A Relaxed Synchronization Approach for Solving Parallel Quadratic Programming Problems with Guaranteed Convergence

Lee, Kooktae; Bhattacharya, Raktim; Dass, Jyotikrishna; Sakuru, V. N. S. Prithvi; Mahapatra, Rabi

doi:10.1109/ipdps.2016.66

Cited by 7 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, due to the degraded numerical accuracy of standard schemes with asynchrony, alternate approaches are needed for asynchronous computations such that numerical errors incurred are minimal. While asynchronous computations have been utilized successfully for iterative linear solvers [17][18][19][20], some of the early work in asynchronous simulations of partial differential equations (PDEs) is limited to simple canonical equations in one-dimension. In [21][22][23] the governing equation is modified apriori to offset the effect of asynchrony on the numerical solution.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

Кумари

Cleary

Donzis

et al. 2023

Journal of Computational Physics

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

Кумари

Cleary

Donzis

et al. 2023

Journal of Computational Physics

View full text Add to dashboard Cite

“…However, due to the degraded numerical accuracy of standard schemes with asynchrony, alternate approaches are needed for asynchronous computations such that numerical errors incurred are minimal. While asynchronous computations have been utilized successfully for iterative linear solvers [17,18,19,20], some of the early work in asynchronous simulations of partial differential equations (PDEs) is limited to simple canonical equations in one-dimension. In [21,22,23] the governing equation is modified apriori to offset the effect of asynchrony on the numerical solution.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

Кумари¹,

Cleary²,

Donzis³

et al. 2022

Preprint

View full text Add to dashboard Cite

Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations of complex physical systems at unprecedented parameter ranges. However, novel numerical methods, scalable algorithms and re-design of current state-of-the art numerical solvers are required for scaling to these machines with minimal overheads. One such approach for partial differential equations based solvers involves computation of spatial derivatives with possibly delayed or asynchronous data using high-order asynchrony-tolerant (AT) schemes to facilitate mitigation of communication and synchronization bottlenecks without affecting the numerical accuracy. In the present study, an effective methodology of implementing temporal discretization using a multi-stage Runge-Kutta method with AT schemes is presented. Together these schemes are used to perform asynchronous simulations of canonical reacting flow problems, demonstrated in one-dimension including auto-ignition of a premixture, premixed flame propagation and non-premixed autoignition. Simulation results show that the AT schemes incur very small numerical errors in all key quantities of interest including stiff intermediate species despite delayed data at processing element (PE) boundaries. For simulations of supersonic flows, the degraded numerical accuracy of well-known shock-resolving WENO (weighted essentially non-oscillatory) schemes when used with relaxed synchronization is also discussed. To overcome this loss of accuracy, high-order AT-WENO schemes are derived and tested on linear and non-linear equations. Finally the novel AT-WENO schemes are demonstrated in the propagation of a detonation wave with delays at PE boundaries.

show abstract

“…Although Bertsekas [3] introduced a sufficient condition for the stability of general asynchronous fixed-point iterations (see chapter 6.2), which is equivalent to a diagonal dominance condition for QP problems, this condition is known to be very strong and thus conservative, according to the literature [22]. More recently, a periodic synchronization method has been developed in [19,16,14]. The key idea is that each node communicates with other nodes at a certain period, instead of synchronizing the data at each iteration step.…”

Section: Introductionmentioning

confidence: 99%

A Stabilizing Control Algorithm for Asynchronous Parallel Quadratic Programming via Dual Decomposition

Lee

2019

Volume 2: Modeling and Control of Engine and Aftertreatment Systems; Modeling and Control of IC Engines and Aftertreatment Syst

Self Cite

View full text Add to dashboard Cite

show abstract

A Relaxed Synchronization Approach for Solving Parallel Quadratic Programming Problems with Guaranteed Convergence

Cited by 7 publications

References 8 publications

Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

A Stabilizing Control Algorithm for Asynchronous Parallel Quadratic Programming via Dual Decomposition

Contact Info

Product

Resources

About