Hierarchical approach for deriving a reproducible unblocked LU factorization

[EN] We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we build upon Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via iterative refinement. Following a bottom-up approach, we finally construct a reproducible unblocked implementation of the LU factorization for GPUs, which accommodates partial pivoting for stability and can be eventually integrated in a high performance and stable algorithm for the (blocked) LU factorization.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The simulations were performed on resources provided by the Swed-ish National Infrastructure for Computing (SNIC) at PDC Centre for High Performance Computing (PDC-HPC). This work was also granted access to the HPC resources of The Institute for Scientific Computing and Simulation financed by Region Ile-de-France and the project Equip@Meso (reference ANR-10-EQPX-29-01) overseen by the French National Agency for Research (ANR) as part of the Investissements d Avenir pro-gram. This work was also partly supported by the FastRelax (ANR-14-CE25-0018-01) project of ANR.Iakymchuk, R.; Graillat, S.; Defour, D.; Quintana-Orti, ES. (2019). Hierarchical approach for deriving a reproducible unblocked LU factorization. International Journal of High Performance Computing Applications. 33(5):791-803. https://doi.org/10.1177/1094342019832968S791803335Arteaga, A., Fuhrer, O., & Hoefler, T. (2014). Designing Bit-Reproducible Portable High-Performance Applications. 2014 IEEE 28th International Parallel and Distributed Processing Symposium. doi:10.1109/ipdps.2014.127Bientinesi, P., Quintana-Ortí, E. S., & Geijn, R. A. van de. (2005). Representing linear algebra algorithms in code: the FLAME application program interfaces. ACM Transactions on Mathematical Software, 31(1), 27-59. doi:10.1145/1055531.1055533Chohra, C., Langlois, P., & Parello, D. (2016). Efficiency of Reproducible Level 1 BLAS. Lecture Notes in Computer Science, 99-108. doi:10.1007/978-3-319-31769-4_8Collange, S., Defour, D., Graillat, S., & Iakymchuk, R. (2015). Numerical reproducibility for the parallel reduction on multi- and many-core architectures. Parallel Computing, 49, 83-97. doi:10.1016/j.parco.2015.09.001Demmel, J., & Hong Diep Nguyen. (2013). Fast Reproducible Floating-Point Summation. 2013 IEEE 21st Symposium on Computer Arithmetic. doi:10.1109/arith.2013.9Demmel, J., & Nguyen, H. D. (2015). Parallel Reproducible Summation. IEEE Transactions on Computers, 64(7), 2060-2070. doi:10.1109/tc.2014.2345391Dongarra, J. J., Du Croz, J., Hammarling, S., & Duff, I. S. (1990). A set of level 3 basic linear algebra subprograms. ACM Transactions on Mathematical Software, 16(1), 1-17. doi:10.1145/77626.79170Dongarra, J., Hittinger, J., Bell, J., Chacon, L., Falgout, R., Heroux, M., … Wild, S. (2014). Applied Mathematics Research for Exascale Computing. doi:10.2172/1149042Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P., & Zimmermann, P. (2007). MPFR. ACM Transactions on Mathematical Software, 33(2), 13. doi:10.1145/1236463.1236468Haidar, A., Dong, T., Luszczek, P., Tomov, S., & Dongarra, J. (2015). Batched matrix computations on hardware accelerators based on GPUs. The International Journal of High Performance Computing Applications, 29(2), 193-208. doi:10.1177/1094342014567546Hida, Y., Li, X. S., & Bailey, D. H. (s. f.). Algorithms for quad-double precision floating point arithmetic. Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001. doi:10.1109/arith.2001.930115Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms. doi:10.1137/1.9780898718027Iakymchuk, R., Defour, D., Collange, S., & Graillat, S. (2015). Reproducible Triangular Solvers for High-Performance Computing. 2015 12th International Conference on Information Technology - New Generations. doi:10.1109/itng.2015.63Iakymchuk, R., Defour, D., Collange, S., & Graillat, S. (2016). Reproducible and Accurate Matrix Multiplication. Lecture Notes in Computer Science, 126-137. doi:10.1007/978-3-319-31769-4_11Kulisch, U., & Snyder, V. (2010). The exact dot product as basic tool for long interval arithmetic. Computing, 91(3), 307-313. doi:10.1007/s00607-010-0127-7Li, X. S., Demmel, J. W., Bailey, D. H., Henry, G., Hida, Y., Iskandar, J., … Yoo, D. J. (2002). Design, implementation and testing of extended and mixed precision BLAS. ACM Transactions on Mathematical Software, 28(2), 152-205. doi:10.1145/567806.567808Muller, J.-M., Brisebarre, N., de Dinechin, F., Jeannerod, C.-P., Lefèvre, V., Melquiond, G., … Torres, S. (2010). Handbook of Floating-Point Arithmetic. doi:10.1007/978-0-8176-4705-6Ogita, T., Rump, S. M., & Oishi, S. (2005). Accurate Sum and Dot Product. SIAM Journal on Scientific Computing, 26(6), 1955-1988. doi:10.1137/030601818Ortega, J. . (1988). The ijk forms of factorization methods I. Vector computers. Parallel Computing, 7(2), 135-147. doi:10.1016/0167-8191(88)90035-xRump, S. M. (2009). Ultimately Fast Accurate Summation. SIAM Journal on Scientific Computing, 31(5), 3466-3502. doi:10.1137/080738490Skeel, R. D. (1979). Scaling for Numerical Stability in Gaussian Elimination. Journal of the ACM, 26(3), 494-526. doi:10.1145/322139.322148Zhu, Y.-K., & Hayes, W. B. (2010). Algorithm 908. ACM Transactions on Mathematical Software, 37(3), 1-13. doi:10.1145/1824801.182481

Predictive Reliability and Fault Management in Exascale Systems: State of the Art and Perspectives

