The Peano Software—Parallel, Automaton-based, Dynamically Adaptive Grid Traversals

Weinzierl, Tobias

doi:10.1145/3319797

Cited by 37 publications

(33 citation statements)

References 72 publications

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“…It is constructed from a spacetree (Weinzierl and Mehl 2011;Weinzierl 2018 ): All Riemann solves for example are embarrassingly parallel but require input from their two neighbouring cells. Along adaptivity boundaries, more than two cells are involved.…”

Section: The Exahype Benchmark Codementioning

confidence: 99%

Studies on the energy and deep memory behaviour of a cache-oblivious, task-based hyperbolic PDE solver

Charrier

Hazelwood

Tutlyaeva³

et al. 2019

The International Journal of High Performance Computing Applica

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We study the performance behaviour of a seismic simulation using the ExaHyPE engine with a specific focus on memory characteristics and energy needs. ExaHyPE combines dynamically adaptive mesh refinement (AMR) with ADER-DG. It is parallelized using tasks, and it is cache efficient. AMR plus ADER-DG yields a task graph which is highly dynamic in nature and comprises both arithmetically expensive tasks and tasks which challenge the memory's latency. The expensive tasks and thus the whole code benefit from AVX vectorization, though we suffer from memory access bursts. A frequency reduction of the chip improves the code's energy-to-solution. Yet, it does not mitigate burst effects. The bursts' latency penalty becomes worse once we add Intel R Optane TM technology, increase the core count significantly, or make individual, computationally heavy tasks fall out of close caches. Thread overbooking to hide away these latency penalties becomes contra-productive with non-inclusive caches as it destroys the cache and vectorization character. In cases where memory-intense and computationally expensive tasks overlap, ExaHyPE's cache-oblivious implementation nevertheless can exploit deep, non-inclusive, heterogeneous memory effectively, as main memory misses arise infrequently and slow down only few cores. We thus propose that upcoming supercomputing simulation codes with dynamic, inhomogeneous task graphs are actively supported by thread runtimes in intermixing tasks of different compute character, and we propose that future hardware actively allows codes to downclock the cores running particular task types.

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Section: The Exahype Benchmark Codementioning

confidence: 99%

Studies on the energy and deep memory behaviour of a cache-oblivious, task-based hyperbolic PDE solver

Charrier

Hazelwood

Tutlyaeva³

et al. 2019

The International Journal of High Performance Computing Applica

Self Cite

View full text Add to dashboard Cite

show abstract

“…In practise, we found DFS an advantageous traversal, as it can be realised as plain recursive function where all multilevel information (which is the next coarser node in the tree and which are its adjacent vertices) for lift and drop is implicitly available through the call stack. Furthermore, DFS in combination with space‐filling curves is well‐known to yield good memory access characteristics …”

Section: Octrees As Multiscale Linked Cell Gridsmentioning

confidence: 99%

“…With 2 d colouring, this gives a concurrency level that alters between eight and one. Techniques how to rewrite DFS automatically and on‐the‐fly into BFS are well‐known . We use them in our experiments.…”

Section: Parallelisationmentioning

confidence: 99%

“…Let there furthermore be a second grid Ω h/k , k ≥ 2 with a mesh size that is a fraction of h. We use k = 3 here as we make our work use. 19 Still, any k ∈ {2, 3, … } is admissible. We enforce Ω h ⊂ Ω h∕k , ie, the finer grid embeds into the coarser grid.…”

Section: Two-scale Linked Cellsmentioning

confidence: 99%

“…In practise, we found DFS an advantageous traversal, as it can be realised as plain recursive function where all multilevel information (which is the next coarser with space-filling curves is well-known to yield good memory access characteristics. 19 Whilst we refer to the works of Weinzierl et al 19,33 for details on the used data management, we elaborate the key finding of a top down traversal for our algorithm. A multiscale element-wise tree traversal knows at any time which vertices are adjacent to the currently processed cell and whether one of these vertices is processed for the first time, with all non-hanging vertices being subject to 2 d "visits".…”

Section: Spacetrees As Locally Adaptive Multiscale Linked Cell Data Smentioning

confidence: 99%

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A multi‐core ready discrete element method with triangles using dynamically adaptive multiscale grids

