Skip to main content
SpringerLink
Log in

Chrono: An Open Source Multi-physics Dynamics Engine

  • Conference paper
  • First Online:
High Performance Computing in Science and Engineering (HPCSE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9611))

Abstract

We provide an overview of a multi-physics dynamics engine called Chrono. Its forte is the handling of complex and large dynamic systems containing millions of rigid bodies that interact through frictional contact. Chrono has been recently augmented to support the modeling of fluid-solid interaction (FSI) problems and linear and nonlinear finite element analysis (FEA). We discuss Chrono’s software layout/design and outline some of the modeling and numerical solution techniques at the cornerstone of this dynamics engine. We briefly report on some validation studies that gauge the predictive attribute of the software solution. Chrono is released as open source under a permissive BSD3 license and available for download on GitHub.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. The JSON data interchange format. Technical report ECMA-404, ECMA International (2013)

    Google Scholar 

  2. Acary, V., Brogliato, B.: Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics, vol. 35. Springer Science & Business Media, Heidelberg (2008)

    MATH  Google Scholar 

  3. Adami, S., Hu, X., Adams, N.: A generalized wall boundary condition for smoothed particle hydrodynamics. J. Comput. Phys. 231, 7057–7075 (2012)

    Article  MathSciNet  Google Scholar 

  4. Andelfinger, U., Ramm, E.: EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. Int. J. Numer. Meth. Eng. 36, 1311–1337 (1993)

    Article  MATH  Google Scholar 

  5. Anitescu, M., Cremer, J.F., Potra, F.A.: Formulating 3D contact dynamics problems. Mech. Struct. Mach. 24(4), 405–437 (1996)

    Article  MathSciNet  Google Scholar 

  6. Anitescu, M., Tasora, A.: An iterative approach for cone complementarity problems for nonsmooth dynamics. Comput. Optim. Appl. 47, 207–235 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bardet, J.-P.: Experimental Soil Mechanics. Prentice Hall, Englewood Cliffs (1997)

    Google Scholar 

  8. Basa, M., Quinlan, N., Lastiwka, M.: Robustness and accuracy of SPH formulations for viscous flow. Int. J. Numer. Meth. Fluids 60, 1127–1148 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bathe, K.-J., Dvorkin, E.N.: A four-node plate bending element based on mindlin/reissner plate theory and a mixed interpolation. Int. J. Numer. Meth. Eng. 21, 367–383 (1985)

    Article  MATH  Google Scholar 

  10. Bauchau, O.A.: DYMORE user’s manual. Georgia Institute of Technology, Atlanta (2007)

    Google Scholar 

  11. Betsch, P., Stein, E.: An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element. Commun. Numer. Methods Eng. 11, 899–909 (1995)

    Article  MATH  Google Scholar 

  12. Buildbot: Buildbot - an open-source framework for automating software build, test, and release. http://buildbot.net/. Accessed 31 May 2015

  13. Colagrossi, A., Landrini, M.: Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 191, 448–475 (2003)

    Article  MATH  Google Scholar 

  14. Crisfield, M.: A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements. Comput. Methods Appl. Mech. Eng. 81, 131–150 (1990)

    Article  MATH  Google Scholar 

  15. Crisfield, M.A., Galvanetto, U., Jelenic, G.: Dynamics of 3-D co-rotational beams. Comput. Mech. 20, 507–519 (1997)

    Article  MATH  Google Scholar 

  16. Dmitrochenko, O., Matikainen, M., Mikkola, A.: The simplest 3-and4-noded fully-parameterized ANCF plate elements. In: ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, pp. 317–322 (2012)

    Google Scholar 

  17. Dmitrochenko, O.N., Pogorelov, D.Y.: Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Sys.Dyn. 10, 17–43 (2003)

    Article  MATH  Google Scholar 

  18. Dowell, E.H., Traybar, J.J.: An experimental study of the nonlinear stiffness of a rotor blade undergoing flap, lag, and twist deformations, Aerospace and Mechanical Science Report 1194, Princeton University, January 1975

    Google Scholar 

  19. Dowell, E.H., Traybar, J.J.: An experimental study of the nonlinear stiffness of a rotor blade undergoing flap, lag, and twist deformations, Aerospace and Mechanical Science Report 1257, Princeton University, December 1975

