Abstract
Irregular problems require the computation of some properties for a set of elements that are irregularly distributed in a domain. The distribution may change at run time in a way that cannot be foreseen in advance. Most irregular problems satisfy a locality property because the properties of an element e depend on the elements that are “close” to e. We propose a methodology to develop a highly parallel solution based upon a load balancing strategy that respects locality because e and most of the elements close to e are mapped onto the same processing node. We also discuss the update of the mapping at run time to recover an unbalancing, together with strategies to acquire data on elements mapped onto other processing node. The proposed methodology is applied to the multigrid adaptive problem and some experimental results are discussed.
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References
E.C. Anderson and J.P. Brooks and C.M. Gassi and S.L. Scott. Performance Analysis of the T3E Multiprocessor SC’97: High Performance Networking and Computing: Proceedings of the 1997 ACM/IEEE SC97, 1997.
F. Baiardi, P. Becuzzi, P. Mori, and M. Paoli. Load balancing and locality in hierarchical N-body algorithms on distributed memory architectures. Lecture Notes in Computer Science, 1401:284–293, 1998.
J.E. Barnes and P. Hut. A hierarchical O(nlogn) force calculation algorithm. Nature, 324:446–449, 1986.
P. Bastian, S. Lang, and K. Eckstein. Parallel adaptive multigrid methods in plane linear elasticity problems. Numerical linear algebra with applications, 4(3):153–176, 1997.
P. Bastian and G. Wittum. Adaptive multigrid methods: The UG concept. In Adaptive Methods — Algorithms, Theory and Applications, volume 46 of Notes on Numerical Fluid Mechanics, pages 17–37, 1994.
M. Berger and J. Oliger. Adaptive mesh refinement for hyperbolic partial differential equations. Journal of Computational Physics, 53:484–512, 1984.
W. Briggs. A multigrid tutorial. SIAM, 1987.
M. Griebel and G. Zumbusch. Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves. Parallel Computing, 25(7):827–843, 1999.
P. Hanrahan, D. Salzman, and L. Aupperle. A rapid hierarchical radiosity algorithm. Computer Graphics, 25(4):197–206, 1991.
Y.S. Hwang, R. Das, J.H. Saltz, M. Hodoscek, and B.R. Brooks. Parallelizing molecular dynamics programs for distributed-memory machines. IEEE Computational Science & Engineering, 2(2):18–29, 1995.
M. Parashar and J.C. Browne. On partitioning dynamic adaptive grid hierarchies. In Proceeding of the 29th annual Hawaii international conference on system sciences, 1996.
J.R. Pilkington and S.B. Baden. Dynamic partitioning of non-uniform structured workloads with space filling curves. IEEE Transaction on parallel and distributed systems, 7(3):288–299, 1996.
M. Prieto, D. Espadas, I.M. Llorente, and F. Tirado. Message passing evaluation and analysis on Cray T3E and SGI Origin 2000 systems. Lecture Notes in Computer Science, 1685:173–182, 1999.
J.K. Salmon. Parallel hierarchical N-body methods. PhD thesis, California Institute of Technology, 1990.
S. Sharma, R. Ponnusamy, B. Moon, Y. Hwang, R. Das, and J. Saltz. Run-time and compile-time support for adaptive irregular problems. In Proceedings of Supercomputing, pages 97–106, 1994.
J.P. Singh. Parallel hierarchical N-body methods and their implications for multiprocessors. PhD thesis, Stanford University, 1993.
J.P Singh, C. Holt, T. Totsuka, A. Gupta and J.L. Hennessy. Load balancing and data locality in adaptive hierarchical n-body methods: Barnes-Hut, Fast Multipole and Radiosity Journal of Parallel and Distributed Computing, 27(2):118–141, 1995.
Y.N. Vorobjev and H.A. Scheraga. A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent. Journal of Computational Chemistry, 18(4):569–583, 1997.
M.S. Warren and J.K. Salmon. A parallel hashed oct-tree N-body algorithm. In Proceedings of Supercomputing’ 93, pages 12–21, 1993.
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Baiardi, F., Chiti, S., Mori, P., Ricci, L. (2000). Parallelization of Irregular Problems Based on Hierarchical Domain Representation. In: Bubak, M., Afsarmanesh, H., Hertzberger, B., Williams, R. (eds) High Performance Computing and Networking. HPCN-Europe 2000. Lecture Notes in Computer Science, vol 1823. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45492-6_8
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DOI: https://doi.org/10.1007/3-540-45492-6_8
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