PC Cluster Implementation of a Mass Transport Two-Dimensional Model
Resumo
This work presents a parallel solution for the continuity and horizontal momentum equations, and for the mass transport equation. They constitute a model for contaminant transport simulation. The first ones were solved spplying Krylov-Schwarz method and for the last one it was used a pipelined Thomas method. The computational model was implemented on a PC cluster using MPI message passing library. Semi-implicit numerical schemes were developed over a staggered grid.
Palavras-chave:
Cluster computing, Krylov-Schwarz method, pipelined Thomas algorithm, Mass Transport Equation, water quality
Referências
AGOSHKOV, V. I. et al. Recent Developments in the Numerical Simulation of Shallow Water Equations I: Boundary Conditions. Applied Numerical Mathematics, v.15, p.175–200, 1994.
BOTT, A. A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of Advective Fluxes. Monthly Weather Review, v.117, p.1006–1015, 1988.
CASALAS, Alejandro B. Modelo Matemático de Correntologia do Estuário do Rio Guaíba. Technical Report 12, Porto Alegre: Instituto de Pesquisas Hidráulicas da UFRGS, 1985.
CASALAS, Alejandro B. IPH-A – Aplicativo para Modelação de Estuários e Lagos – Manual de utilização do Sistema. Porto Alegre: Instituto de Pesquisas Hidráulicas da UFRGS, 1996.
CASULLI, Vincenzo. Semi-Implicit Finite Difference Methods for the Two-Dimensional Shallow Water Equations. Journal of Computational Physics, v.86, p.56–74, 1990.
CHAN, Tony F.; MATHEW, T. P. Domain Decomposition Algorithms. Acta Numerica, p.61–143, 1994.
CHENG, R. Eulerian-Lagrangian Solution of the Convection-Dispersion Equation in Natural Coordinates. Water Resources Research, v.20, p.944–952, July 1984.
CHEFFER, J. G. et al. Domain Decomposition for the Shallow Water Equations. Proceedings of the Ninth International Conference on Domain Decomposition Methods in Scientific and Engineering Computing, 1998. Available at [link].
CIARLET Jr., P. et al. On the Influence of Partitioning Schemes on the Efficiency of Overlapping Domain Decomposition Methods. 1994.
DIEKMANN, Ralf et al. Load Balancing Strategies for Distributed Memory Machines. In Multi-Scale Phenomena and Their Simulation. World Scientific, 1997.
GOOSSENS, S. et al. An Efficient FGMRES Solver for the Shallow Water Equations based on Domain Decomposition. Proceedings of the Seventh International Conference on Domain Decomposition Methods in Scientific and Engineering Computing. Available at [link], Nov. 1993.
GROPP, William et al. A High Performance, Portable Implementation of the MPI Message Passing Standard. Parallel Computing, v.22, n.6, p.789–828, Sep. 1996.
KAPLAN, Elias A. Shallow Water Model Distributed Using Domain Decomposition. Sweden: The Royal Institute of Technology, 1998. (Master Thesis).
LEENDERTSE, J. J. A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas – vol. I. Principles of Computation. Technical Report RM-6230-RC, Santa Monica: The Rand Corp., 1970.
LEENDERTSE, J. J.; GRITTON, E. C. A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas – vol. II. Computation Procedures. Technical Report R-708-NYC, Santa Monica: The Rand Corp., 1971.
MESSINGER, F. Numerical Methods: The Arakawa Approach. Horizontal Grid. Global and Limited-Area Modeling. Camp Springs: Academic Press, 1998.
NASCIMENTO, W. D. et al. Um Estudo Sobre Algoritmos para Particionamento de Malhas Não Estruturadas. Rio de Janeiro: COPPE/UFRJ, 1996.
POVITSKY, A. Parallelization of the Pipeline Thomas Algorithm. NASA/CR-1998-208736 ICASE Report n° 98-48. Institute for Computer Application in Science and Engineering. Hampton: NASA Langley Res. Center, 1998.
RIZZI, Rogério L. et al. Fluvial Flow of the Guaíba River – A Parallel Solution for the Shallow Water Equations Model. Proceedings of the Fourth Vecpar 2000, Part III, June 23, p.895–896.
SHEWCHUCK, Jonathan R. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain. School of Computer Science, Carnegie Mellon University, 1994. Available at [link].
SILVA, Renato et al. Iterative Local Solvers for Distributed Krylov-Schwarz Method Applied to Convection-Diffusion Problems. Preprint submitted to Elsevier Science, 1997.
SMITH, Barry et al. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University, 1996.
VARGA, Richard S. Matrix Iterative Analysis. 2nd ed., rev. and expanded. Springer Series in Computational Mathematics, 1999.
VOOLEBREGT, Edwin A. H. Parallel Software Development Techniques for Shallow Water Models. Delft: Technische Universiteit Delft, 1997. (PhD Thesis).