© ACM, 2020. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Computing Surveys, Vol. 53, No. 5, Article 95. Publication date: September 2020. https://doi.org/10.1145/3403956[EN] Performance and power constraints come together with Complementary Metal Oxide Semiconductor technology scaling in future Exascale systems. Technology scaling makes each individual transistor more prone to faults and, due to the exponential increase in the number of devices per chip, to higher system fault rates. Consequently, High-performance Computing (HPC) systems need to integrate prediction, detection, and recovery mechanisms to cope with faults efficiently. This article reviews fault detection, fault prediction, and recovery techniques in HPC systems, from electronics to system level. We analyze their strengths and limitations. Finally, we identify the promising paths to meet the reliability levels of Exascale systems.This work has received funding from the European Union's Horizon 2020 (H2020) research and innovation program under the FET-HPC Grant Agreement No. 801137 (RECIPE). Jaume Abella was also partially supported by the Ministry of Economy and Competitiveness of Spain under Contract No. TIN2015-65316-P and under Ramon y Cajal Postdoctoral Fellowship No. RYC-2013-14717, as well as by the HiPEAC Network of Excellence. Ramon Canal is partially supported by the Generalitat de Catalunya under Contract No. 2017SGR0962.Canal, R.; Hernández Luz, C.; Tornero-Gavilá, R.; Cilardo, A.; Massari, G.; Reghenzani, F.; Fornaciari, W.... (2020). Predictive Reliability and Fault Management in Exascale Systems: State of the Art and Perspectives. ACM Computing Surveys. 53(5):1-32. https://doi.org/10.1145/3403956S132535Abella, J., Hernandez, C., Quinones, E., Cazorla, F. J., Conmy, P. R., Azkarate-askasua, M., … Vardanega, T. (2015). WCET analysis methods: Pitfalls and challenges on their trustworthiness. 10th IEEE International Symposium on Industrial Embedded Systems (SIES). doi:10.1109/sies.2015.7185039E. Agullo L. Giraud A. Guermouche J. Roman and M. Zounon. 2013. Towards resilient parallel linear Krylov solvers: Recover-restart strategies. INRIA Research Report RR-8324. E. Agullo L. Giraud A. Guermouche J. Roman and M. Zounon. 2013. Towards resilient parallel linear Krylov solvers: Recover-restart strategies. INRIA Research Report RR-8324.Agullo, E., Giraud, L., Salas, P., & Zounon, M. (2016). Interpolation-Restart Strategies for Resilient Eigensolvers. SIAM Journal on Scientific Computing, 38(5), C560-C583. doi:10.1137/15m1042115Al-Qawasmeh, A. M., Pasricha, S., Maciejewski, A. A., & Siegel, H. J. (2015). Power and Thermal-Aware Workload Allocation in Heterogeneous Data Centers. IEEE Transactions on Computers, 64(2), 477-491. doi:10.1109/tc.2013.116ARM. 2017. ARM Reliability Availability and Serviceability (RAS) Specification—ARMv8 for the ARMv8-A Architecture Profile. White paper. Retrieved from https://developer.arm.com/docs/ddi0587/latest. ARM. 2017. ARM Reliability Availability and Serviceability (RAS) Specification—ARMv8 for the ARMv8-A Architecture Profile. White paper. Retrieved from https://developer.arm.com/docs/ddi0587/latest.Avizienis, A., Laprie, J.-C., Randell, B., & Landwehr, C. (2004). Basic concepts and taxonomy of dependable and secure computing. IEEE Transactions on Dependable and Secure Computing, 1(1), 11-33. doi:10.1109/tdsc.2004.2Bautista-Gomez, L., Zyulkyarov, F., Unsal, O., & McIntosh-Smith, S. (2016). Unprotected Computing: A Large-Scale Study of DRAM Raw Error Rate on a Supercomputer. SC16: International Conference for High Performance Computing, Networking, Storage and Analysis. doi:10.1109/sc.2016.54Berrocal, E., Bautista-Gomez, L., Di, S., Lan, Z., & Cappello, F. (2017). Toward General Software Level Silent Data Corruption Detection for Parallel Applications. IEEE Transactions on Parallel and Distributed Systems, 28(12), 3642-3655. doi:10.1109/tpds.2017.2735971M.-A. Breuer and A. D. Friedman. 1976. Diagnosis 8 Reliable Design of Digital Systems. Springer. M.-A. Breuer and A. D. Friedman. 1976. Diagnosis 8 Reliable Design of Digital Systems. Springer.P. Bridges K. Ferreira M. Heroux and M. Hoemmen. 2012. Fault-tolerant linear solvers via selective reliability. ArXiv e-prints June 2012. arXiv:1206.1390 [math.NA]. P. Bridges K. Ferreira M. Heroux and M. Hoemmen. 2012. Fault-tolerant linear solvers via selective reliability. ArXiv e-prints June 2012. arXiv:1206.1390 [math.NA].F. Cappello A. Geist W. Gropp S. Kale B. Kramer and M. Snir. 2014. Toward exascale resilience: 2014 update. Supercomput. Front. Innovat. 1 1 (2014). http://superfri.org/superfri/article/view/14. F. Cappello A. Geist W. Gropp S. Kale B. Kramer and M. Snir. 2014. Toward exascale resilience: 2014 update. Supercomput. Front. Innovat. 1 1 (2014). http://superfri.org/superfri/article/view/14.F. J. Cazorla L. Kosmidis E. Mezzetti C. Hernandez J. Abella and T. Vardanega. 2019. Probabilistic worst-case timing analysis: Taxonomy and comprehensive survey. ACM Comput. Surv. 52 1 Article 14 (Feb. 2019) 35 pages. DOI:https://doi.org/10.1145/3301283 F. J. Cazorla L. Kosmidis E. Mezzetti C. Hernandez J. Abella and T. Vardanega. 