Krestenitis

Weinzierl

2018

Concurrency and Computation

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Summary The simulation of vast numbers of rigid bodies of non‐analytical shapes and of tremendously different sizes that collide with each other is computationally challenging. A bottleneck is the identification of all particle contact points per time step. We propose a tree‐based multilevel meta data structure to administer the particles. The data structure plus a purpose‐made tree traversal identifying the contact points introduce concurrency to the particle comparisons, whilst they keep the absolute number of particle‐to‐particle comparisons low. Furthermore, a novel adaptivity criterion allows explicit time stepping to work with comparably large time steps. It optimises both toward low algorithmic complexity per time step and low numbers of time steps. We study three different parallelisation strategies exploiting our traversal's concurrency. The fusion of two of them yields promising speedups once we rely on maximally asynchronous task‐based realisations. Our work shows that new computer architecture can push the boundary of rigid particle computability, yet if and only if the right data structures and data processing schemes are chosen.

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Lightweight task offloading exploiting MPI wait times for parallel adaptive mesh refinement

Samfass

Weinzierl

Charrier

et al. 2020

Concurrency and Computation

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Balancing the workload of sophisticated simulations is inherently difficult, since we have to balance both computational workload and memory footprint over meshes that can change any time or yield unpredictable cost per mesh entity, while modern supercomputers and their interconnects start to exhibit fluctuating performance. We propose a novel lightweight balancing technique for MPI+X to accompany traditional, prediction-based load balancing. It is a reactive diffusion approach that uses online measurements of MPI idle time to migrate tasks temporarily from overloaded to underemployed ranks. Tasks are deployed to ranks which otherwise would wait, processed with high priority, and made available to the overloaded ranks again. This migration is nonpersistent. Our approach hijacks idle time to do meaningful work and is totally nonblocking, asynchronous and distributed without a global data view. Tests with a seismic simulation code developed in the ExaHyPE engine uncover the method's potential. We found speed-ups of up to 2-3 for ill-balanced scenarios without logical modifications of the code base and show that the strategy is capable to react quickly to temporarily changing workload or node performance. K E Y W O R D S adaptive mesh refinement, MPI+X, reactive load balancing, task-based parallelism 1 INTRODUCTION Load balancing that decomposes work prior to a certain compute phase-a time step or iteration of an equation system solver-is doomed to underperform in many sophisticated simulation codes. There are multiple reasons for this: The clock frequency of processors changes over runtime, 1-3 the network speed is subject to noise due to other applications 4,5 or IO, and task-based multicore parallelization (MPI+X) tends to yield fluttering throughput due to effects of the memory hierarchy, 6 work stealing and nondeterminism in the MPI progression. While this list is not comprehensive, notably modern numerics drive the nonpredictability: They build atop of dynamic adaptive mesh refinement (AMR) that changes the mesh throughout a time step or mesh sweep, 7 combine different physical models, 7-9 or solve nonlinear equation systems with iterative solvers in substeps. 10 It becomes hard or even impossible to predict a step's computational load. As adjusting parallel partitions and respective data migration is often costly, many AMR codes consequently repartition only every 10th or 100th time step and tolerate certain load imbalances in-between. We propose a novel, lightweight load redistribution scheme that acts on top of traditional load balancing. It, first, assumes that parts of the underlying simulation code are phrased in terms of many expensive tasks. It, second, assumes that good AMR codes manage to hide data exchange behind computations yet cannot keep all cores busy all the time. In every solver step, some cores on some ranks have to wait for MPI data to drop in. Our idea is to offload tasks from overbooked to waiting ranks to make these work productively rather than being idle. 11 The code plugs into the Thi...

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The Peano Software—Parallel, Automaton-based, Dynamically Adaptive Grid Traversals

Cited by 37 publications

References 72 publications

Studies on the energy and deep memory behaviour of a cache-oblivious, task-based hyperbolic PDE solver

Studies on the energy and deep memory behaviour of a cache-oblivious, task-based hyperbolic PDE solver

A multi‐core ready discrete element method with triangles using dynamically adaptive multiscale grids

Lightweight task offloading exploiting MPI wait times for parallel adaptive mesh refinement

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