    Google Scholar 

  20. Doxygen: Doxygen - A Documentation Generator From Annotated C++ Code. http://www.doxygen.org. Accessed 31 May 2015

  21. Dufva, K., Shabana, A.: Analysis of thin plate structures using the absolute nodal coordinate formulation. Proc. Inst. Mech. Eng. Part K: J. Multi-body Dyn. 219, 345–355 (2005)

    Article  Google Scholar 

  22. Felippa, C., Haugen, B.: A unified formulation of small-strain corotational finite elements: I. theory. Comput. Methods Appl. Mech. Eng. 194, 2285–2335 (2005). Computational Methods for Shells

    Article  MATH  Google Scholar 

  23. Filippov, A.F., Arscott, F.M.: Differential Equations with Discontinuous Righthand Sides: Control Systems, vol. 18. Springer, Heidelberg (1988)

    Google Scholar 

  24. Fleischmann, J.: DEM-PM contact model with multi-step tangential contact displacement history. Technical report TR-2015-06, Simulation-Based Engineering Laboratory, University of Wisconsin-Madison (2015)

    Google Scholar 

  25. Fleischmann, J.A., Serban, R., Negrut, D., Jayakumar, P.: On the importance of displacement history in soft-body contact models. ASME J. Comput. Nonlinear Dyn. (2015). doi:10.1115/1.4031197

    Google Scholar 

  26. Gerstmayr, J., Shabana, A.: Analysis of thin beams and cables using the absolute nodal co-ordinate formulation. Nonlinear Dyn. 45, 109–130 (2006)

    Article  MATH  Google Scholar 

  27. Gerstmayr, J., Sugiyama, H., Mikkola, A.: Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. ASME J. Comput. Nonlinear Dyn. 8, 031016-1–031016-12 (2013)

    Google Scholar 

  28. Gilardi, G., Sharf, I.: Literature survey of contact dynamics modelling. Mech. Mach. Theor. 37, 1213–1239 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  29. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics-theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)

    Article  MATH  Google Scholar 

  30. Glocker, C., Pfeiffer, F.: An LCP-approach for multibody systems with planar friction. In: Proceedings of the CMIS 92 Contact Mechanics Int. Symposium, Lausanne, Switzerland, pp. 13–20 (2006)

    Google Scholar 

  31. Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer, Heidelberg (1996)

    Book  MATH  Google Scholar 

  32. Hartl, J., Ooi, J.: Experiments and simulations of direct sheartests: porosity, contact friction and bulk friction. Granular Matter 10, 263–271 (2008)

    Article  Google Scholar 

  33. Haug, E.J.: Computer-Aided Kinematics and Dynamics of Mechanical Systems Volume-I. Prentice-Hall, Englewood Cliffs (1989)

    Google Scholar 

  34. Heyn, T.: On the modeling, simulation, and visualization of many-body dynamics problems with friction and contact. Ph.D. thesis, Department of Mechanical Engineering, University of Wisconsin–Madison (2013). http://sbel.wisc.edu/documents/TobyHeynThesis_PhDfinal.pdf

  35. Hindmarsh, A., Brown, P., Grant, K., Lee, S., Serban, R., Shumaker, D., Woodward, C.: SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. (TOMS) 31, 363–396 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  36. Hu, W., Tian, Q., Hu, H.: Dynamic simulation of liquid-filled flexible multibody systems via absolute nodal coordinate formulation and SPH method. Nonlinear Dyn. 75, 653–671 (2013)

    Article  MathSciNet  Google Scholar 

  37. Kaufman, D.M., Pai, D.K.: Geometric numerical integration of inequality constrained. SIAM J. Sci. Comput. Nonsmooth Hamiltonian Syst. 34, A2670–A2703 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  38. Kitware: CMake – A cross-platform, open-source build system. http://www.cmake.org. Accessed 31 May 2015

  39. Kruggel-Emden, H., Simsek, E., Rickelt, S., Wirtz, S., Scherer, V.: Review and extension of normal force models for the discrete element method. Powder Technol. 171, 157–173 (2007)

    Article  Google Scholar 

  40. Kruggel-Emden, H., Wirtz, S., Scherer, V.: A study of tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior. Chem. Eng. Sci. 63, 1523–1541 (2008)