2019. Probabilistic worst-case timing analysis: Taxonomy and comprehensive survey. ACM Comput. Surv. 52 1 Article 14 (Feb. 2019) 35 pages. DOI:https://doi.org/10.1145/3301283Chan, C. S., Pan, B., Gross, K., Vaidyanathan, K., & Rosing, T. Š. (2014). Correcting vibration-induced performance degradation in enterprise servers. ACM SIGMETRICS Performance Evaluation Review, 41(3), 83-88. doi:10.1145/2567529.2567555Chantem, T., Hu, X. S., & Dick, R. P. (2011). Temperature-Aware Scheduling and Assignment for Hard Real-Time Applications on MPSoCs. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 19(10), 1884-1897. doi:10.1109/tvlsi.2010.2058873Chen, M. Y., Kiciman, E., Fratkin, E., Fox, A., & Brewer, E. (s. f.). Pinpoint: problem determination in large, dynamic Internet services. Proceedings International Conference on Dependable Systems and Networks. doi:10.1109/dsn.2002.1029005Chen, Z. (2011). Algorithm-based recovery for iterative methods without checkpointing. Proceedings of the 20th international symposium on High performance distributed computing - HPDC ’11. doi:10.1145/1996130.1996142Chen, Z. (2013). Online-ABFT. Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming - PPoPP ’13. doi:10.1145/2442516.2442533Coskun, A. K., Rosing, T. S., Mihic, K., De Micheli, G., & Leblebici, Y. (2006). Analysis and Optimization of MPSoC Reliability. Journal of Low Power Electronics, 2(1), 56-69. doi:10.1166/jolpe.2006.007G. Da Costa A. Oleksiak W. Piatek J. Salom and L. Sisó. 2015. Minimization of costs and energy consumption in a data center by a workload-based capacity management. In Energy Efficient Data Centers S. Klingert M. Chinnici and M. Rey Porto (Eds.). Springer International Publishing Cham 102--119. G. Da Costa A. Oleksiak W. Piatek J. Salom and L. Sisó. 2015. Minimization of costs and energy consumption in a data center by a workload-based capacity management. In Energy Efficient Data Centers S. Klingert M. Chinnici and M. Rey Porto (Eds.). Springer International Publishing Cham 102--119.Cupertino, L., Da Costa, G., Oleksiak, A., Pia¸tek, W., Pierson, J.-M., Salom, J., … Zilio, T. (2015). Energy-efficient, thermal-aware modeling and simulation of data centers: The CoolEmAll approach and evaluation results. Ad Hoc Networks, 25, 535-553. doi:10.1016/j.adhoc.2014.11.002Dally, W. J. (1991). Express cubes: improving the performance of k-ary n-cube interconnection networks. IEEE Transactions on Computers, 40(9), 1016-1023. doi:10.1109/12.83652Dauwe, D., Pasricha, S., Maciejewski, A. A., & Siegel, H. J. (2018). Resilience-Aware Resource Management for Exascale Computing Systems. IEEE Transactions on Sustainable Computing, 3(4), 332-345. doi:10.1109/tsusc.2018.2797890R. I. Davis and A. Burns. 2011. A survey of hard real-time scheduling for multiprocessor systems. ACM Comput. Surv. 43 4 Article 35 (Oct. 2011) 44 pages. DOI:https://doi.org/10.1145/1978802.1978814 R. I. Davis and A. Burns. 2011. A survey of hard real-time scheduling for multiprocessor systems. ACM Comput. Surv. 43 4 Article 35 (Oct. 2011) 44 pages. DOI:https://doi.org/10.1145/1978802.1978814Di, S., & Cappello, F. (2016). Adaptive Impact-Driven Detection of Silent Data Corruption for HPC Applications. IEEE Transactions on Parallel and Distributed Systems, 27(10), 2809-2823. doi:10.1109/tpds.2016.2517639Di, S., Guo, H., Gupta, R., Pershey, E. R., Snir, M., & Cappello, F. (2019). Exploring Properties and Correlations of Fatal Events in a Large-Scale HPC System. IEEE Transactions on Parallel and Distributed Systems, 30(2), 361-374. doi:10.1109/tpds.2018.2864184Di, S., Robert, Y., Vivien, F., & Cappello, F. (2017). Toward an Optimal Online Checkpoint Solution under a Two-Level HPC Checkpoint Model. IEEE Transactions on Parallel and Distributed Systems, 28(1), 244-259. doi:10.1109/tpds.2016.2546248J. Dongarra T. Herault and Y. Robert. 2015. Fault Tolerance Techniques for High-Performance Computing. Springer. J. Dongarra T. Herault and Y. Robert. 2015. Fault Tolerance Techniques for High-Performance Computing. Springer.DOWNING, S., & SOCIE, D. (1982). Simple rainflow counting algorithms. International Journal of Fatigue, 4(1), 31-40. doi:10.1016/0142-1123(82)90018-4Eghbalkhah, B., Kamal, M., Afzali-Kusha, H., Afzali-Kusha, A., Ghaznavi-Ghoushchi, M. B., & Pedram, M. (2015). Workload and temperature dependent evaluation of BTI-induced lifetime degradation in digital circuits. Microelectronics Reliability, 55(8), 1152-1162. doi:10.1016/j.microrel.2015.06.004Gottscho, M., Shoaib, M., Govindan, S., Sharma, B., Wang, D., & Gupta, P. (2017). Measuring the Impact of Memory Errors on Application  Performance. IEEE Computer Architecture Letters, 16(1), 51-55. doi:10.1109/lca.2016.2599513Greenberg, A., Hamilton, J. R., Jain, N., Kandula, S., Kim, C., Lahiri, P., … Sengupta, S. (2011). VL2. Communications of the ACM, 54(3), 95-104. doi:10.1145/1897852.1897877Heroux, M. A., Bartlett, R. A., Howle, V. E., Hoekstra, R. J., Hu, J. J., Kolda, T. G., … Stanley, K. S. (2005). An overview of the Trilinos project. ACM Transactions on Mathematical Software, 31(3), 397-423. doi:10.1145/1089014.1089021Hoffmann, G. A., Trivedi, K. S., & Malek, M. (2007). A Best Practice Guide to Resource Forecasting for Computing Systems. IEEE Transactions on Reliability, 56(4), 615-628. doi:10.1109/tr.2007.909764Hsiao, M. Y., Carter, W. C., Thomas, J. W., & Stringfellow, W. R. (1981). Reliability, Availability, and Serviceability of IBM Computer Systems: A Quarter Century of Progress. IBM Journal of Research and Development, 25(5), 453-468. doi:10.1147/rd.255.0453Hughes, G. F., Murray, J. F., Kreutz-Delgado, K., & Elkan, C. (2002). Improved disk-drive failure warnings. IEEE Transactions on Reliability, 51(3), 350-357. doi:10.1109/tr.2002.802886S. Hukerikar and C. Engelmann. 