Parallel algorithms for transport sweeps on unstructured meshes

Colomer, G.; Borrell, R.; Trias, F. X.; Rodríguez, I.

doi:10.1016/j.jcp.2012.07.009

Cited by 32 publications

(14 citation statements)

References 28 publications

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“…This is a similar approach to that developed in [57] ( AIR), but nAIR can offer setup-times that are orders of magnitude faster than AIR in some cases. Steady state transport is used as a model problem, which arises in large-scale simulation of neutron and radiation transport [1,5,18,30,49]. Results in Section 6 show that nAIR outperforms current state-of-the art methods, and is able to attain an order-of-magnitude reduction in residual in only 1-2 iterations, even for high-order discretizations on unstructured grids.…”

mentioning

confidence: 99%

Nonsymmetric Reduction-Based Algebraic Multigrid

Manteuffel¹,

Münzenmaier²,

Ruge³

et al. 2019

SIAM J. Sci. Comput.

104

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Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence theory and most variations of AMG rely on A being SPD. Hyperbolic PDEs, which arise often in large-scale scientific simulations, remain a challenge for AMG, as well as other fast linear solvers, in part because the resulting linear systems are often highly nonsymmetric. Here, a novel convergence framework is developed for nonsymmetric, reduction-based AMG, and sufficient conditions derived for 2 -convergence of error and residual. In particular, classical multigrid approximation properties are connected with reduction-based measures to develop a robust framework for nonsymmetric, reduction-based AMG.Matrices with block-triangular structure are then recognized as being amenable to reductiontype algorithms, and a reduction-based AMG method is developed for upwind discretizations of hyperbolic PDEs, based on the concept of a Neumann approximation to ideal restriction (nAIR). nAIR can be seen as a variation of local AIR ( AIR) introduced in previous work, specifically targeting matrices with triangular structure. Although less versatile than AIR, setup times for nAIR can be substantially faster for problems with high connectivity. nAIR is shown to be an effective and scalable solver of steady state transport for discontinuous, upwind discretizations, with unstructured meshes, and up to 6th-order finite elements, offering a significant improvement over existing AMG methods. nAIR is also shown to be effective on several classes of "nearly triangular" matrices, resulting from curvilinear finite elements and artificial diffusion.

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mentioning

confidence: 99%

Nonsymmetric Reduction-Based Algebraic Multigrid

Manteuffel¹,

Münzenmaier²,

Ruge³

et al. 2019

SIAM J. Sci. Comput.

104

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“…To decouple these functions from the equations, a functional-type iteration called the source iteration (SI) [27,36] (also referred to as the grid sweeping algorithm) has been widely used for solving the system in a Gauss-Seidel-like manner. To be specific, assuming that the -th iteration solutions I h( ) m,K (x, y, t n+1 ) (for m = 1, · · · , N a and K ∈ T h (t n+1 )) are known, we compute the new approximations I h( +1) m,K (x, y, t n+1 ) element by element in a sweeping direction [10] and through all angular directions m = 1, · · · , N a for each given element. Thus, for K ∈ T h (t n+1 ), we…”

Section: )mentioning

confidence: 99%

An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation

Zhang¹

2020

CICP

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The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time, space and angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needs to handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions. Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinate method for angular discretization. The former employs a dynamic mesh adaptation strategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency are demonstrated in a selection of one-and two-dimensional numerical examples.

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“…The algorithm they presented is applicable to more general cases than radiation transport problems as it uses no geometric information about the mesh. In the paper [11], the authors presented new algorithms for the sweep operation on unstructured meshes by designing algorithms that achieve overlap of communication by computations, as well as message buffering to reduce cost associated with the latency of parallel machines which are used.…”

Section: Related Workmentioning

confidence: 99%

3D Cartesian Transport Sweep for Massively Parallel Architectures with PaRSEC

Moustafa

Faverge

Plagne

et al. 2015

2015 IEEE International Parallel and Distributed Processing Symposium

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High-fidelity nuclear power plant core simulations require solving the Boltzmann transport equation. In discrete ordinates methods, the most computationally demanding operation of this equation is the sweep operation. Considering the evolution of computer architectures, we propose in this paper, as a first step toward heterogeneous distributed architectures, a hybrid parallel implementation of the sweep operation on top of the generic task-based runtime system: PARSEC. Such an implementation targets three nested levels of parallelism: message passing, multi-threading, and vectorization. A theoretical performance model was designed to validate the approach and help the tuning of the multiple parameters involved in such an approach. The proposed parallel implementation of the Sweep achieves a sustained performance of 6.1 Tflop/s, corresponding to 33.9% of the peak performance of the targeted supercomputer. This implementation compares favorably with state-ofart solvers such as PARTISN; and it can therefore serve as a building block for a massively parallel version of the neutron transport solver DOMINO developed at EDF.

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Parallel algorithms for transport sweeps on unstructured meshes

Cited by 32 publications

References 28 publications

Nonsymmetric Reduction-Based Algebraic Multigrid

Nonsymmetric Reduction-Based Algebraic Multigrid

An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation

3D Cartesian Transport Sweep for Massively Parallel Architectures with PaRSEC

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