A Flexible Numerical Framework for Engineering—A Response Surface Modelling Application

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 72)


This work presents an innovative approach adopted for the development of a new numerical software framework for accelerating dense linear algebra calculations and its application within an engineering context. In particular, response surface models (RSM) are a key tool to reduce the computational effort involved in engineering design processes like design optimization. However, RSMs may prove to be too expensive to be computed when the dimensionality of the system and/or the size of the dataset to be synthesized is significantly high or when a large number of different response surfaces has to be calculated in order to improve the overall accuracy (e.g. like when using ensemble modelling techniques). On the other hand, the potential of modern hybrid hardware (e.g. multicore, GPUs) is not exploited by current engineering tools, while they can lead to a significant performance improvement. To fill this gap, a software framework is being developed that enables the hybrid and scalable acceleration of the linear algebra core for engineering applications and especially of RSMs calculations with a user-friendly syntax that allows good portability between different hardware architectures, with no need of specific expertise in parallel programming and accelerator technology. The effectiveness of this framework is shown by comparing an accelerated code to a single-core calculation of a radial basis function RSM on some benchmark datasets. This approach is then validated within a real-life engineering application and the achievements are presented and discussed.


Response surface modelling GPU computing Linear algebra Armadillo 



This work has been partially supported by ITEA2 project 12002 MACH, the EU FP7 REPARA project (no. 609666), the EU H2020 Rephrase project (no. 644235) and the “NVidia GPU research centre” programme.


  1. 1.
    Agullo E, Demmel J, Dongarra J et al (2009) Numerical linear algebra on emerging architectures: the PLASMA and MAGMA projects. J Phys: Conf Ser 180:12037Google Scholar
  2. 2.
    Anderson E, Bai Z, Bischof C et al (1999) LAPACK users’ guide, 3rd edn. Society for Industrial and Applied Mathematics, PhiladelphiaGoogle Scholar
  3. 3.
    Booker AJ, Dennis JE, Frank PD et al (1999) A rigorous framework for optimization of expensive functions by surrogates. Struct Multidiscip Optim 17:1–13CrossRefGoogle Scholar
  4. 4.
    Dongarra J, Du Croz J, Hammarling S, Hanson RJ (1988) An extended set of FORTRAN basic linear algebra subprograms. ACM Trans Math Softw 14:1–17CrossRefzbMATHGoogle Scholar
  5. 5.
    Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, BaltimorezbMATHGoogle Scholar
  6. 6.
    Guennebaud G, Jacob B (2010) Eigen v3Google Scholar
  7. 7.
    Humphrey JR, Price DK, Spagnoli KE et al (2010) CULA: hybrid GPU accelerated linear algebra routines. In: Modeling and Simulation for Defense Systems and Applications V. {SPIE}-Intl Soc Optical EngGoogle Scholar
  8. 8.
    Kraus J, Förster M, Brandes T, Soddemann T (2012) Using LAMA for efficient AMG on hybrid clusters. Comput Sci Res Dev 28:211–220CrossRefGoogle Scholar
  9. 9.
    NVIDIA Corporation (2016) CUDA Toolkit Documentation. Accessed 25 Nov 2016
  10. 10.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2002) Numerical recipes in CGoogle Scholar
  11. 11.
    Sanderson C (2010) Armadillo: an open source C++ linear algebra library for fast prototyping and computationally intensive experiments. In: NICTA. AustraliaGoogle Scholar
  12. 12.
    Tillet P, Rupp K, Selberherr S, Lin C-T (2013) Towards performance-portable, scalable, and convenient linear algebra. In: 5th USENIX Workshop on Hot Topics in Parallelism. USENIX, BerkeleyGoogle Scholar
  13. 13.
    Tomov S, Dongarra J, Baboulin M (2010) Towards dense linear algebra for hybrid GPU accelerated manycore systems. Parallel Comput 36:232–240CrossRefzbMATHGoogle Scholar
  14. 14.
    Wang Q, Zhang X, Zhang Y, Yi Q (2013) AUGEM: automatically generate high performance dense linear algebra kernels on x86 CPUs. In: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis. ACM, New York, pp 25:1–25:12Google Scholar
  15. 15.
    Yalamanchili P, Arshad U, Mohammed Z et al (2015) ArrayFire—a high performance software library for parallel computing with an easy-to-use API. AccelerEyes, AtlantaGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità degli Studi di TorinoTurinItaly
  2. 2.Noesis SolutionsLeuvenBelgium
  3. 3.Department of Electronics and Informatics (ETRO)Vrije Universiteit BrusselBrusselsBelgium
  4. 4.Noesis Solutions srl c/o Ufficio 201NovaraItaly

Personalised recommendations