2017. Resilience design patterns: A structured approach to resilience at extreme scale. Supercomput. Front. Innov. 4 3 (2017). DOI:https://doi.org/10.14529/jsfi170301 S. Hukerikar and C. Engelmann. 2017. Resilience design patterns: A structured approach to resilience at extreme scale. Supercomput. Front. Innov. 4 3 (2017). DOI:https://doi.org/10.14529/jsfi170301Hussain, H., Malik, S. U. R., Hameed, A., Khan, S. U., Bickler, G., Min-Allah, N., … Rayes, A. (2013). A survey on resource allocation in high performance distributed computing systems. Parallel Computing, 39(11), 709-736. doi:10.1016/j.parco.2013.09.009Intel Corporation. [n.d.]. Intel Xeon Processor E7 Family: Reliability Availability and Serviceability. White paper. https://www.intel.com/content/www/us/en/processors/xeon/xeon-e7-family-ras-server-paper.html. Intel Corporation. [n.d.]. Intel Xeon Processor E7 Family: Reliability Availability and Serviceability. White paper. https://www.intel.com/content/www/us/en/processors/xeon/xeon-e7-family-ras-server-paper.html.Jha, S., Formicola, V., Martino, C. D., Dalton, M., Kramer, W. T., Kalbarczyk, Z., & Iyer, R. K. (2018). Resiliency of HPC Interconnects: A Case Study of Interconnect Failures and Recovery in Blue Waters. IEEE Transactions on Dependable and Secure Computing, 15(6), 915-930. doi:10.1109/tdsc.2017.2737537Kiciman, E., & Fox, A. (2005). Detecting Application-Level Failures in Component-Based Internet Services. IEEE Transactions on Neural Networks, 16(5), 1027-1041. doi:10.1109/tnn.2005.853411Kim, T., Sun, Z., Cook, C., Zhao, H., Li, R., Wong, D., & Tan, S. X.-D. (2016). Invited - Cross-layer modeling and optimization for electromigration induced reliability. Proceedings of the 53rd Annual Design Automation Conference. doi:10.1145/2897937.2905010Kurowski, K., Oleksiak, A., Piątek, W., Piontek, T., Przybyszewski, A., & Węglarz, J. (2013). DCworms – A tool for simulation of energy efficiency in distributed computing infrastructures. Simulation Modelling Practice and Theory, 39, 135-151. doi:10.1016/j.simpat.2013.08.007Langou, J., Chen, Z., Bosilca, G., & Dongarra, J. (2008). Recovery Patterns for Iterative Methods in a Parallel Unstable Environment. SIAM Journal on Scientific Computing, 30(1), 102-116. doi:10.1137/040620394J. C. Laprie (Ed.). 1995. Dependability—Its Attributes Impairments and Means. Springer-Verlag Berlin. J. C. Laprie (Ed.). 1995. Dependability—Its Attributes Impairments and Means. Springer-Verlag Berlin.Laprie, J.-C. (s. f.). DEPENDABLE COMPUTING AND FAULT TOLERANCE : CONCEPTS AND TERMINOLOGY. Twenty-Fifth International Symposium on Fault-Tolerant Computing, 1995, ’ Highlights from Twenty-Five Years’. doi:10.1109/ftcsh.1995.532603Lasance, C. J. M. (2003). Thermally driven reliability issues in microelectronic systems: status-quo and challenges. Microelectronics Reliability, 43(12), 1969-1974. doi:10.1016/s0026-2714(03)00183-5Yinglung Liang, Yanyong Zhang, Sivasubramaniam, A., Jette, M., & Sahoo, R. (s. f.). BlueGene/L Failure Analysis and Prediction Models. International Conference on Dependable Systems and Networks (DSN’06). doi:10.1109/dsn.2006.18Lin, T.-T. Y., & Siewiorek, D. P. (1990). Error log analysis: statistical modeling and heuristic trend analysis. IEEE Transactions on Reliability, 39(4), 419-432. doi:10.1109/24.58720Losada, N., González, P., Martín, M. J., Bosilca, G., Bouteiller, A., & Teranishi, K. (2020). Fault tolerance of MPI applications in exascale systems: The ULFM solution. Future Generation Computer Systems, 106, 467-481. doi:10.1016/j.future.2020.01.026Lyons, R. E., & Vanderkulk, W. (1962). The Use of Triple-Modular Redundancy to Improve Computer Reliability. IBM Journal of Research and Development, 6(2), 200-209. doi:10.1147/rd.62.0200M. Médard and S. S. Lumetta. 2003. Network Reliability and Fault Tolerance. American Cancer Society. Retrieved from arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/0471219282.eot281. M. Médard and S. S. Lumetta. 2003. Network Reliability and Fault Tolerance. American Cancer Society. Retrieved from arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/0471219282.eot281.Moody, A., Bronevetsky, G., Mohror, K., & de Supinski, B. (2010). Detailed Modeling, Design, and Evaluation of a Scalable Multi-level Checkpointing System. doi:10.2172/984082Moor Insights 8 Strategy. 2017. AMD EPYC Brings New RAS Capability. White paper. Retrieved from https://www.amd.com/system/files/2017-06/AMD-EPYC-Brings-New-RAS-Capability.pdf. Moor Insights 8 Strategy. 2017. AMD EPYC Brings New RAS Capability. White paper. Retrieved from https://www.amd.com/system/files/2017-06/AMD-EPYC-Brings-New-RAS-Capability.pdf.Mulas, F., Atienza, D., Acquaviva, A., Carta, S., Benini, L., & De Micheli, G. (2009). Thermal Balancing Policy for Multiprocessor Stream Computing Platforms. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 28(12), 1870-1882. doi:10.1109/tcad.2009.2032372Oleksiak, A., Kierzynka, M., Piatek, W., Agosta, G., Barenghi, A., Brandolese, C., … Janssen, U. (2017). M2DC – Modular Microserver DataCentre with heterogeneous hardware. Microprocessors and Microsystems, 52, 117-130. doi:10.1016/j.micpro.2017.05.019Oxley, M. A., Jonardi, E., Pasricha, S., Maciejewski, A. A., Siegel, H. J., Burns, P. J., & Koenig, G. A. (2018). Rate-based thermal, power, and co-location aware resource management for heterogeneous data centers. Journal of Parallel and Distributed Computing, 112, 126-139. doi:10.1016/j.jpdc.2017.04.015K. O’brien I. Pietri R. Reddy A. Lastovetsky and R. Sakellariou. 