matrix entries. Such constructions are shown to be widely achievable through the use of locally-structured meshes. Therefore, this methodology can be applied to a wide variety of physically meaningful problems, including nonlinear problems and problems with curvilinear geometries. Rigorous a priori error analysis certifies the convergence of a novel surrogate method for the variable coefficient Poisson equation. The flexibility of the methodology is also demonstrated through the construction of novel methods for linear elasticity and nonlinear diffusion problems. In numerous numerical experiments, we demonstrate the efficacy of these new methods in a matrix-free environment with geometric multigrid solvers. In our experiments, up to a twenty-fold decrease in computation time is witnessed over the classical method with an otherwise identical implementation.

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The HyTeG finite-element software framework for scalable multigrid solvers

Cited by 23 publications

References 29 publications

Code generation approaches for parallel geometric multigrid solvers

Code generation approaches for parallel geometric multigrid solvers

waLBerla: A block-structured high-performance framework for multiphysics simulations

The Surrogate Matrix Methodology: A Priori Error Estimation

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