Asynchronous Parallel Solvers for Linear Systems arising in Computational Engineering

Jimack, P.K.; Walkley, M.A.

doi:10.4203/ctr.3.1

Cited by 9 publications

(3 citation statements)

References 49 publications

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“…The asynchronous fast adaptive composite grid (AFAC) solver family finally modifies the operators to anticipate overshooting. We may read BPX as particular modification of additive multigrid and AFAC as a generalization of BPX 37 …”

Section: Related Work and Methodological Ingredientsmentioning

confidence: 99%

Stabilized asynchronous fast adaptive composite multigrid using additive damping

Murray

Weinzierl

2020

Numerical Linear Algebra App

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Summary Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an expensive coarse grid identification phase plus adaptive mesh refinement overhead. We propose a new additive multigrid variant for spacetrees, that is, meshes as they are constructed from octrees and quadtrees: It is an additive scheme, that is, all multigrid resolution levels are updated concurrently. This ensures a high concurrency level, while the transfer operators between the mesh levels can still be constructed algebraically. The novel flavor of the additive scheme is an augmentation of the solver with an additive, auxiliary damping parameter per grid level per vertex that is in turn constructed through the next coarser level—an idea which utilizes smoothed aggregation principles or the motivation behind AFACx: Per level, we solve an additional equation whose purpose is to damp too aggressive solution updates per vertex which would otherwise, in combination with all the other levels, yield an overcorrection and, eventually, oscillations. This additional equation is constructed additively as well, that is, is once more solved concurrently to all other equations. This yields improved stability, closer to what is seen with multiplicative schemes, while pipelining techniques help us to write down the additive solver with single‐touch semantics for dynamically adaptive meshes.

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Section: Related Work and Methodological Ingredientsmentioning

confidence: 99%

Stabilized asynchronous fast adaptive composite multigrid using additive damping

Murray

Weinzierl

2020

Numerical Linear Algebra App

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“…A good preconditioning is still required in order to obtain satisfactory performance, making the schemes not completely matrix-free. Nevertheless, this can be formed based upon an approximation of the true Jacobian matrix which is easy to implement [21][22][23]. Regarding the specific Krylov subspace method, in this work we consider only GMRES since it is appropriate for non-symmetric and indefinite linear systems.…”

Section: Introductionmentioning

confidence: 99%

A Study of Preconditioned Jacobian-Free Newton-Krylov Discontinuous Galerkin Method for Compressible Flows on 3D Hexahedral Grids

Wanglong¹

2018

AAMM

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Storage requirement and computational efficiency have always been challenges for the efficient implementation of discontinuous Galerkin (DG) methods for real life applications. In this paper, a fully implicit Jacobian-Free Newton-Krylov (JFNK) method is developed in the context of DG discretizations for the threedimensional compressible Euler and Navier-Stokes equations. Compared with the Jacobian-based methods, the Jacobian-Free approach saves the storage for the Jacobian matrix which can be of great importance for DG methods. Three types of preconditioners are investigated in which the block diagonal preconditioner requires the least storage, while the block LU-SGS and ILU0 preconditioners require more storage but are more computationally efficient. An implicit time-stepping strategy is adopted for the stability of the current solver, which is based upon a hexahedral spatial mesh, and the nonlinear solver package Kinsol is used to improve the computational efficiency and robustness. Numerical results demonstrate that the preconditioned JFNK-DG solver can substantially reduce the storage requirement compared with the Jacobian based method without significantly compromising accuracy or efficiency. Furthermore, as a good compromise between efficiency and storage requirement, the ILU0 preconditioner shows the best choice of the preconditioners presented.

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“…The second alternative uses asynchronous communication and computation between subdomains to avoid all synchronization between processors. Use of asynchronous method in CFD is not common, but there are discussions and implementations by some researchers [12][13][14]. Some of them concluded that asynchronous computation has a better future because of heterogeneous clusters that have compute units with variable communication latencies, for example, CPU, GPU, and FGPA.…”

Section: Introductionmentioning

confidence: 99%

Asynchronous Parallelization of a CFD Solver

Abdi

Bitsuamlak

2015

Journal of Computational Engineering

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A Navier-Stokes equations solver is parallelized to run on a cluster of computers using the domain decomposition method. Two approaches of communication and computation are investigated, namely, synchronous and asynchronous methods. Asynchronous communication between subdomains is not commonly used in CFD codes; however, it has a potential to alleviate scaling bottlenecks incurred due to processors having to wait for each other at designated synchronization points. A common way to avoid this idle time is to overlap asynchronous communication with computation. For this to work, however, there must be something useful and independent a processor can do while waiting for messages to arrive. We investigate an alternative approach of computation, namely, conducting asynchronous iterations to improve local subdomain solution while communication is in progress. An in-house CFD code is parallelized using message passing interface (MPI), and scalability tests are conducted that suggest asynchronous iterations are a viable way of parallelizing CFD code.

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Asynchronous Parallel Solvers for Linear Systems arising in Computational Engineering

Cited by 9 publications

References 49 publications

Stabilized asynchronous fast adaptive composite multigrid using additive damping

Stabilized asynchronous fast adaptive composite multigrid using additive damping

A Study of Preconditioned Jacobian-Free Newton-Krylov Discontinuous Galerkin Method for Compressible Flows on 3D Hexahedral Grids

Asynchronous Parallelization of a CFD Solver

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