2017. A survey of power and energy predictive models in HPC systems and applications. ACM Comput. Surv. 50 3 Article 37 (June 2017) 38 pages. DOI:https://doi.org/10.1145/3078811 K. O’brien I. Pietri R. Reddy A. Lastovetsky and R. Sakellariou. 2017. A survey of power and energy predictive models in HPC systems and applications. ACM Comput. Surv. 50 3 Article 37 (June 2017) 38 pages. DOI:https://doi.org/10.1145/3078811Park, S.-M., & Humphrey, M. (2011). Predictable High-Performance Computing Using Feedback Control and Admission Control. IEEE Transactions on Parallel and Distributed Systems, 22(3), 396-411. doi:10.1109/tpds.2010.100Pfefferman, J. D., & Cernuschi-Frias, B. (2002). A nonparametric nonstationary procedure for failure prediction. IEEE Transactions on Reliability, 51(4), 434-442. doi:10.1109/tr.2002.804733Rangan, K. K., Wei, G.-Y., & Brooks, D. (2009). Thread motion. ACM SIGARCH Computer Architecture News, 37(3), 302-313. doi:10.1145/1555815.1555793Paolo Rech. [n.d.]. Reliability Issues in Current and Future Supercomputers. Retrieved from http://energysfe.ufsc.br/slides/Paolo-Rech-260917.pdf. Paolo Rech. [n.d.]. Reliability Issues in Current and Future Supercomputers. Retrieved from http://energysfe.ufsc.br/slides/Paolo-Rech-260917.pdf.F. Reghenzani G. Massari and W. Fornaciari. 2019. The real-time Linux kernel: A survey on PREEMPT_RT. Comput. Surveys 52 1 Article 18 (Feb. 2019) 36 pages. DOI:https://doi.org/10.1145/3297714 F. Reghenzani G. Massari and W. Fornaciari. 2019. The real-time Linux kernel: A survey on PREEMPT_RT. Comput. Surveys 52 1 Article 18 (Feb. 2019) 36 pages. DOI:https://doi.org/10.1145/3297714F. Salfner M. Lenk and M. Malek. 2010. A survey of online failure prediction methods. ACM Comput. Surv. 42 3 Article 10 (March 2010) 42 pages. DOI:https://doi.org/10.1145/1670679.1670680 F. Salfner M. Lenk and M. Malek. 2010. A survey of online failure prediction methods. ACM Comput. Surv. 42 3 Article 10 (March 2010) 42 pages. DOI:https://doi.org/10.1145/1670679.1670680Salfner, F., Schieschke, M., & Malek, M. (2006). Predicting failures of computer systems: a case study for a telecommunication system. Proceedings 20th IEEE International Parallel & Distributed Processing Symposium. doi:10.1109/ipdps.2006.1639672Shi, L., Chen, H., Sun, J., & Li, K. (2012). vCUDA: GPU-Accelerated High-Performance Computing in Virtual Machines. IEEE Transactions on Computers, 61(6), 804-816. doi:10.1109/tc.2011.112D. P. Siewiorek and R. S. Swarz. 1998. Reliable Computer Systems 3rd ed. A. K. Peters Ltd. D. P. Siewiorek and R. S. Swarz. 1998. Reliable Computer Systems 3rd ed. A. K. Peters Ltd.Singh, S., & Chana, I. (2016). A Survey on Resource Scheduling in Cloud Computing: Issues and Challenges. Journal of Grid Computing, 14(2), 217-264. doi:10.1007/s10723-015-9359-2Slegel, T. J., Averill, R. M., Check, M. A., Giamei, B. C., Krumm, B. W., Krygowski, C. A., … Webb, C. F. (1999). IBM’s S/390 G5 microprocessor design. IEEE Micro, 19(2), 12-23. doi:10.1109/40.755464Sridhar, A., Sabry, M. M., & Atienza, D. (2014). A Semi-Analytical Thermal Modeling Framework for Liquid-Cooled ICs. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 33(8), 1145-1158. doi:10.1109/tcad.2014.2323194Sridharan, V., DeBardeleben, N., Blanchard, S., Ferreira, K. B., Stearley, J., Shalf, J., & Gurumurthi, S. (2015). Memory Errors in Modern Systems. ACM SIGARCH Computer Architecture News, 43(1), 297-310. doi:10.1145/2786763.2694348Stathis, J. H. (2018). The physics of NBTI: What do we really know? 2018 IEEE International Reliability Physics Symposium (IRPS). doi:10.1109/irps.2018.8353539Stellner, G. (s. f.). CoCheck: checkpointing and process migration for MPI. Proceedings of International Conference on Parallel Processing. doi:10.1109/ipps.1996.508106Stone, J. E., Gohara, D., & Shi, G. (2010). OpenCL: A Parallel Programming Standard for Heterogeneous Computing Systems. Computing in Science & Engineering, 12(3), 66-73. doi:10.1109/mcse.2010.69Subasi, O., Di, S., Bautista-Gomez, L., Balaprakash, P., Unsal, O., Labarta, J., … Cappello, F. (2018). Exploring the capabilities of support vector machines in detecting silent data corruptions. Sustainable Computing: Informatics and Systems, 19, 277-290. doi:10.1016/j.suscom.2018.01.004Tang, D., & Iyer, R. K. (1993). Dependability measurement and modeling of a multicomputer system. IEEE Transactions on Computers, 42(1), 62-75. doi:10.1109/12.192214D. Turnbull and N. Alldrin. 2003. Failure Prediction in Hardware Systems. Tech. rep. University of California San Diego CA. Retrieved from http://www.cs.ucsd.edu/ dturnbul/Papers/ServerPrediction.pdf. D. Turnbull and N. Alldrin. 2003. Failure Prediction in Hardware Systems. Tech. rep. University of California San Diego CA. Retrieved from http://www.cs.ucsd.edu/ dturnbul/Papers/ServerPrediction.pdf.Vilalta, R., Apte, C. V., Hellerstein, J. L., Ma, S., & Weiss, S. M. (2002). Predictive algorithms in the management of computer systems. IBM Systems Journal, 41(3), 461-474. doi:10.1147/sj.413.0461Vinoski, S. (2007). Reliability with Erlang. IEEE Internet Com

