Proxy-equation' paradigm - A novel strategy for massively-parallel asynchronous computations (original) (raw)

2016

Massively parallel simulations of transport equation systems call for a paradigm change in algorithm development to achieve efficient scalability. Traditional approaches require time synchronization of processing elements (PEs) which severely restricts scalability. Relaxing synchronization requirement introduces error and slows down convergence. In this paper, we propose and develop a novel `proxy-equation' concept for a general transport equation that (i) tolerates asynchrony with manageable added error, (ii) preserves convergence order and (iii) scales efficiently on massively parallel machines. The central idea is to modify a priori the transport equation at the PE boundaries to offset asynchrony errors. Proof-of-concept computations are performed using a one-dimensional advection-diffusion equation. The results demonstrate the promise and advantages of the present strategy.

A numerical approach for a system of transport equations

isara solutions, 2012

The numerical solution of the transport equation, describing the fate of a passive scaler in a moving fluid, has been the object of intense research for the past few decades. So much interest concerning an apparently inoffensive (in many occasions it is even linear) equation may seem, at first sight, misplaced. However, there is a fundamental difficulty in the solution of the transport equation, which results from the fact that, while advection and dispersion are simultaneous processes, they promote mass transport very differently: in the case of advection, transport is along characteristic lines that follow the flow, while in the case of dispersion, it is both along and between characteristic lines. Mathematically, this

A scalable weakly-synchronous algorithm for solving partial differential equations

arXiv: Computational Physics, 2019

Synchronization overheads pose a major challenge as applications advance towards extreme scales. In current large-scale algorithms, synchronization as well as data communication delay the parallel computations at each time step in a time-dependent partial differential equation (PDE) solver. This creates a new scaling wall when moving towards exascale. We present a weakly-synchronous algorithm based on novel asynchrony-tolerant (AT) finite-difference schemes that relax synchronization at a mathematical level. We utilize remote memory access programming schemes that have been shown to provide significant speedup on modern supercomputers, to efficiently implement communications suitable for AT schemes, and compare to two-sided communications that are state-of-practice. We present results from simulations of Burgers' equation as a model of multi-scale strongly non-linear dynamical systems. Our algorithm demonstrate excellent scalability of the new AT schemes for large-scale computin...

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