    Article  Google Scholar 

  41. Lee, E., Moulinec, C., Xu, R., Violeau, D., Laurence, D., Stansby, P.: Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J. Comput. Phys. 227, 8417–8436 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  42. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1024 (1977)

    Article  Google Scholar 

  43. Machado, M., Moreira, P., Flores, P., Lankarani, H.M.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theor. 53, 99–121 (2012)

    Article  Google Scholar 

  44. Madsen, J.: Validation of a single contact point tire model based on the transient pacejka model in the open-source dynamics software chrono. Technical report, University of Wisconsin - Madison Simulation Based Engineering Lab (2014)

    Google Scholar 

  45. Malvern, L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice Hall, Englewood Cliffs (1969)

    MATH  Google Scholar 

  46. Masarati, P., Morandini, M., Quaranta, G., Mantegazza, P.: Computational aspects and recent improvements in the open-source multibody analysis software MBDyn. In: Multibody Dynamics, pp. 21–24 (2005)

    Google Scholar 

  47. Mazhar, H., Bollmann, J., Forti, E., Praeger, A., Osswald, T., Negrut, D.: Studying the effect of powder geometry on the selective laser sintering process. In: Society of Plastics Engineers (SPE) ANTEC (2014)

    Google Scholar 

  48. Mazhar, H., Heyn, T., Pazouki, A., Melanz, D., Seidl, A., Bartholomew, A., Tasora, A., Negrut, D.: Chrono: a parallel multi-physics library for rigid-body, flexible-body, and fluid dynamics. Mech. Sci. 4, 49–64 (2013)

    Article  Google Scholar 

  49. Mazhar, H., Heyn, T., Tasora, A., Negrut, D.: Using Nesterov’s method to accelerate multibody dynamics with friction and contact. ACM Trans. Graph. 34, 32 (2015)

    Article  MATH  Google Scholar 

  50. Mazhar, H., Osswald, T., Negrut, D.: On the use of computational multibody dynamics for increasing throughput in 3D printing. Addit. Manuf. (2016, accepted)

    Google Scholar 

  51. Melanz, D.: On the validation and applications of a parallel flexible multi-body dynamics implementation. M.S. thesis, University of Wisconsin-Madison (2012)

    Google Scholar 

  52. Melanz, D., Tupy, M., Smith, B., Turner, K., Negrut, D.: On the validation of a differential variational inequality approach for the dynamics of granular material-DETC2010-28804. In: Fukuda, S., Michopoulos, J.G. (eds.) Proceedings to the 30th Computers and Information in Engineering Conference, ASME International Design Engineering Technical Conferences (IDETC) and Computers and Information in Engineering Conference (CIE) (2010)

    Google Scholar 

  53. Mikkola, A.: Lugre tire model for HMMWV. Technical report TR-2014-15, Simulation-Based Engineering Laboratory, University of Wisconsin-Madison (2014)

    Google Scholar 

  54. Monaghan, J.J.: On the problem of penetration in particle methods. J. Comput. Phys. 82, 1–15 (1989)

    Article  MATH  Google Scholar 

  55. Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 1703–1759 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  56. Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136, 214–226 (1997)

    Article  MATH  Google Scholar 

  57. MPICH2: High Performance Portable MPI (2013). http://www.mpich.org/

  58. Negrut, D., Heyn, T., Seidl, A., Melanz, D., Gorsich, D., Lamb, D.: Enabling computational dynamics in distributed computing environments using a heterogeneous computing template. In: NDIA Ground Vehicle Systems Engineering and Technology Symposium (2011)

    Google Scholar 

  59. Negrut, D., Rampalli, R., Ottarsson, G., Sajdak, A.: On an implementation of the Hilber-Hughes-Taylor method in the context of index 3 differential-algebraic equations of multibody dynamics (detc2005-85096). J. Comput. Nonlinear Dyn 2, 73–85 (2007)

    Article  Google Scholar 

  60. Nemat-Nasser, S.: Plasticity: A Treatise on Finite Deformation of Heterogeneous Inelastic Materials. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  61. NVIDIA: CUDA Programming Guide (2015). http://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html

