zbMATH — the first resource for mathematics

OpenCL implementation of a high performance 3D peridynamic model on graphics accelerators. (English) Zbl 06928457
Summary: Parallel processing is one of the major trends in the computational mechanics community. Due to inherent limitations in processor design, manufacturers have shifted towards the multi- and many-core architectures. The graphics processing units (GPUs) are gaining more and more popularity due to high availability and processing power as well as maturity of development tools and community experience. In this research we describe a rather general approach to using OpenCL implementation of 3D Peridynamics model on GPU platform. Peridynamics is a non-local continuum theory for describing the behavior of material used especially when damage and crack nucleation or propagation is of interest. The steps taken for developing an OpenMP code from the serial one as well as the comparison between OpenCL and OpenMP codes are provided. Optimization techniques and their effects on the performance of the code are described. The implementations are tested on some 3D benchmarks with hundred of thousands to millions of nodes. The behavior of codes in terms of being memory or compute bound are analyzed. In all test cases reported, the OpenCL implementation consistently outperforms serial and OpenMP ones and paves the road for the development of high performance Peridynamics codes.

65Y10 Numerical algorithms for specific classes of architectures
74 Mechanics of deformable solids
kdtree++; OpenCL; SOFA
Full Text: DOI
[1] Mossaiby, F.; Bazrpach, M.; Shojaei, A., Extending the method of exponential basis functions to problems with singularities, Eng. Comput., 32, 2, 406-423, (2015)
[2] Alfano, G.; Crisfield, M. A., Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, Internat. J. Numer. Methods Engrg., 50, 7, 1701-1736, (2001) · Zbl 1011.74066
[3] Belytschko, T.; Moës, N.; Usui, S.; Parimi, C., Arbitrary discontinuities in finite elements, Internat. J. Numer. Methods Engrg., 50, 4, 993-1013, (2001) · Zbl 0981.74062
[4] Belytschko, T.; Black, T., Elastic crack growth in finite elements with minimal remeshing, Internat. J. Numer. Methods Engrg., 45, 5, 601-620, (1999) · Zbl 0943.74061
[5] Daux, C.; Moës, N.; Dolbow, J.; Sukumar, N.; Belytschko, T., Arbitrary branched and intersecting cracks with the extended finite element method, Internat. J. Numer. Methods Engrg., 48, 12, 1741-1760, (2000) · Zbl 0989.74066
[6] Munoz, J. J.; Galvanetto, U.; Robinson, P., On the numerical simulation of fatigue driven delamination with interface elements, J. Fatigue, 28, 10, 1136-1146, (2006) · Zbl 1139.74364
[7] Noormohammadi, N.; Boroomand, B., Construction of equilibrated singular basis functions without a priori knowledge of analytical singularity order, Comput. Math. Appl., 73, 7, 1611-1626, (2017) · Zbl 1372.65311
[8] Bobaru, F.; Zhang, G., Why do cracks branch? A peridynamic investigation of dynamic brittle fracture, Int. J. Fract., 196, 1-2, 59-98, (2015)
[9] Rabczuk, T., Computational methods for fracture in brittle and quasi-brittle solids: state-of-the-art review and future perspectives, ISRN Appl. Math., 2013, (2013) · Zbl 1298.74002
[10] Silling, S., Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids, 48, 1, 175-209, (2000) · Zbl 0970.74030
[11] Silling, S.; Askari, E., A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct., 83, 17-18, 1526-1535, (2005)
[12] Diyaroglu, C.; Oterkus, E.; Oterkus, S.; Madenci, E., Peridynamics for bending of beams and plates with transverse shear deformation, Int. J. Solids Struct., 69-70, 152-168, (2015)
[13] Ghajari, M.; Iannucci, L.; Curtis, P., A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media, Comput. Methods Appl. Mech. Engrg., 276, 431-452, (2014) · Zbl 1423.74882
