# Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems

PhD Thesis

*Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems.*PhD Thesis Doctor of Philosophy. University of Southern Queensland.

Title | Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems |
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Type | PhD Thesis |

Authors | |

Author | Pham-Sy, Nam |

Supervisor | Tran, Canh-Dung |

Mai-Duy, Nam | |

Tran-Cong, Thanh | |

Institution of Origin | University of Southern Queensland |

Qualification Name | Doctor of Philosophy |

Number of Pages | 207 |

Year | 2015 |

Abstract | The thesis reports a contribution to the development of parallel algorithms based on Domain Decomposition (DD) method and Compact Local Integrated Radial Basis Function (CLIRBF) method. This development aims to solve large scale In parallel computation, there is a challenge called Distributed Termination Detection (DTD) problem. DTD concerns the discovery whether all processes in a In the first attempt, the combination of the DD method and CLIRBF based collocation approach yields an effective parallel algorithm to solve PDEs. This approach has enabled not only the problem to be solved separately in each subdomain by a Central Processing Unit (CPU) but also compact local stencils to be independently treated. The present algorithm has achieved high throughput A new parallel algorithm is developed using the Control Volume Method (CVM) for the solution of PDEs. The goal is to develop an efficient parallel algorithm Although overlapping method yields a straightforward implementation and stable convergence, overlapping of sub-domains makes it less applicable for complex Finally, when comparing the overlapping and non-overlapping parallel algorithms, it is found that the non-overlapping one is less stable. The numerical results show that the non-overlapping method is not able to converge for high Reynolds number while overlapping method reaches the same convergence profile as the sequential CLIRBF method. Thus, in this research when dealing with non-Newtonian |

Keywords | domain decomposition; compact local integrated radial basis function; fluid flow; parallel high performance computing |

ANZSRC Field of Research 2020 | 401706. Numerical modelling and mechanical characterisation |

Byline Affiliations | Computational Engineering and Science Research Centre |

https://research.usq.edu.au/item/q35qx/parallel-computations-based-on-domain-decompositions-and-integrated-radial-basis-functions-for-fluid-flow-problems

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##### Parallel Computation Using Non-Overlapping Domain Decomposition Coupled with Compact Local Integrated RBF for Navier-Stokes Equations

Pham-Sy, Nam and Tran, Canh-Dung. 2022. "Parallel Computation Using Non-Overlapping Domain Decomposition Coupled with Compact Local Integrated RBF for Navier-Stokes Equations."*International Journal of Computational Fluid Dynamics.*36 (10), pp. 835-856. https://doi.org/10.1080/10618562.2023.2229250

##### A high-order coupled compact integrated RBF approximation based domain decomposition algorithm for second-order differential problems

Tien, C. M. T., Pham-Sy, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2015. "A high-order coupled compact integrated RBF approximation based domain decomposition algorithm for second-order differential problems."*CMES Computer Modeling in Engineering and Sciences.*104 (4), pp. 251-304. https://doi.org/10.3970/cmes.2015.104.251

##### Parallel control-volume method based on compact local integrated RBFs for the solution of fluid flow problems

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Pham-Sy, N., Tran, C.-D., Hoang-Trieu, T.-T., Mai-Duy, N. and Tran-Cong, T.. 2013. "Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm."*CMES Computer Modeling in Engineering and Sciences.*92 (1), pp. 1-31. https://doi.org/10.3970/cmes.2013.092.001

##### Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition

Pham-Sy, N., Hoang-Trieu, T.-T., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition." Gu, Y. T. and Saha, Suvash C. (ed.)*4th International Conference on Computational Methods (ICCM 2012).*Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.