Gunrock: GPU Graph Analytics

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs, have presented two significant challenges to developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We characterize the performance of various optimization strategies and evaluate Gunrock's overall performance on different GPU architectures on a wide range of graph primitives that span from traversal-based algorithms and ranking algorithms, to triangle counting and bipartite-graph-based algorithms. The results show that on a single GPU, Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives and CPU shared-memory graph libraries such as Ligra and Galois, and better performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing (TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance Graph Processing Library on the GPU

CAP Theorem: Revision of its related consistency models

[EN] The CAP theorem states that only two of these properties can be simultaneously guaranteed in a distributed service: (i) consistency, (ii) availability, and (iii) network partition tolerance. This theorem was stated and proved assuming that "consistency" refers to atomic consistency. However, multiple consistency models exist and atomic consistency is located at the strongest edge of that spectrum. Many distributed services deployed in cloud platforms should be highly available and scalable. Network partitions may arise in those deployments and should be tolerated. One way of dealing with CAP constraints consists in relaxing consistency. Therefore, it is interesting to explore the set of consistency models not supported in an available and partition-tolerant service (CAP-constrained models). Other weaker consistency models could be maintained when scalable services are deployed in partitionable systems (CAP-free models). Three contributions arise: (1) multiple other CAP-constrained models are identified, (2) a borderline between CAP-constrained and CAP-free models is set, and (3) a hierarchy of consistency models depending on their strength and convergence is built.Muñoz-Escoí, FD.; Juan Marín, RD.; García Escriva, JR.; González De Mendívil Moreno, JR.; Bernabeu Aubán, JM. (2019). CAP Theorem: Revision of its related consistency models. The Computer Journal. 62(6):943-960. https://doi.org/10.1093/comjnl/bxy142S943960626Davidson, S. B., Garcia-Molina, H., & Skeen, D. (1985). Consistency in a partitioned network: a survey. ACM Computing Surveys, 17(3), 341-370. doi:10.1145/5505.5508Gilbert, S., & Lynch, N. (2002). Brewer’s conjecture and the feasibility of consistent, available, partition-tolerant web services. ACM SIGACT News, 33(2), 51-59. doi:10.1145/564585.564601Muñoz-Escoí, F. D., & Bernabéu-Aubán, J. M. (2016). A survey on elasticity management in PaaS systems. Computing, 99(7), 617-656. doi:10.1007/s00607-016-0507-8Brewer, E. (2012). CAP twelve years later: How the «rules» have changed. Computer, 45(2), 23-29. doi:10.1109/mc.2012.37Attiya, H., Ellen, F., & Morrison, A. (2017). Limitations of Highly-Available Eventually-Consistent Data Stores. IEEE Transactions on Parallel and Distributed Systems, 28(1), 141-155. doi:10.1109/tpds.2016.2556669Viotti, P., & Vukolić, M. (2016). Consistency in Non-Transactional Distributed Storage Systems. ACM Computing Surveys, 49(1), 1-34. doi:10.1145/2926965Burckhardt, S. (2014). Principles of Eventual Consistency. Foundations and Trends® in Programming Languages, 1(1-2), 1-150. doi:10.1561/2500000011Herlihy, M. P., & Wing, J. M. (1990). Linearizability: a correctness condition for concurrent objects. ACM Transactions on Programming Languages and Systems, 12(3), 463-492. doi:10.1145/78969.78972Lamport. (1979). How to Make a Multiprocessor Computer That Correctly Executes Multiprocess Programs. IEEE Transactions on Computers, C-28(9), 690-691. doi:10.1109/tc.1979.1675439Ladin, R., Liskov, B., Shrira, L., & Ghemawat, S. (1992). Providing high availability using lazy replication. ACM Transactions on Computer Systems, 10(4), 360-391. doi:10.1145/138873.138877Yu, H., & Vahdat, A. (2002). Design and evaluation of a conit-based continuous consistency model for replicated services. ACM Transactions on Computer Systems, 20(3), 239-282. doi:10.1145/566340.566342Curino, C., Jones, E., Zhang, Y., & Madden, S. (2010). Schism. Proceedings of the VLDB Endowment, 3(1-2), 48-57. doi:10.14778/1920841.1920853Das, S., Agrawal, D., & El Abbadi, A. (2013). ElasTraS. ACM Transactions on Database Systems, 38(1), 1-45. doi:10.1145/2445583.2445588Chen, Z., Yang, S., Tan, S., He, L., Yin, H., & Zhang, G. (2014). A new fragment re-allocation strategy for NoSQL database systems. Frontiers of Computer Science, 9(1), 111-127. doi:10.1007/s11704-014-3480-4Kamal, J., Murshed, M., & Buyya, R. (2016). Workload-aware incremental repartitioning of shared-nothing distributed databases for scalable OLTP applications. Future Generation Computer Systems, 56, 421-435. doi:10.1016/j.future.2015.09.024Elghamrawy, S. M., & Hassanien, A. E. (2017). A partitioning framework for Cassandra NoSQL database using Rendezvous hashing. The Journal of Supercomputing, 73(10), 4444-4465. doi:10.1007/s11227-017-2027-5Muñoz-Escoí, F. D., García-Escrivá, J.-R., Sendra-Roig, J. S., Bernabéu-Aubán, J. M., & González de Mendívil, J. R. (2018). Eventual Consistency: Origin and Support. Computing and Informatics, 37(5), 1037-1072. doi:10.4149/cai_2018_5_1037Fischer, M. J., Lynch, N. A., & Paterson, M. S. (1985). Impossibility of distributed consensus with one faulty process. Journal of the ACM, 32(2), 374-382. doi:10.1145/3149.21412

A Domain-Specific Language and Editor for Parallel Particle Methods

Domain-specific languages (DSLs) are of increasing importance in scientific high-performance computing to reduce development costs, raise the level of abstraction and, thus, ease scientific programming. However, designing and implementing DSLs is not an easy task, as it requires knowledge of the application domain and experience in language engineering and compilers. Consequently, many DSLs follow a weak approach using macros or text generators, which lack many of the features that make a DSL a comfortable for programmers. Some of these features---e.g., syntax highlighting, type inference, error reporting, and code completion---are easily provided by language workbenches, which combine language engineering techniques and tools in a common ecosystem. In this paper, we present the Parallel Particle-Mesh Environment (PPME), a DSL and development environment for numerical simulations based on particle methods and hybrid particle-mesh methods. PPME uses the meta programming system (MPS), a projectional language workbench. PPME is the successor of the Parallel Particle-Mesh Language (PPML), a Fortran-based DSL that used conventional implementation strategies. We analyze and compare both languages and demonstrate how the programmer's experience can be improved using static analyses and projectional editing. Furthermore, we present an explicit domain model for particle abstractions and the first formal type system for particle methods.Comment: Submitted to ACM Transactions on Mathematical Software on Dec. 25, 201

Exploiting nested task-parallelism in the H-LU factorization

[EN] We address the parallelization of the LU factorization of hierarchical matrices (H-matrices) arising from boundary element methods. Our approach exploits task-parallelism via the OmpSs programming model and runtime, which discovers the data-flow parallelism intrinsic to the operation at execution time, via the analysis of data dependencies based on the memory addresses of the tasks' operands. This is especially challenging for H-matrices, as the structures containing the data vary in dimension during the execution. We tackle this issue by decoupling the data structure from that used to detect dependencies. Furthermore, we leverage the support for weak operands and early release of dependencies, recently introduced in OmpSs-2, to accelerate the execution of parallel codes with nested task-parallelism and fine-grain tasks. As a result, we obtain a significant improvement in the parallel performance with respect to our previous work.The researchers from Universidad Jaume I (UJI) were supported by projects CICYT TIN2014-53495-R and TIN2017-82972-R of MINECO and FEDER; project UJI-B2017-46 of UJI; and the FPU program of MECD.Carratalá-Sáez, R.; Christophersen, S.; Aliaga, JI.; Beltrán, V.; Börm, S.; Quintana Ortí, ES. (2019). Exploiting nested task-parallelism in the H-LU factorization. Journal of Computational Science. 33:20-33. https://doi.org/10.1016/j.jocs.2019.02.004S203333Hackbusch, W. (1999). A Sparse Matrix Arithmetic Based on \Cal H -Matrices. Part I: Introduction to {\Cal H} -Matrices. Computing, 62(2), 89-108. doi:10.1007/s006070050015Grasedyck, L., & Hackbusch, W. (2003). Construction and Arithmetics of H -Matrices. Computing, 70(4), 295-334. doi:10.1007/s00607-003-0019-1Dongarra, J. J., Du Croz, J., Hammarling, S., & Duff, I. S. (1990). A set of level 3 basic linear algebra subprograms. ACM Transactions on Mathematical Software, 16(1), 1-17. doi:10.1145/77626.79170Buttari, A., Langou, J., Kurzak, J., & Dongarra, J. (2009). A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Computing, 35(1), 38-53. doi:10.1016/j.parco.2008.10.002Quintana-Ortí, G., Quintana-Ortí, E. S., Geijn, R. A. V. D., Zee, F. G. V., & Chan, E. (2009). Programming matrix algorithms-by-blocks for thread-level parallelism. ACM Transactions on Mathematical Software, 36(3), 1-26. doi:10.1145/1527286.1527288Badia, R. M., Herrero, J. R., Labarta, J., Pérez, J. M., Quintana-Ortí, E. S., & Quintana-Ortí, G. (2009). Parallelizing dense and banded linear algebra libraries using SMPSs. Concurrency and Computation: Practice and Experience, 21(18), 2438-2456. doi:10.1002/cpe.1463Aliaga, J. I., Badia, R. M., Barreda, M., Bollhofer, M., & Quintana-Orti, E. S. (2014). Leveraging Task-Parallelism with OmpSs in ILUPACK’s Preconditioned CG Method. 2014 IEEE 26th International Symposium on Computer Architecture and High Performance Computing. doi:10.1109/sbac-pad.2014.24Agullo, E., Buttari, A., Guermouche, A., & Lopez, F. (2016). Implementing Multifrontal Sparse Solvers for Multicore Architectures with Sequential Task Flow Runtime Systems. ACM Transactions on Mathematical Software, 43(2), 1-22. doi:10.1145/2898348Aliaga, J. I., Carratala-Saez, R., Kriemann, R., & Quintana-Orti, E. S. (2017). Task-Parallel LU Factorization of Hierarchical Matrices Using OmpSs. 2017 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). doi:10.1109/ipdpsw.2017.124The OpenMP API specification for parallel programming, http://www.openmp.org/.OmpSs project home page, http://pm.bsc.es/ompss.Perez, J. M., Beltran, V., Labarta, J., & Ayguade, E. (2017). Improving the Integration of Task Nesting and Dependencies in OpenMP. 2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS). doi:10.1109/ipdps.2017.69HLIBpro library home page, https://www.hlibpro.com/.Bempp library home page, https://bempp.com/.HACApK library github repository, https://github.com/hoshino-UTokyo/hacapk-gpu.hmglib library github repository, https://github.com/zaspel/hmglib.HiCMA library github repository, https://github.com/ecrc/hicma.Hackbusch, W., & Börm, S. (2002). -matrix approximation of integral operators by interpolation. Applied Numerical Mathematics, 43(1-2), 129-143. doi:10.1016/s0168-9274(02)00121-

