Abstract
As HPC systems are becoming increasingly heterogeneous and diverse, writing software that attains maximum performance and scalability while remaining portable as well as easily composable is getting more and more challenging. Additionally, code that has been aggressively optimized for certain execution platforms is usually not easily portable to others without either losing a great share of performance or investing many hours by re-applying optimizations. One possible remedy is to exploit the potential given by technologies such as domain-specific languages (DSLs) that provide appropriate abstractions and allow the application of technologies like automatic code generation and auto-tuning. In the domain of geometric multigrid solvers, project ExaStencils follows this road by aiming at providing highly optimized and scalable numerical solvers, specifically tuned for a given application and target platform. Here, we introduce its DSL ExaSlang with data types for local vectors to support computations that use point-local vectors and matrices. These data types allow an intuitive modeling of many physical problems represented by systems of partial differential equations (PDEs), e.g., the simulation of flows that include vector-valued velocities.
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
Notes
References
Bezanson, J., Karpinski, S., Shah, V.B., Edelman, A.: Julia: a fast dynamic language for technical computing. CoRR (2012). arXiv:1209.5145
Brandt, A.: Rigorous quantitative analysis of multigrid, I: constant coefficients two-level cycle with L 2-norm. SIAM J. Numer. Anal. 31 (6), 1695–1730 (1994)
Christen, M., Schenk, O., Burkhart, H.: PATUS: A code generation and autotuning framework for parallel iterative stencil computations on modern microarchitectures. In: Proceedings of IEEE International Parallel & Distributed Processing Symposium (IPDPS). pp. 676–687. IEEE (2011)
DeVito, Z., Joubert, N., Palaciosy, F., Oakleyz, S., Medinaz, M., Barrientos, M., Elsenz, E., Hamz, F., Aiken, A., Duraisamy, K., Darvez, E., Alonso, J., Hanrahan, P.: Liszt: A domain specific language for building portable mesh-based PDE solvers. In: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis (SC). ACM (2011), paper 9, 12pp.
Gysi, T., Osuna, C., Fuhrer, O., Bianco, M., Schulthess, T.C.: STELLA: a domain-specific tool for structured grid methods in weather and climate models. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC), pp. 41:1–41:12. ACM (2015)
Hackbusch, W.: Multi-Grid Methods and Applications. Springer, Berlin/New York (1985)
Köstler, H.: A multigrid framework for variational approaches in medical image processing and computer vision. Ph.D. thesis, Friedrich-Alexander University of Erlangen-Nürnberg (2008)
Kronawitter, S., Lengauer, C.: Optimizations applied by the ExaStencils code generator. Technical Report, MIP-1502, Faculty of Informatics and Mathematics, University of Passau (2015)
Lengauer, C., Apel, S., Bolten, M., Größlinger, A., Hannig, F., Köstler, H., Rüde, U., Teich, J., Grebhahn, A., Kronawitter, S., Kuckuk, S., Rittich, H., Schmitt, C.: ExaStencils: advanced stencil-code engineering. In: Euro-Par 2014: Parallel Processing Workshops. Lecture Notes in Computer Science, vol. 8806, pp. 553–564. Springer (2014)
Logg, A., Mardal, K.A., Wells, G.N. (eds.): Automated Solution of Differential Equations by the Finite Element Method. Lecture Notes in Computational Science and Engineering, vol. 84. Springer, Berlin/New York (2012)
Membarth, R., Reiche, O., Hannig, F., Teich, J., Körner, M., Eckert, W.: HIPAcc: a domain-specific language and compiler for image processing. IEEE T. Parall. Distr. (2015), early view, 14 pages. doi:10.1109/TPDS.2015.2394802