ZHENG, Chunmiao; BENNETT, Gordon D. Applied Contaminant Transport Modeling. Van Nostrand Reinhold, 1995.
BOTT, A. A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of Advective Fluxes. Monthly Weather Review, v.117, p.1006–1015, 1988.
CASALAS, Alejandro B. Modelo Matemático de Correntologia do Estuário do Rio Guaíba. Technical Report 12, Porto Alegre: Instituto de Pesquisas Hidráulicas da UFRGS, 1985.
CASALAS, Alejandro B. IPH-A – Aplicativo para Modelação de Estuários e Lagos – Manual de utilização do Sistema. Porto Alegre: Instituto de Pesquisas Hidráulicas da UFRGS, 1996.
CASULLI, Vincenzo. Semi-Implicit Finite Difference Methods for the Two-Dimensional Shallow Water Equations. Journal of Computational Physics, v.86, p.56–74, 1990.
CHAN, Tony F.; MATHEW, T. P. Domain Decomposition Algorithms. Acta Numerica, p.61–143, 1994.
CHENG, R. Eulerian-Lagrangian Solution of the Convection-Dispersion Equation in Natural Coordinates. Water Resources Research, v.20, p.944–952, July 1984.
CHEFFER, J. G. et al. Domain Decomposition for the Shallow Water Equations. Proceedings of the Ninth International Conference on Domain Decomposition Methods in Scientific and Engineering Computing, 1998. Available at [link].
CIARLET Jr., P. et al. On the Influence of Partitioning Schemes on the Efficiency of Overlapping Domain Decomposition Methods. 1994.
DIEKMANN, Ralf et al. Load Balancing Strategies for Distributed Memory Machines. In Multi-Scale Phenomena and Their Simulation. World Scientific, 1997.
GOOSSENS, S. et al. An Efficient FGMRES Solver for the Shallow Water Equations based on Domain Decomposition. Proceedings of the Seventh International Conference on Domain Decomposition Methods in Scientific and Engineering Computing. Available at [link], Nov. 1993.
GROPP, William et al. A High Performance, Portable Implementation of the MPI Message Passing Standard. Parallel Computing, v.22, n.6, p.789–828, Sep. 1996.
KAPLAN, Elias A. Shallow Water Model Distributed Using Domain Decomposition. Sweden: The Royal Institute of Technology, 1998. (Master Thesis).
LEENDERTSE, J. J. A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas – vol. I. Principles of Computation. Technical Report RM-6230-RC, Santa Monica: The Rand Corp., 1970.
LEENDERTSE, J. J.; GRITTON, E. C. A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas – vol. II. Computation Procedures. Technical Report R-708-NYC, Santa Monica: The Rand Corp., 1971.
MESSINGER, F. Numerical Methods: The Arakawa Approach. Horizontal Grid. Global and Limited-Area Modeling. Camp Springs: Academic Press, 1998.
NASCIMENTO, W. D. et al. Um Estudo Sobre Algoritmos para Particionamento de Malhas Não Estruturadas. Rio de Janeiro: COPPE/UFRJ, 1996.
POVITSKY, A. Parallelization of the Pipeline Thomas Algorithm. NASA/CR-1998-208736 ICASE Report n° 98-48. Institute for Computer Application in Science and Engineering. Hampton: NASA Langley Res. Center, 1998.
RIZZI, Rogério L. et al. Fluvial Flow of the Guaíba River – A Parallel Solution for the Shallow Water Equations Model. Proceedings of the Fourth Vecpar 2000, Part III, June 23, p.895–896.
SHEWCHUCK, Jonathan R. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain. School of Computer Science, Carnegie Mellon University, 1994. Available at [link].
SILVA, Renato et al. Iterative Local Solvers for Distributed Krylov-Schwarz Method Applied to Convection-Diffusion Problems. Preprint submitted to Elsevier Science, 1997.
SMITH, Barry et al. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University, 1996.
VARGA, Richard S. Matrix Iterative Analysis. 2nd ed., rev. and expanded. Springer Series in Computational Mathematics, 1999.
VOOLEBREGT, Edwin A. H. Parallel Software Development Techniques for Shallow Water Models. Delft: Technische Universiteit Delft, 1997. (PhD Thesis).
ZHENG, Chunmiao; BENNETT, Gordon D. Applied Contaminant Transport Modeling. Van Nostrand Reinhold, 1995.
Publicado
24/10/2000
Como Citar
DORNELES, Ricardo Vargas; RIZZI, Rogério Luis; ZEFERINO, Cesar Albenes; DIVERIO, Tiaraju A.; NAVAUX, Philippe O. A.; SUSIN, Altamiro A.; BAMPI, Sergio.
PC Cluster Implementation of a Mass Transport Two-Dimensional Model. In: INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE AND HIGH PERFORMANCE COMPUTING (SBAC-PAD), 12. , 2000, São Pedro/SP.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2000
.
p. 191-198.
DOI: https://doi.org/10.5753/sbac-pad.2000.41220.