Reproducibility strategies for parallel preconditioned Conjugate Gradient

[EN] The Preconditioned Conjugate Gradient method is often used in numerical simulations. While being widely used, the solver is also known for its lack of accuracy while computing the residual. In this article, we aim at a twofold goal: enhance the accuracy of the solver but also ensure its reproducibility in a message-passing implementation. We design and employ various strategies starting from the ExBLAS approach (through preserving every bit of information until final rounding) to its more lightweight performance-oriented variant (through expanding the intermediate precision). These algorithmic strategies are reinforced with programmability suggestions to assure deterministic executions. Finally, we verify these strategies on modern HPC systems: both versions deliver reproducible number of iterations, residuals, direct errors, and vector-solutions for the overhead of only 29% (ExBLAS) and 4% (lightweight) on 768 processes.To begin with, we would like to thank the reviewers for their thorough reading of the article as well as their valuable comments and suggestions. This research was partially supported by the European Union's Horizon 2020 research, innovation programme under the Marie Sklodowska-Curie grant agreement via the Robust project No. 842528 as well as the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the H2020 EC RIA Programme; in particular, the author gratefully acknowledges the support of Vicenc Beltran and the computer resources and technical support provided by BSC. The researchers from Universitat Jaume I (UJI) and Universidad Politecnica de Valencia (UPV) were supported by MINECO, Spain project TIN2017-82972-R. Maria Barreda was also supported by the POSDOC-A/2017/11 project from the Universitat Jaume I, Spain.Iakymchuk, R.; Barreda, M.; Wiesenberger, M.; Aliaga, JI.; Quintana Ortí, ES. (2020). Reproducibility strategies for parallel preconditioned Conjugate Gradient. Journal of Computational and Applied Mathematics. 371:1-13. https://doi.org/10.1016/j.cam.2019.112697S113371Lawson, C. L., Hanson, R. J., Kincaid, D. R., & Krogh, F. T. (1979). Basic Linear Algebra Subprograms for Fortran Usage. ACM Transactions on Mathematical Software, 5(3), 308-323. doi:10.1145/355841.355847Dongarra, J. J., Du Croz, J., Hammarling, S., & Duff, I. S. (1990). A set of level 3 basic linear algebra subprograms. ACM Transactions on Mathematical Software, 16(1), 1-17. doi:10.1145/77626.79170Demmel, J., & Nguyen, H. D. (2015). Parallel Reproducible Summation. IEEE Transactions on Computers, 64(7), 2060-2070. doi:10.1109/tc.2014.2345391Iakymchuk, R., Graillat, S., Defour, D., & Quintana-Ortí, E. S. (2019). Hierarchical approach for deriving a reproducible unblocked LU factorization. The International Journal of High Performance Computing Applications, 33(5), 791-803. doi:10.1177/1094342019832968Iakymchuk, R., Defour, D., Collange, S., & Graillat, S. (2016). Reproducible and Accurate Matrix Multiplication. Lecture Notes in Computer Science, 126-137. doi:10.1007/978-3-319-31769-4_11Rump, S. M., Ogita, T., & Oishi, S. (2009). Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest. SIAM Journal on Scientific Computing, 31(2), 1269-1302. doi:10.1137/07068816xBurgess, N., Goodyer, C., Hinds, C. N., & Lutz, D. R. (2019). High-Precision Anchored Accumulators for Reproducible Floating-Point Summation. IEEE Transactions on Computers, 68(7), 967-978. doi:10.1109/tc.2018.2855729D. Mukunoki, T. Ogita, K. Ozaki, Accurate and reproducible BLAS routines with Ozaki scheme for many-core architectures, in: Proc. International Conference on Parallel Processing and Applied Mathematics, PPAM2019, 2019, accepted.Ogita, T., Rump, S. M., & Oishi, S. (2005). Accurate Sum and Dot Product. SIAM Journal on Scientific Computing, 26(6), 1955-1988. doi:10.1137/030601818Kulisch, U., & Snyder, V. (2010). The exact dot product as basic tool for long interval arithmetic. Computing, 91(3), 307-313. doi:10.1007/s00607-010-0127-7Boldo, S., & Melquiond, G. (2008). Emulation of a FMA and Correctly Rounded Sums: Proved Algorithms Using Rounding to Odd. IEEE Transactions on Computers, 57(4), 462-471. doi:10.1109/tc.2007.70819Wiesenberger, M., Einkemmer, L., Held, M., Gutierrez-Milla, A., Sáez, X., & Iakymchuk, R. (2019). Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures. Computer Physics Communications, 238, 145-156. doi:10.1016/j.cpc.2018.12.006Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P., & Zimmermann, P. (2007). MPFR. ACM Transactions on Mathematical Software, 33(2), 13. doi:10.1145/1236463.1236468J. Demmel, H.D. Nguyen, Fast reproducible floating-point summation, in: Proceedings of ARITH-21, 2013, pp. 163–172.Ozaki, K., Ogita, T., Oishi, S., & Rump, S. M. (2011). Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications. Numerical Algorithms, 59(1), 95-118. doi:10.1007/s11075-011-9478-1Carson, E., & Higham, N. J. (2018). Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions. SIAM Journal on Scientific Computing, 40(2), A817-A847. doi:10.1137/17m114081

