Abstract
We consider large scale finite element modeling on 3D unstructured grids. Large scale problems imply the use of parallel hardware and software. In general, the computational process on unstructured grids includes: mesh generation, mesh partitioning, optional mesh refinement, discretization, and the solution. The impact of the domain partitioning strategy on the performance of the discretization and solution stages is studied.
Our investigations are focused on the Blue Gene/P massively parallel computer. The mapping of the communications to the underlying 3D tours interconnect topology is considered as well.
As a sample problem, we consider the simulation of the thermal and electrical processes, involved in the radio-frequency (RF) ablation procedure. RF ablation is a low invasive technique for the treatment of hepatic tumors, utilizing AC current to destroy the tumor cells by heating.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Karypis, G., Kumar, V.: Multilevel k-way partitioning scheme for irregular graphs. Journal of Parallel and DistributedComputing 48(1) (1998)
Karypis, G., Kumar, V.: A coarse-grain parallel multilevel k-way partitioning algorithm. In: Proceedings of the 8th SIAM Conference on Parallel Processing for Scientific Computing (1997)
ParMETIS - Parallel Graph Partitioning and Fill-reducing Matrix Ordering, http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview
Henson, V.E., Yang, U.M.: BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics 41(1), 155–177 (2002)
Pellegrini, F., Roman, J.: Experimental analysis of the dual recursive bipartitioning algorithm for static mapping. Research Report, LaBRI, Universit e Bordeaux I (August 1996), http://www.labri.fr/~pelegrin/papers/scotch_expanalysis.ps.gz
Scotch and PT-Scotch: Software package and libraries for sequential and parallel graph partitioning, static mapping, and sparse matrix block ordering, and sequential mesh and hypergraph partitioning, http://www.labri.fr/perso/pelegrin/scotch/
Tungjitkusolmun, S., Staelin, S.T., Haemmerich, D., Tsai, J.Z., Cao, H., Webster, J.G., Lee, F.T., Mahvi, D.M., Vorperian, V.R.: Three-dimensional finite-element analyses for radio-frequency hepatic tumor ablation. IEEE Transactions on Biomedical Engineering 49(1), 3–9 (2002)
Tungjitkusolmun, S., Woo, E.J., Cao, H., Tsai, J.Z., Vorperian, V.R., Webster, J.G.: Thermal-electrical finite element modelling for radio frequency cardiac ablation: Effects of changes in myocardial properties. Medical and Biological Engineering and Computing 38(5), 562–568 (2000)
Axelsson, O.: Iterative Solution Methods. Cambridge University Press (1996)
Brenner, S., Scott, L.: The mathematical theory of finite element methods. Texts in Applied Mathematics, vol. 15. Springer, Heidelberg (1994)
Hairer, E., Norsett, S.P., Wanner, G.: Solving ordinary differential equations I, II. Springer Series in Comp. Math. (2002)
Kosturski, N., Margenov, S.: Supercomputer Simulation of Radio-Frequency Hepatic Tumor Ablation, AMiTaNS 2010 Proceedings. AIP CP, vol. 1301, pp. 486–493 (2010)
Lawrence Livermore National Laboratory, Scalable Linear Solvers Project, http://www.llnl.gov/CASC/linear_solvers/
Netgen Mesh Generator, http://sourceforge.net/apps/mediawiki/netgen-mesher/
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kosturski, N., Margenov, S., Vutov, Y. (2012). Balancing the Communications and Computations in Parallel FEM Simulations on Unstructured Grids. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31500-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-31500-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31499-5
Online ISBN: 978-3-642-31500-8
eBook Packages: Computer ScienceComputer Science (R0)