Abstract
In this work, we consider large-scale finite element modeling on voxel grids. We are targeting the IBM Blue Gene/P computer, which features a 3D torus interconnect. Our previous parallelization approach was to divide the domain in one spatial direction only, which lead to limited parallelism. Here, we extend it to all three spatial directions in order to match the interconnect topology.
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. A 3D voxel approach is used for finite element method (FEM) approximation of the involved partial differential equations. After the space discretization, the backward Euler scheme is used for the time stepping.
We study the impact of the domain partitioning on the performance of a parallel preconditioned conjugate gradient (PCG) solver for the arising large linear systems. As a preconditioner, we use BoomerAMG – a parallel algebraic multigrid implementation from the package Hypre, developed in LLNL, Livermore. The implementation is tested on the IBM Blue Gene/P massively parallel computer.
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References
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. 2000 (2002)
Henson, V.E., Yang, U.M.: BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics 41(1), 155–177 (2002)
Kosturski, N., Margenov, S.: Supercomputer Simulation of Radio-Frequency Hepatic Tumor Ablation. In: AMiTaNS 2010 Proceedings. AIP CP, vol. 1301, pp. 486–493 (2010)
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)
Lawrence Livermore National Laboratory, Scalable Linear Solvers Project, http://www.llnl.gov/CASC/linear_solvers/
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Kosturski, N., Margenov, S., Vutov, Y. (2012). Improving the Efficiency of Parallel FEM Simulations on Voxel Domains. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_65
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DOI: https://doi.org/10.1007/978-3-642-29843-1_65
Publisher Name: Springer, Berlin, Heidelberg
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