Abstract
We examine a modified implementation of the v-cycle multigrid scheme which takes into account the memory traffic, i.e. the movement of data between the memory and the processing units. It is known that the relatively slow data transfer is responsible for the poor parallel performance of multigrid algorithms on certain shared memory architectures e.g. those with a front-side bus memory controller. The modification is simple but it speeds up computations by up to 15%.
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References
Emans, M., van der Meer, A.: Mixed-precision AMG as linear equation solver for definite systems. In: Sloot, P.M.A., Dongarra, G.V.A., Dongarra, J. (eds.) ICCS 2010, Part I. Procedia Computer Science, vol. 1, pp. 175–183. Elsevier Science, North Holland (2010)
Haase, G., Reitzinger, S.: Cache issues of algebraic multigrid methods for linear systems with multiple right-hand sides. SIAM Journal on Scientific Computing 27(1), 1–18 (2005)
Douglas, C., Hu, J., Ray, J., Thorne, D., Tuminaro, R.: Cache aware multigrid for variable coefficient elliptic problems on adaptive mesh refinement hierarchies. Numerical Linear Algebra with Applications 11, 173–187 (2004)
Falgout, R.D., Yang, U.M.: hypre: A Library of High Performance Preconditioners. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J.J., Hoekstra, A.G. (eds.) ICCS-ComputSci 2002. LNCS, vol. 2331, pp. 632–641. Springer, Heidelberg (2002)
Gee, M., Siefert, C., Hu, J., Tuminaro, R., Sala, M.: ML 5.0 Smoothed Aggregation User’s Guide. SAND 2006-2009 Unlimited Release (2006)
McCalpin, J.: Memory bandwidth and machine balance in current high performance computers. IEEE Computer Society Technical Committee on Computer Architecture (TCCA) Newsletter, 19–25 (December 1995)
Emans, M.: Efficient parallel AMG methods for approximate solutions of linear systems in CFD applications. SIAM Journal on Scientific Computing 32, 2235–2254 (2010)
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20, 359–392 (1998)
Vaněk, P., Mandel, J., Brezina, M.: Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56, 179–196 (1996)
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Emans, M. (2012). Combining Smoother and Residual Calculation in v-cycle AMG for Symmetric Problems. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31464-3_66
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DOI: https://doi.org/10.1007/978-3-642-31464-3_66
Publisher Name: Springer, Berlin, Heidelberg
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