Membarth, R., Reiche, O., Schmitt, C., Hannig, F., Teich, J., Stürmer, M., Köstler, H.: Towards a performance-portable description of geometric multigrid algorithms using a domain-specific language. J. Parallel Distrib. Comput. 74 (12), 3191–3201 (2014)
Odersky, M., Spoon, L., Venners, B.: Programming in Scala, 2nd edn. Artima, Walnut Creek (2011)
Püschel, M., Franchetti, F., Voronenko, Y.: SPIRAL. In: Padua, D.A., et al. (eds.) Encyclopedia of Parallel Computing, pp. 1920–1933. Springer (2011)
Rathgeber, F., Ham, D.A., Mitchell, L., Lange, M., Luporini, F., McRae, A.T.T., Bercea, G.T., Markall, G.R., Kelly, P.H.J.: Firedrake: automating the finite element method by composing abstractions. CoRR (2015). arXiv:1501.01809
Rathgeber, F., Markall, G.R., Mitchell, L., Loriant, N., Ham, D.A., Bertolli, C., Kelly, P.H.: PyOP2: A high-level framework for performance-portable simulations on unstructured meshes. In: Proceedings of the 2nd International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC), pp. 1116–1123. IEEE Computer Society (2012)
Rawat, P., Kong, M., Henretty, T., Holewinski, J., Stock, K., Pouchet, L.N., Ramanujam, J., Rountev, A., Sadayappan, P.: SDSLc: A multi-target domain-specific compiler for stencil computations. In: Proceedings of the 5th International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC). pp. 6:1–6:10. ACM (2015)
Schmitt, C., Kuckuk, S., Hannig, F., Köstler, H., Teich, J.: ExaSlang: A Domain-Specific Language for Highly Scalable Multigrid Solvers. In: Proceedings of the 4th International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC), pp. 42–51. ACM (2014)
Schmitt, C., Kuckuk, S., Köstler, H., Hannig, F., Teich, J.: An evaluation of domain-specific language technologies for code generation. In: Proceedings of the International Conference on Computational Science and its Applications (ICCSA), pp. 18–26. IEEE Computer Society (2014)
Schmitt, C., Schmid, M., Hannig, F., Teich, J., Kuckuk, S., Köstler, H.: Generation of multigrid-based numerical solvers for FPGA accelerators. In: Größlinger, A., Köstler, H. (eds.) Proceedings of the 2nd International Workshop on High-Performance Stencil Computations (HiStencils), pp. 9–15 (2015)
Siegmund, N., Grebhahn, A., Apel, S., Kästner, C.: Performance-influence models for highly configurable systems. In: Proceedings of the European Software Engineering Conference and ACM SIGSOFT Symposium on the Foundations of Software Engineering (ESEC/FSE), pp. 284–294. ACM (2015)
Tang, Y., Chowdhury, R.A., Kuszmaul, B.C., Luk, C.K., Leiserson, C.E.: The Pochoir stencil compiler. In: Proceedings of the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 117–128. ACM (2011)
Trottenberg, U., Oosterlee, C.W., Schüller, A.: Multigrid. Academic, San Diego (2001)
Unat, D., Cai, X., Baden, S.B.: Mint: Realizing CUDA performance in 3D stencil methods with annotated C. In: Proceedings of the International Conference on Supercomputing (ISC), pp. 214–224. ACM (2011)
Wienands, R., Joppich, W.: Practical Fourier Analysis for Multigrid Methods. Chapman Hall/CRC Press, Boca Raton (2005)
Acknowledgements
This work is supported by the German Research Foundation (DFG), as part of Priority Program 1648 “Software for Exascale Computing” in project under contracts TE 163/17-1, RU 422/15-1 and LE 912/15-1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Schmitt, C. et al. (2016). Systems of Partial Differential Equations in ExaSlang. In: Bungartz, HJ., Neumann, P., Nagel, W. (eds) Software for Exascale Computing - SPPEXA 2013-2015. Lecture Notes in Computational Science and Engineering, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-40528-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-40528-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40526-1
Online ISBN: 978-3-319-40528-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)