  62. OpenMP: Specification Standard 4.0 (2013). http://openmp.org/wp/

  63. O’Sullivan, C., Bray, J.D.: Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme. Eng. Comput. 21, 278–303 (2004)

    Article  MATH  Google Scholar 

  64. Pazouki, A., Negrut, D.: Numerical investigation of microfluidic sorting of microtissues. Comput. Math. Appl. (2015, accepted)

    Google Scholar 

  65. Pazouki, A., Negrut, D.: A numerical study of the effect of particle properties on the radial distribution of suspensions in pipe flow. Comput. Fluids 108, 1–12 (2015)

    Article  MathSciNet  Google Scholar 

  66. Pazouki, A., Serban, R., Negrut, D.: A high performance computing approach to the simulation of fluid-solid interaction problems with rigid and flexible components. Arch. Mech. Eng. 61, 227–251 (2014)

    Article  Google Scholar 

  67. Pazouki, A., Serban, R., Negrut, D.: A Lagrangian-Lagrangian framework for the simulation of rigid and deformable bodies in fluid. In: Terze, Z. (ed.) Multibody Dynamics. Computaional Methods in Applied Sciences, pp. 33–52. Springer International Publishing, Heidelberg (2014)

    Google Scholar 

  68. Pazouki, A., Song, B., Negrut, D.: Boundary condition enforcing methods for smoothed particle hydrodynamics. Technical report: TR-2015-08 (2015)

    Google Scholar 

  69. Rankin, C., Nour-Omid, B.: The use of projectors to improve finite element performance. Comput. Struct. 30, 257–267 (1988)

    Article  MATH  Google Scholar 

  70. Project Chrono: Chrono: An Open Source Framework for thePhysics-Based Simulation of Dynamic Systems. http://www.projectchrono.org. Accessed 7 Feb 2015

  71. Project Chrono: Chrono: An OpenSource Framework for the Physics-Based Simulation of Dynamic Systems. https://github.com/projectchrono/chrono. Accessed 15 Aug 2015

  72. Schwertassek, R., Wallrapp, O., Shabana, A.A.: Flexible multibody simulation and choice of shape functions. Nonlinear Dyn. 20, 361–380 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  73. Serban, R., Mazhar, H., Melanz, D., Jayakumar, P., Negrut, D.: A comparative study of penalty and complementarity methods for handling frictional contact in large multibody dynamics problems. In: 17th U.S. National Congress on Theoretical and Applied Mechanics (USNC-TAM) (2014)

    Google Scholar 

  74. Shabana, A.A.: Dynamics of Multibody Systems, 4th edn. Cambridge University Press, Cambridge (2013)

    Book  MATH  Google Scholar 

  75. Shotwell, R.: A comparison of chrono::engines primitive jointswith ADAMS results. Technical report TR-2012-01, Simulation-Based Engineering Laboratory, University of Wisconsin-Madison (2012). http://sbel.wisc.edu/documents/TR-2012-01.pdf

  76. Silbert, L.E., Ertaş, D., Grest, G.S., Halsey, T.C., Levine, D., Plimpton, S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 051302 (2001)

    Article  Google Scholar 

  77. Simo, J.C., Rifai, M.: A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 29, 1595–1638 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  78. Simulation-Based Engineering Lab (SBEL): Movies, Physics-Based Modeling and Simulation. http://sbel.wisc.edu/Animations. Accessed 09 June 2015

  79. Simulation-Based Engineering Lab (SBEL): Chrono Vimeo Movies. https://vimeo.com/uwsbel. Accessed 09 June 2015

  80. Sin, F.S., Schroeder, D., Barbič, J.: Vega: non-linear FEM deformable object simulator. Comput. Graph. Forum 32, 36–48 (2013). Wiley Online Library

    Article  Google Scholar 

  81. Stewart, D.E.: Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3–39 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  82. Stewart, D.E., Trinkle, J.C.: An implicit time-stepping scheme for rigid-body dynamics with inelastic collisions and Coulomb friction. Int. J. Numer. Meth. Eng. 39, 2673–2691 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  83. Sugiyama, H., Yamashita, H., Jayakumar, P.: Right on tracks - an integrated tire model for ground vehicle simulation. Tire Technol. Int. 67, 52–55 (2014)

    Google Scholar 

  84. Sugiyama, H., Yamashita, H., Jayakumar, P.: ANCF tire models for multibody ground vehicle simulation. In: Proceedings of International Tyre Colloquium: Tyre Models for Vehicle Dynamics Analysis, 25–28 June 2015

