An Experience Report on (Auto-)tuning of Mesh-Based PDE Solvers on Shared Memory Systems

Charrier, Dominic Etienne; Weinzierl, Tobias

doi:10.1007/978-3-319-78054-2_1

Cited by 5 publications

(8 citation statements)

References 7 publications

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“…Second, we have to continue to investigate and to invest into the methods under the hood of ExaHyPE. Examples for such new ingredients on our agenda are accelerator support, local time stepping, and more dynamic load balancing and autotuning [67,68]. Finally, we plan extensions of the core paradigm of the engine.…”

Section: Discussionmentioning

confidence: 99%

ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems

Reinarz

Charrier

Bäder

et al. 2020

Computer Physics Communications

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ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are useful in a wide range of application areas. Applications powered by ExaHyPE can be run on a student's laptop, but are also able to exploit thousands of processor cores on state-of-the-art supercomputers. The engine is able to dynamically increase the accuracy of the simulation using adaptive mesh refinement where required. Due to the robustness and shock capturing abilities of ExaHyPE's numerical methods, users of the engine can simulate linear and non-linear hyperbolic PDEs with very high accuracy.Users can tailor the engine to their particular PDE by specifying evolved quantities, fluxes, and source terms. A complete simulation code for a new hyperbolic PDE can often be realised within a few hours -a task that, traditionally, can take weeks, months, often years for researchers starting from scratch. In this paper, we showcase ExaHyPE's workflow and capabilities through real-world scenarios from our two main application areas: seismology and astrophysics.PDEs written in first order form. The systems may contain both conservative and non-conservative terms. Solution method:ExaHyPE employs the discontinuous Galerkin (DG) method combined with explicit one-step ADER (arbitrary high-order derivative) time-stepping. An a-posteriori limiting approach is applied to the ADER-DG solution, whereby spurious solutions are discarded and recomputed with a robust, patch-based finite volume scheme. ExaHyPE uses dynamical adaptive mesh refinement to enhance the accuracy of the solution around shock waves, complex geometries, and interesting features.

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Section: Discussionmentioning

confidence: 99%

ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems

Reinarz

Charrier

Bäder

et al. 2020

Computer Physics Communications

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“…Extensions of the sole grid and its traversal are available via a template mechanism and small routine collections (toolkits) that inject plotting facilities for Paraview/VisIt, realize shared memory autotuning [23] or add dynamic load balancing based upon graph partitioning or the underlying Peano space-filling curve. Further examples for toolkits are routine collections for matrix-free multigrid [56,73], Particle-in-Cell features [78] similar to [45] or patch-based PDE solvers [75].…”

Section: A Software Basementioning

confidence: 99%

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

Weinzierl

2019

ACM Trans. Math. Softw.

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We discuss the design decisions, design alternatives and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata-one automaton for the multiscale grid traversal and one for the applicationspecific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized, before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a "one way to implement things" code description into a generic discussion and summary of some alternatives, rationale and design decisions to be made for any tree-based adaptive mesh refinement software.

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“…Peano offers a plug-in point to inject proper problem size dependent into any application. If a manual identification is too cumbersome, then its toolbox collection provides a generic machine-learning algorithm to derive proper grain size choices onthe-fly (Charrier and Weinzierl 2017).…”

Section: Concurrency Impact Of the Dfs-bfs Transformationmentioning

confidence: 99%

“…Extensions of the sole grid and its traversal are available via a template mechanism and small routine collections (toolkits) that inject plotting facilities for Paraview/VisIt, realize shared memory autotuning (Charrier and Weinzierl 2017) or add dynamic load balancing based upon graph partitioning or the underlying Peano space-filling curve. Further examples for toolkits are routine collections for matrix-free multigrid (Reps and Weinzierl 2017; Weinzierl and Weinzierl 2018), Particle-in-Cell features (Weinzierl et al 2016) similar to (Kolobov and Arslanbekov 2016) or patchbased PDE solvers (Weinzierl et al 2014).…”

Section: Appendices a Software Basementioning

confidence: 99%

Untitled

2019

ACM Trans. Math. Softw.

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We discuss the design decisions, design alternatives, and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata-one automaton for the multiscale grid traversal and one for the application-specific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a "one way to implement things" code description into a generic discussion and summary of some alternatives, rationale, and design decisions to be made for any tree-based adaptive mesh refinement software.

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An Experience Report on (Auto-)tuning of Mesh-Based PDE Solvers on Shared Memory Systems

Cited by 5 publications

References 7 publications

ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems

ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems

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

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