Abstract
Load balancing is an important issue in parallel numerical simulations. However, state-of-the-art libraries addressing this problem show several deficiencies: they are hard to parallelize, focus on small edge-cuts rather than few boundary vertices, and often produce disconnected partitions.
We present a distributed implementation of a load balancing heuristic for parallel adaptive FEM simulations. It is based on a disturbed diffusion scheme embedded in a learning framework. This approach incorporates a high degree of parallelism that can be exploited and it computes well-shaped partitions as shown in previous publications. Our focus lies on improving the condition of the involved matrix and solving the resulting linear systems with local accuracy. This helps to omit unnecessary computations as well as allows to replace the domain decomposition by an alternative data distribution scheme reducing the communication overhead, as shown by experiments with our new MPI based implementation.
This work is supported by German Science Foundation (DFG) Research Training Group GK-693 of the Paderborn Institute for Scientific Computation (PaSCo) and DFG Collaborative Research Centre SFB-376.
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Cybenko, G.: Dynamic load balancing for distributed memory multiprocessors. Parallel and Distributed Computing 7(2), 279–301 (1989)
Diekmann, R., Frommer, A., Monien, B.: Efficient schemes for nearest neighbor load balancing. Parallel Computing 25(7), 789–812 (1999)
Diekmann, R., Preis, R., Schlimbach, F., Walshaw, C.: Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM. J. Parallel Computing 26, 1555–1581 (2000)
Elsässer, R., Monien, B., Preis, R.: Diffusion schemes for load balancing on heterogeneous networks. Theory of Computing Systems 35, 305–320 (2002)
Fox, G., Williams, R., Messina, P.: Parallel Computing Works! Morgan Kaufmann, San Francisco (1994)
Hendrickson, B.: Graph partitioning and parallel solvers: Has the emperor no clothes? In: Ferreira, A., Rolim, J.D.P., Teng, S.-H. (eds.) IRREGULAR 1998. LNCS, vol. 1457, pp. 218–225. Springer, Heidelberg (1998)
Hendrickson, B., Leland, R.: A multi-level algorithm for partitioning graphs. In: Supercomputing 1995 (1995)
Hromkovic, J., Monien, B.: The bisection problem for graphs of degree 4. In: Tarlecki, A. (ed.) MFCS 1991. LNCS, vol. 520, pp. 211–220. Springer, Heidelberg (1991)
Hu, Y.F., Blake, R.F.: An improved diffusion algorithm for dynamic load balancing. Parallel Computing 25(4), 417–444 (1999)
Kaasschieter, E.F.: Preconditioned conjugate gradients for solving singular systems. J. of Computational and Applied Mathematics 24(1-2), 265–275 (1988)
Karypis, G., Kumar, V.: MeTis: A Software Package for Partitioning Unstrctured Graphs, Partitioning Meshes, [...], Version 4.0 (1998)
Kernighan, B.W., Lin, S.: An efficient heuristic for partitioning graphs. Bell Systems Technical Journal 49, 291–308 (1970)
MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proc. of 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297. University of California Press, Berkeley (1967)
Meyerhenke, H., Monien, B., Schamberger, S.: Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid. In: Proc. 20th IEEE Intern. Parallel and Distributed Processing Symposium (IPDPS 2006), p. 57. IEEE Computer Society, Los Alamitos (2006) (CD)
Meyerhenke, H., Schamberger, S.: Balancing parallel adaptive fem computations by solving systems of linear equations. In: Cunha, J.C., Medeiros, P.D. (eds.) Euro-Par 2005. LNCS, vol. 3648, pp. 209–219. Springer, Heidelberg (2005)
Oliker, L., Biswas, R.: PLUM: Parallel load balancing for adaptive unstructured meshes. J. Par. Dist. Comp. 52(2), 150–177 (1998)
Schamberger, S.: Graph partitioning with the Party library: Helpful-sets in practice. In: Comp. Arch. and High Perf. Comp., pp. 198–205 (2004)
Schamberger, S.: On partitioning FEM graphs using diffusion. In: HPGC, Intern. Par. and Dist. Processing Symposium, IPDPS 2004, p. 277 (2004) (CD)
Schamberger, S.: A shape optimizing load distribution heuristic for parallel adaptive FEM computations. In: Malyshkin, V.E. (ed.) PaCT 2005. LNCS, vol. 3606, pp. 263–277. Springer, Heidelberg (2005)
Schloegel, K., Karypis, G., Kumar, V.: Multilevel diffusion schemes for repartitioning of adaptive meshes. J. Par. Dist. Comp. 47(2), 109–124 (1997)
Walshaw, C.: The parallel JOSTLE library user guide: Version 3.0 (2002)
Walshaw, C., Cross, M.: Parallel optimisation algorithms for multilevel mesh partitioning. J. Parallel Computing 26(12), 1635–1660 (2000)
Walshaw, C., Cross, M., Everett, M.G.: A Localised Algorithm for Optimising Unstructured Mesh Partitions. Intl. J. Supercomputer Appl. 9(4), 280–295 (1995)
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Meyerhenke, H., Schamberger, S. (2006). A Parallel Shape Optimizing Load Balancer. In: Nagel, W.E., Walter, W.V., Lehner, W. (eds) Euro-Par 2006 Parallel Processing. Euro-Par 2006. Lecture Notes in Computer Science, vol 4128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11823285_24
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DOI: https://doi.org/10.1007/11823285_24
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