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Original Articles

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

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Pages 370-385 | Received 23 Jul 2016, Accepted 01 Sep 2016, Published online: 20 Sep 2016

References

  • Adams, M.F. 2001. “A Distributed Memory Unstructured Gauss-Seidel Algorithm for Multigrid Smoothers.” In Supercomputing ’01: Proceedings of the 2001 ACM/IEEE Conference on Supercomputing, 44, New York, NY: ACM Press.
  • Adams, L.M., and J. Ortega. 1982. “A Multi-Color SOR Method for Parallel Computation.” Proceeding of 1982 international conference on parallel processing, 53–58, Bellaire, MI.
  • Adelmann, A., P. Arbenz, and Y. Ineichen. 2012. “Improvements of a Fast Parallel Poisson Solver on Irregular Domains.” In Applied Parallel and Scientific Computing, 65–74, Berlin: Springer.
  • Amodio, P., and F. Mazzia. 1995. “A Parallel Gauss-Seidel Method for Block Tridiagonal Linear Systems.” SIAM Journal on Scientific Computing 16 (6): 1451–1461.
  • Aubry, R., F. Mut, R. Lohner, and R.J. Cebral. 2008. “Deflated Preconditioned Conjugate Gradient Solvers for the Pressure-Poisson Equation.” Journal of Computational Physics 227 (24): 10196–10208.
  • Block, U., A. Frommer, and G. Mayer. 1990. “Block Coloring Schemes for the SOR Method on Local Memory Parallel Computers.” Parallel Computing 14: 61.
  • Burgess, D.A., and B.M. Giles. 1997. “Renumbering Unstructured Grids to Improve the Performance of Codes on Hierarchical Memory Machines.” Advances in Engineering Software 28: 189–201.
  • Cheng, M., G. Wang, and H. Hameed Mian. 2014. “Reordering of Hybrid Unstructured Grids for an Implicit Navier–Stokes Solver Based on OpenMP Parallelization.” Computers & Fluids 110: 245–253.
  • Christon, M.A. 2002. “Dealing with Pressure: FEM Solution Strategies for the Pressure in the Time-Dependent Navier-Stokes Equations.” International Journal for Numerical Methods in Fluids 38 (12): 1177–1198.
  • Coutinho, A.L., A.M. Martins, R.M. Sydenstricker, and N.R. Elias. 2006. “Performance Comparison of Data-reordering Algorithms for Sparse Matrix-Vector Multiplication in Edge-Based Unstructured Grid Computations.” International Journal for Numerical Methods in Engineering 66 (3): 431–460.
  • Fringer, O.B., M. Gerritsen, and L.R. Street. 2006. “An Unstructured-Grid, Finite-Volume, Nonhydrostatic, Parallel Coastal Ocean Simulator.” Ocean Modelling 14 (3): 139–173.
  • Gropp, W., E. Lusk, and A. Skjellum. 1999. Using MPI: Portable Parallel Programming with the Message-Passsing Interface. 2nd ed. Cambridge: The MIT Press.
  • Hendrickson, B., and R. Leland. 1993. A User's Guide to the Graph Partitioning Code Chaco. Technical Report SAND93-2339. Albuquerque, NM: Sandia National Laboratories.
  • Hsu, H.W., N.F. Hwang, H.Z. Wei, H.S. Lai, and A.C. Lin. 2011. “A Parallel Multilevel Preconditioned Iterative Pressure Poisson Solver for the Large-Eddy Simulation of Turbulent Flow Inside a Duct.” Computers & Fluids 45 (1): 138–146.
  • Jin, H., D. Jespersen, P. Mehrotra, R. Biswas, L. Huang, and B. Chapman. 2011. “High Performance Computing Using MPI and OpenMP on Multi-Core Parallel Systems.” Parallel Computing 37 (9): 562–575.
  • Jofre, L., R. Borrell, O. Lehmkuhl, and A. Oliva ,. 2015. “Parallel Load Balancing Strategy for Volume-of-Fluid Methods on 3-D Unstructured Meshes.” Journal of Computational Physics 282 (1): 269–288.
  • Kim, T., and O.C. Lee. 1999. “A Parallel Gaus-Seidel Method Using NR Data Flow Ordering.” Applied Mathematics and Computation 99 (2): 209–220.
  • Koric, S., Q. Lu, and E. Guleryuz. 2014. “Evaluation of Massively Parallel Linear Sparse Solvers on Unstructured Finite Element Meshes.” Computers and Structures 141: 19–25.
  • Lemmer, A., and H. Rudolf. 2015. “Parallel Domain Decomposition Method with Non-Blocking Communication for Flow Through Porous Media.” Journal of Computational Physics 281: 970–981.
  • Notay, Y., and A. Napov. 2015. “A Massively Parallel Solver for Discrete Poisson-Like Problems.” Journal of Computational Physics 281: 237–250.
  • NRC-CHC,. 2010. Blue Kenue Reference Manual. Ottawa, ON: National Research Council Canada, Canadian Hydraulics Centre.
  • Oliker, , L., X. Li, G. Heber, and R. Biswas. 2000. “Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems.” Lecture Notes in Computer Science 1800: 497–503.
  • Phillips, N.A. 1957. “A Coordinate System Having Some Special Advantages for Numerical Forecasting.” Journal of Meteorology 14: 184–185.
  • Ramamurti, R., R. Lohner, and C.W. Sandberg. 1994. “Evaluation of a Scalable 3-D Incompressible Finite Element Solver.” AIAA Paper, 94-0756.
  • Saad, Y., M. Yeung, J. Erhel, and F. Guyomarc’h. 2000. “A Deflated Version of the Conjugate Gradient Algorithm.” SIAM Journal on Scientific Computing 21 (5): 1909–1926.
  • Sato, Y., T. Hino, and K. Ohashi 2013. “Parallelization of an Unstructured Navier-Stokes Solver Using a Multi-Color Ordering Method for OpenMP.” Computers & Fluids 88: 496–509.
  • Schwarz, H.A. 1870. “Über einen Grenzübergang durch alternierendes Verfahren.” Vierteljahrsschrift der Naturforschenden Gesellschaft Zurich 15: 272–286.
  • Shadid, J., S. Hutchinson, G. Hennigan, H. Moffat, K. Devine, and G.A. Salinger. 1997. “Efficient Parallel Computation of Unstructured Finite Element Reacting Flow Solutions.” Parallel Computing 23 (9): 1307–1325.
  • Shang, Y. 2009. “A Distributed Memory Parallel Gauss-Seidel Algorithm for Linear Algebraic Systems.” Computers & Mathematics with Applications 57 (8): 1369–1376.
  • Shi, Y., K.R. Ray, and K.D. Nguyen. 2013. “A Projection Method-Based Model with the Exact C-Property for Shallow-Water Flows Over Dry and Irregular Bottom Using Unstructured Finite-Volume Technique.” Computers & Fluids 76: 178–195.
  • Smith, B.F., P.E. Bjørstad, and W.D. Gropp. 1996. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge: Cambridge University Press.
  • Su, M., and J.-D. Yu. 2012. “A Parallel Large Eddy Simulation with Unstructured Meshes Applied to Turbulent Flow Around Car Side Mirror.” Computers & Fluids 55: 24–28.
  • Tavakoli, R., and P. Davami. 2007. “A New Parallel Gauss-Seidel Method based on Alternating Group Explicit Method and Domain Decomposition Method.” Applied Mathematics and Computation 188 (1): 713–719.
  • Uh Zapata, M., D. Pham Van Bang, and D.K. Nguyen. 2014. “An Unstructured Finite Volume Technique for the 3D Poisson Equation on Arbitrary Geometry Using a σ-Coordinate System.” International Journal for Numerical Methods in Fluids 76 (10): 611–631.
  • Walker, E., Nikitopoulos, D., and Tromeur-Dervout, D., 2013. “Parallel Solution Methods for Poisson-Like Equations in Two-Phase Flows.” Computers & Fluids 80: 152–157.
  • Waltz, J. 2004. “Parallel Adaptive Refinement for Unsteady Flow Calculations on 3D Unstructured Grids.” International Journal for Numerical Methods in Fluids 46 (1): 37–57.
  • Xie, D. 2006. “A New Block Parallel SOR Method and Its Analysis.” SIAM Journal on Scientific Computing 27 (5): 1513–1533.
  • Xie, D., and L. Adams. 1999. “New Parallel SOR Method by Domain Partitioning.” SIAM Journal on Scientific Computing 20 (6): 2261–2281.

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