    Google Scholar 

  85. Swegle, J., Hicks, D., Attaway, S.: Smoothed particle hydrodynamics stability analysis. J. Comput. Phys. 116, 123–134 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  86. Tasora, A., Anitescu, M.: A complementarity-based rolling friction model for rigid contacts. Meccanica 48, 1643–1659 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  87. Tasora, A., Anitescu, M., Negrini, S., Negrut, D.: A compliant visco-plastic particle contact model based on differential variational inequalities. Int. J. Non-Linear Mech. 53, 2–12 (2013)

    Article  Google Scholar 

  88. Taylor, M., Serban, R.: Validation of basic modeling elements in chrono. Technical report TR-2015-05, Simulation-BasedEngineering Laboratory, University of Wisconsin-Madison (2015). http://sbel.wisc.edu/documents/TR-2015-05.pdf

  89. Trinkle, J., Pang, J.-S., Sudarsky, S., Lo, G.: On dynamic multi-rigid-body contact problems with Coulomb friction. Zeitschrift fur angewandte Mathematik und Mechanik 77, 267–279 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  90. Uehara, J.S., Ambroso, M.A., Ojha, R.P., Durian, D.J.: Erratum: low-speed impact craters in loose granular media [phys. rev. lett.prltao0031-9007 90, 194301 (2003)]. Phys. Rev. Lett. 91, 149902 (2003)

    Article  Google Scholar 

  91. Yamashita, H., Matsutani, Y., Sugiyama, H.: Longitudinal tire dynamics model for transient braking analysis: ANCF-LuGre tire model. J. Comput. Nonlinear Dyn. 10, 031003 (2015)

    Article  Google Scholar 

  92. Yamashita, H., Valkeapää, A.I., Jayakumar, P., Sugiyama, H.: Continuum mechanics based bilinear shear deformable shell element using absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 10, 051012 (2015)

    Article  Google Scholar 

  93. Zhang, H.P., Makse, H.A.: Jamming transition in emulsions and granular materials. Phys. Rev. E 72, 011301 (2005)

    Article  Google Scholar 

Download references

Acknowledgments

This work has been possible owing to US Army Research Office Rapid Innovation Funding grant W56HZV-14-C-0254, US National Science Foundation grant GOALI-CMMI 1362583, and US Army Research Office grant W911NF-12-1-0395. Milad Rakhsha is gratefully acknowledged for his help in the preparation of this manuscript.

Author information

Authors and Affiliations

  1. University of Parma, Parma, Italy

    Alessandro Tasora

  2. University of Wisconsin–Madison, Madison, WI, USA

    Radu Serban, Hammad Mazhar, Arman Pazouki, Daniel Melanz, Jonathan Fleischmann, Michael Taylor & Dan Negrut

  3. University of Iowa, Iowa City, IA, USA

    Hiroyuki Sugiyama

Authors
  1. Alessandro Tasora
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Radu Serban
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hammad Mazhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arman Pazouki
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Daniel Melanz
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jonathan Fleischmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Michael Taylor
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Hiroyuki Sugiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Dan Negrut
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan Negrut .

Editor information

Editors and Affiliations

  1. VSB - Technical University of Ostrava, Ostrava, Czech Republic

    Tomáš Kozubek

  2. Institute of Geonics of the CAS, Ostrava, Czech Republic

    Radim Blaheta

  3. Institute of Mathematics of the CAS, Prague, Czech Republic

    Jakub Šístek

  4. Institute of Computer Science of the CAS, Prague, Czech Republic

    Miroslav Rozložník

  5. VSB - Technical University of Ostrava, Ostrava, Czech Republic

    Martin Čermák

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Tasora, A. et al. (2016). Chrono: An Open Source Multi-physics Dynamics Engine. In: Kozubek, T., Blaheta, R., Šístek, J., Rozložník, M., Čermák, M. (eds) High Performance Computing in Science and Engineering. HPCSE 2015. Lecture Notes in Computer Science(), vol 9611. Springer, Cham. https://doi.org/10.1007/978-3-319-40361-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40361-8_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40360-1

  • Online ISBN: 978-3-319-40361-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation