A General Space-filling Curve Algorithm for Partitioning 2D Meshes

Sasidharan, Aparna; Dennis, John M.; Snir, Marc

doi:10.1109/hpcc-css-icess.2015.192

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…BoxLib contains a number of strategies for distributing work in this way, and by default uses a space-filling curve approach with a Morton ordering (e.g. Sasidharan & Snir (2015); Beichl & Sullivan (1998)). By experiment we have found that the most efficient loadbalancing strategy for our problem is actually a simple knapsack algorithm.…”

Section: Parallel Strategy and Performancementioning

confidence: 99%

“…The distribution obeys a loadbalancing algorithm that attempts to equalize the amount of work done by each processor. BoxLib contains a number of strategies for distributing work in this way, and by default uses a space-filling curve approach with a Morton ordering (e.g., Beichl & Sullivan 1998;Sasidharan & Snir 2015). By experiment we have found that the most efficient loadbalancing strategy for our problem is actually a simple knapsack algorithm.…”

Section: Parallel Strategy and Performancementioning

confidence: 99%

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White Dwarf Mergers on Adaptive Meshes. I. Methodology and Code Verification

Katz

Zingale

Calder

et al. 2016

ApJ

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The Type Ia supernova (SN Ia) progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf (WD) merger scenario, which has the potential to naturally explain many of the observed characteristics of SNe Ia. To date there have been relatively few self-consistent simulations of merging WD systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.

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Section: Parallel Strategy and Performancementioning

confidence: 99%

Section: Parallel Strategy and Performancementioning

confidence: 99%

White Dwarf Mergers on Adaptive Meshes. I. Methodology and Code Verification

Katz

Zingale

Calder

et al. 2016

ApJ

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“…They provide a good partitioning heuristic (cmp. [1,8,10,9,11,18,19,23,25]): As the ordering of the cells is given, there is no freedom how to cut the linearisation. A user can only decide where to cut.…”

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confidence: 99%

The maximum discrete surface-to-volume ratio of space-filling curve partitions

Gadouleau,

Weinzierl

2021

Preprint

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Space-filling curves (SFCs) are used in high performance computing to distribute a computational domain or its mesh, respectively, amongst different compute units, i.e. cores or nodes or accelerators. The part of the domain allocated to each compute unit is called a partition. Besides the balancing of the work, the communication cost to exchange data between units determines the quality of a chosen partition. This cost can be approximated by the surface-to-volume ratio of partitions: the volume represents the amount of local work, while the surface represents the amount of data to be transmitted. Empirical evidence suggests that space-filling curves yield advantageous surface-to-volume ratios. Formal proofs are available only for regular grids. We investigate the surface-to-volume ratio of space-filling curve partitions for adaptive grids and derive the maximum surface-to-volume ratio as a function of the number of cells in the partition. In order to prove our main theorem, we construct a new framework for the study of adaptive grids, notably introducing the concepts of a shape and of classified partitions. The new methodological framework yields insight about the SFC-induced partition character even if the grids refine rather aggressively in localised areas: it quantifies the obtained surface-to-volume ratio. This framework thus has the potential to guide the design of better load balancing algorithms on the long term.

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