Efficient Application of Hanging-Node Constraints for Matrix-Free High-Order FEM Computations on CPU and GPU

Münch, Peter; Ljungkvist, Karl; Kronbichler, Martin

doi:10.1007/978-3-031-07312-0_7

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…In these layers, processes need a comparatively large number of ghosted information from other processes. This behavior can be linked back to the way deal.II distributes the cells and DoFs among processes [45], which might lead to non-contiguous subdomains and a non-uniform distribution of expensive hanging nodes [75]. Again, fine tuning might give a speedup in the problematic configuration but is not further investigated in this work since on a global view it would only give a negligible speedup.…”

Section: Cantilever Benchmarkmentioning

confidence: 99%

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

Proell,

Munch,

Kronbichler

et al. 2024

Additive Manufacturing

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Section: Cantilever Benchmarkmentioning

confidence: 99%

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

Proell,

Munch,

Kronbichler

et al. 2024

Additive Manufacturing

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“…Note that R i might also resolve constraints of type x i = P c ij x j + b i , for example, hanging-node constraints, implying a non-pure Boolean matrix. Without loss of generality, we consider here only homogeneous Dirichlet constraints (x i = 0) and refer the reader to Kronbichler and Kormann (2012); Munch et al (2022). For the sake of simplicity, we first discuss implementation details on R i for the cells of a FEM mesh and study the adoption to patches subsequently.…”

Section: Restriction and Data Locality In Cell Loopsmentioning

confidence: 99%

Cache-optimized and low-overhead implementations of additive Schwarz methods for high-order FEM multigrid computations

Munch,

Kronbichler

2023

The International Journal of High Performance Computing Applica

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This contribution presents data-locality optimizations of the additive Schwarz method (ASM) based on the fast-diagonalization method defined on overlapping cell-centric and vertex-star patches in the context of high-order matrix-free finite-element computations on modern CPU-based hardware. The developments are guided by detailed performance models of the ASM in the context of Chebyshev iterations when used as smoothers for p-multigrid. The proposed efficient implementation of ASM adopts concepts known from cell-loop infrastructures for efficient operator evaluation, in particular, the storage of information per geometric entity and the cache-friendly interleaving of cell loops and vector updates as a means to increase data locality. We use the latter concept for both applying the weights required by ASM and performing the vector updates required by the Chebyshev iteration, which are memory-bound operations with non-negligible costs in comparison to efficient operator evaluation. Furthermore, the solution of a scalar Poisson problem on a highly anisotropic and an unstructured mesh with p-multigrid using the developed smoothers indicates that efficient implementations of the additive Schwarz method can outperform optimized point-Jacobi preconditioners already for simple problems despite being more than twice as expensive per iteration. Even though ASM introduces additional communication steps per smoother application, the reduced number of iterations can lead to improved parallel scalability for intermediate problem sizes. At the scaling limit, the results are inconclusive due to these two opposing effects.

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Fast hardware-aware matrix-free algorithms for higher-order finite-element discretized matrix multivector products on distributed systems

Panigrahi,

Kodali,

Panda

et al. 2024

Journal of Parallel and Distributed Computing

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Efficient Application of Hanging-Node Constraints for Matrix-Free High-Order FEM Computations on CPU and GPU

Cited by 5 publications

References 24 publications

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

Cache-optimized and low-overhead implementations of additive Schwarz methods for high-order FEM multigrid computations

Fast hardware-aware matrix-free algorithms for higher-order finite-element discretized matrix multivector products on distributed systems

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