Abstract
Adaptive multigrid methods solve partial differential equations through a discrete representation of the domain that introduces more points in those zones where the equation behavior is highly irregular. The distribution of the points changes at run time in a way that cannot be foreseen in advance. We propose a methodology to develop a highly parallel solution based upon a load balancing strategy that respects the locality property of adaptive multigrid method, where the value of a point p depends on the points that are ”close” to p according to a neighborhood stencil. We also describe the update of the mapping at run time to recover an unbalancing, together with strategies to acquire data mapped onto other processing nodes. A MPI implementation is presented together with some experimental results.
This work has been partially supported by CINECA
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
F. Baiardi, P. Becuzzi, P. Mori, and M. Paoli. Load balancing and locality in hierarchical N-body algorithms on distributed memory architectures. Proceedings of HPCN 1998: Lecture Notes in Computer Science, 1401:284–293, 1998.
F. Baiardi, P. Becuzzi, S. Chiti, P. Mori, and L. Ricci. A hierarchical approach to irregular problems. Proceedings of Europar 2000: Lecture Notes in Computer Science.
F. Baiardi, S. Chiti, P. Mori, and L. Ricci. Parallelization of irregular problems based on hierarchical domain representation. Proceedings of HPCN 2000: Lecture Notes in Computer Science, 1823:71–80, 2000.
P. Bastian, S. Lang, and K. Eckstein. Parallel adaptive multigrid methods in plane linear elasticity problems. Numerical linear algebra with appl., 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. In Proceeding of ParCo 97, pages 589–599, 1998.
W.F. Mitchell. Refinement tree based partitioning for adaptive grids. In Proceedings of the 27th Conference on Parallel Processing for Scientific Computing, pages 587–592, 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. Transaction on parallel and distributed systems, 7(3):288–299, 1996.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baiardi, F., Chiti, S., Mori, P., Ricci, L. (2000). Adaptive Multigrid Methods in MPI. In: Dongarra, J., Kacsuk, P., Podhorszki, N. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 2000. Lecture Notes in Computer Science, vol 1908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45255-9_14
Download citation
DOI: https://doi.org/10.1007/3-540-45255-9_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41010-2
Online ISBN: 978-3-540-45255-3
eBook Packages: Springer Book Archive