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Chaotic linear equation-system solvers for unsteady CFD

Chaotic linear equation-system solvers for unsteady CFD
Chaotic linear equation-system solvers for unsteady CFD
A Chaotic Iterative Method, which is a form of totally asynchronous linear equation-system solver, is implemented within an open-source framework. The solver is similar to simple Jacobi or Gauss-Seidel methods, but is highly optimized for massively-parallel computations. Processes or threads are free to run computations regardless of the current state of other processes, iterating individual equations with no limitations on the state of the variables which they use. Each individual iteration may pull variables from the same iteration, the previous iteration, or indeed any iteration. This effectively removes all synchronization from the Jacobi or Gauss-Seidel algorithm, allowing computations to run efficiently with high concurrency.

The trade-off is that the numerical convergence rate of these simple algorithms is slower compared to the classical Krylov Subspace methods, which are popular today. However, unique features of the computational fluid dynamics algorithm work in favour of Chaotic methods, allowing the fluid dynamics field to exploit these algorithms when other's cannot.

The results of the Chaotic solver are presented, verifying the numerical results and benchmarking performance against the Generalized Minimal Residual (GMRES) solver and a Pipelined GMRES solver. The results show that, under certain circumstances, Chaotic methods could be used as a standalone solver due to their superior scalability. The potential to use Chaotic methods as a pre-conditioner or hybrid solver is also revealed.
Hawkes, James N.
61e73197-51e8-4d0d-9f28-ff34fa76585b
Turnock, Stephen R.
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Vaz, Guilherme
a053069d-9831-4b28-a9c0-6503ddaab25d
Cox, Simon J.
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Philips, Alexander B.
f565b1da-6881-4e2a-8729-c082b869028f
Hawkes, James N.
61e73197-51e8-4d0d-9f28-ff34fa76585b
Turnock, Stephen R.
d6442f5c-d9af-4fdb-8406-7c79a92b26ce
Vaz, Guilherme
a053069d-9831-4b28-a9c0-6503ddaab25d
Cox, Simon J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
Philips, Alexander B.
f565b1da-6881-4e2a-8729-c082b869028f

Hawkes, James N., Turnock, Stephen R., Vaz, Guilherme, Cox, Simon J. and Philips, Alexander B. (2015) Chaotic linear equation-system solvers for unsteady CFD. VI International Conference on Computational Methods in Marine Engineering, Rome, Italy. 14 - 16 Jun 2015.

Record type: Conference or Workshop Item (Paper)

Abstract

A Chaotic Iterative Method, which is a form of totally asynchronous linear equation-system solver, is implemented within an open-source framework. The solver is similar to simple Jacobi or Gauss-Seidel methods, but is highly optimized for massively-parallel computations. Processes or threads are free to run computations regardless of the current state of other processes, iterating individual equations with no limitations on the state of the variables which they use. Each individual iteration may pull variables from the same iteration, the previous iteration, or indeed any iteration. This effectively removes all synchronization from the Jacobi or Gauss-Seidel algorithm, allowing computations to run efficiently with high concurrency.

The trade-off is that the numerical convergence rate of these simple algorithms is slower compared to the classical Krylov Subspace methods, which are popular today. However, unique features of the computational fluid dynamics algorithm work in favour of Chaotic methods, allowing the fluid dynamics field to exploit these algorithms when other's cannot.

The results of the Chaotic solver are presented, verifying the numerical results and benchmarking performance against the Generalized Minimal Residual (GMRES) solver and a Pipelined GMRES solver. The results show that, under certain circumstances, Chaotic methods could be used as a standalone solver due to their superior scalability. The potential to use Chaotic methods as a pre-conditioner or hybrid solver is also revealed.

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More information

e-pub ahead of print date: 18 June 2015
Venue - Dates: VI International Conference on Computational Methods in Marine Engineering, Rome, Italy, 2015-06-14 - 2015-06-16
Organisations: National Oceanography Centre, Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 376523
URI: http://eprints.soton.ac.uk/id/eprint/376523
PURE UUID: e9597875-f7dc-4890-9f26-68f7e873831f
ORCID for Stephen R. Turnock: ORCID iD orcid.org/0000-0001-6288-0400
ORCID for Alexander B. Philips: ORCID iD orcid.org/0000-0003-3234-8506

Catalogue record

Date deposited: 30 Apr 2015 10:20
Last modified: 09 Jan 2022 03:17

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Contributors

Author: James N. Hawkes
Author: Guilherme Vaz
Author: Simon J. Cox
Author: Alexander B. Philips ORCID iD

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