Computing subdominant unstable modes of turbulent plasma with a parallel Jacobi-Davidson eigensolver

In the numerical solution of large-scale eigenvalue problems, Davidson-type methods are an increasingly popular alternative to Krylov eigensolvers. The main motivation is to avoid the expensive factorizations that are often needed by Krylov solvers when the problem is generalized or interior eigenvalues are desired. In Davidson-type methods, the factorization is replaced by iterative linear solvers that can be accelerated by a smart preconditioner. Jacobi-Davidson is one of the most effective variants. However, parallel implementations of this method are not widely available, particularly for non-symmetric problems. We present a parallel implementation that has been included in SLEPc, the Scalable Library for Eigenvalue Problem Computations, and test it in the context of a highly scalable plasma turbulence simulation code. We analyze its parallel efficiency and compare it with a Krylov-Schur eigensolver. © 2011 John Wiley and Sons, Ltd..The authors are indebted to Florian Merz for providing us with the test cases and for his useful suggestions. The authors acknowledge the computer resources provided by the Barcelona Supercomputing Center (BSC). This work was supported by the Spanish Ministerio de Ciencia e Innovacion under project TIN2009-07519.Romero Alcalde, E.; Román Moltó, JE. (2011). Computing subdominant unstable modes of turbulent plasma with a parallel Jacobi-Davidson eigensolver. Concurrency and Computation: Practice and Experience. 23:2179-2191. https://doi.org/10.1002/cpe.1740S2179219123Hochstenbach, M. E., & Notay, Y. (2009). Controlling Inner Iterations in the Jacobi–Davidson Method. SIAM Journal on Matrix Analysis and Applications, 31(2), 460-477. doi:10.1137/080732110Heuveline, V., Philippe, B., & Sadkane, M. (1997). Numerical Algorithms, 16(1), 55-75. doi:10.1023/a:1019126827697Arbenz, P., Bečka, M., Geus, R., Hetmaniuk, U., & Mengotti, T. (2006). On a parallel multilevel preconditioned Maxwell eigensolver. Parallel Computing, 32(2), 157-165. doi:10.1016/j.parco.2005.06.005Genseberger, M. (2010). Improving the parallel performance of a domain decomposition preconditioning technique in the Jacobi–Davidson method for large scale eigenvalue problems. Applied Numerical Mathematics, 60(11), 1083-1099. doi:10.1016/j.apnum.2009.07.004Stathopoulos, A., & McCombs, J. R. (2010). PRIMME. ACM Transactions on Mathematical Software, 37(2), 1-30. doi:10.1145/1731022.1731031Baker, C. G., Hetmaniuk, U. L., Lehoucq, R. B., & Thornquist, H. K. (2009). Anasazi software for the numerical solution of large-scale eigenvalue problems. ACM Transactions on Mathematical Software, 36(3), 1-23. doi:10.1145/1527286.1527287Hernandez, V., Roman, J. E., & Vidal, V. (2005). SLEPc. ACM Transactions on Mathematical Software, 31(3), 351-362. doi:10.1145/1089014.1089019Romero, E., Cruz, M. B., Roman, J. E., & Vasconcelos, P. B. (2011). A Parallel Implementation of the Jacobi-Davidson Eigensolver for Unsymmetric Matrices. High Performance Computing for Computational Science – VECPAR 2010, 380-393. doi:10.1007/978-3-642-19328-6_35Romero, E., & Roman, J. E. (2010). A Parallel Implementation of the Jacobi-Davidson Eigensolver and Its Application in a Plasma Turbulence Code. Lecture Notes in Computer Science, 101-112. doi:10.1007/978-3-642-15291-7_11Über ein leichtes Verfahren die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen*). (1846). Journal für die reine und angewandte Mathematik (Crelles Journal), 1846(30), 51-94. doi:10.1515/crll.1846.30.51G. Sleijpen, G. L., & Van der Vorst, H. A. (1996). A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems. SIAM Journal on Matrix Analysis and Applications, 17(2), 401-425. doi:10.1137/s0895479894270427Fokkema, D. R., Sleijpen, G. L. G., & Van der Vorst, H. A. (1998). Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils. SIAM Journal on Scientific Computing, 20(1), 94-125. doi:10.1137/s1064827596300073Morgan, R. B. (1991). Computing interior eigenvalues of large matrices. Linear Algebra and its Applications, 154-156, 289-309. doi:10.1016/0024-3795(91)90381-6Paige, C. C., Parlett, B. N., & van der Vorst, H. A. (1995). Approximate solutions and eigenvalue bounds from Krylov subspaces. Numerical Linear Algebra with Applications, 2(2), 115-133. doi:10.1002/nla.1680020205Stathopoulos, A., Saad, Y., & Wu, K. (1998). Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods. SIAM Journal on Scientific Computing, 19(1), 227-245. doi:10.1137/s1064827596304162Sleijpen, G. L. G., Booten, A. G. L., Fokkema, D. R., & van der Vorst, H. A. (1996). Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT Numerical Mathematics, 36(3), 595-633. doi:10.1007/bf01731936Balay S Buschelman K Eijkhout V Gropp W Kaushik D Knepley M McInnes LC Smith B Zhang H PETSc users manual 2010Hernandez, V., Roman, J. E., & Tomas, A. (2007). Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement. Parallel Computing, 33(7-8), 521-540. doi:10.1016/j.parco.2007.04.004Dannert, T., & Jenko, F. (2005). Gyrokinetic simulation of collisionless trapped-electron mode turbulence. Physics of Plasmas, 12(7), 072309. doi:10.1063/1.1947447Roman, J. E., Kammerer, M., Merz, F., & Jenko, F. (2010). Fast eigenvalue calculations in a massively parallel plasma turbulence code. Parallel Computing, 36(5-6), 339-358. doi:10.1016/j.parco.2009.12.001Merz, F., & Jenko, F. (2010). Nonlinear interplay of TEM and ITG turbulence and its effect on transport. Nuclear Fusion, 50(5), 054005. doi:10.1088/0029-5515/50/5/054005Simoncini, V., & Szyld, D. B. (2002). Flexible Inner-Outer Krylov Subspace Methods. SIAM Journal on Numerical Analysis, 40(6), 2219-2239. doi:10.1137/s0036142902401074Morgan, R. B. (2002). GMRES with Deflated Restarting. SIAM Journal on Scientific Computing, 24(1), 20-37. doi:10.1137/s106482759936465