[14] Huang, D.; Lu, G.; Qiao, P., An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis, Int. J. Mech. Sci., 94-95, 111-122, (2015)
[15] Liu, N.; Liu, D.; Zhou, W., Peridynamic modelling of impact damage in three-point bending beam with offset notch, Appl. Math. Mech., 38, 1, 99-110, (2017)
[16] Madenci, E.; Colavito, K.; Phan, N., Peridynamics for unguided crack growth prediction under mixed-mode loading, Eng. Fract. Mech., 1-11, (2015)
[17] Silling, S. A.; Bobaru, F., Peridynamic modeling of membranes and fibers, Int. J. Non-Linear Mech., 40, 2, 395-409, (2005) · Zbl 1349.74231
[18] Seleson, P.; Littlewood, D. J., Convergence studies in meshfree peridynamic simulations, Comput. Math. Appl., 71, 11, 2432-2448, (2016)
[19] Madenci, E.; Oterkus, E., Peridynamic theory and its applications, (2014), Springer · Zbl 1295.74001
[20] Nguyen, V. P.; Rabczuk, T.; Bordas, S.; Duflot, M., Meshless methods: a review and computer implementation aspects, Math. Comput. Simulation, 79, 3, 763-813, (2008) · Zbl 1152.74055
[21] Shojaei, A.; Boroomand, B.; Mossaiby, F., A simple meshless method for challenging engineering problems, Eng. Comput., 32, 6, 1567-1600, (2015)
[22] Shojaei, A.; Mossaiby, F.; Zaccariotto, M.; Galvanetto, U., The meshless finite point method for transient elastodynamic problems, Acta Mech., (2017), (in press) · Zbl 1384.74052
[23] Mossaiby, F.; Ghaderian, M., A preliminary study on the meshless local exponential basis functions method for nonlinear and variable coefficient pdes, Eng. Comput., 33, 8, 2238-2263, (2016)
[24] Rabczuk, T.; Belytschko, T., Cracking particles: a simplified meshfree method for arbitrary evolving cracks, Internat. J. Numer. Methods Engrg., 61, 13, 2316-2343, (2004) · Zbl 1075.74703
[25] Rabczuk, T.; Bordas, S.; Zi, G., On three-dimensional modelling of crack growth using partition of unity methods, Comput. Struct., 88, 23, 1391-1411, (2010)
[26] Rabczuk, T.; Zi, G., A meshfree method based on the local partition of unity for cohesive cracks, Comput. Mech., 39, 6, 743-760, (2007) · Zbl 1161.74055
[27] Rabczuk, T.; Zi, G.; Bordas, S.; Nguyen-Xuan, H., A simple and robust three-dimensional cracking-particle method without enrichment, Comput. Methods Appl. Mech. Engrg., 199, 37, 2437-2455, (2010) · Zbl 1231.74493
[28] Yang, S.-W.; Budarapu, P. R.; Mahapatra, D. R.; Bordas, S. P.; Zi, G.; Rabczuk, T., A meshless adaptive multiscale method for fracture, Comput. Mater. Sci., 96, 382-395, (2015)
[29] Bordas, S.; Rabczuk, T.; Zi, G., Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment, Eng. Fract. Mech., 75, 5, 943-960, (2008)
[30] Lee, J.; Oh, S. E.; Hong, J.-W., Parallel programming of a peridynamics code coupled with finite element method, Int. J. Fract., (2016)
[31] Wildman, R. A.; Gazonas, G. A., A finite difference-augmented peridynamics method for reducing wave dispersion, Int. J. Fract., 190, 1-2, 39-52, (2014)
[32] Bobaru, F.; Ha, Y. D., Adaptive refinement and multiscale modeling in 2D peridynamics, Int. J. Multiscale Comput. Eng., 9, 6, 635-659, (2011)
[33] Dipasquale, D.; Zaccariotto, M.; Galvanetto, U., Crack propagation with adaptive grid refinement in 2D peridynamics, Int. J. Fract., 190, 1-2, 1-22, (2014)
[34] Azdoud, Y.; Han, F.; Lubineau, G., The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture, Comput. Mech., 54, 3, 711-722, (2014) · Zbl 1311.74009
[35] Galvanetto, U.; Mudric, T.; Shojaei, A.; Zaccariotto, M., An effective way to couple FEM meshes and peridynamics grids for the solution of static equilibrium problems, Mech. Res. Commun., 76, 41-47, (2016)
[36] Liu, W.; Hong, J.-W., A coupling approach of discretized peridynamics with finite element method, Comput. Methods Appl. Mech. Engrg., 245-246, 163-175, (2012) · Zbl 1354.74284
[37] Seleson, P.; Ha, Y. D.; Beneddine, S., Concurrent coupling of bond-based peridynamics and the Navier equation of classical elasticity by blending, J. Multiscale Comput. Eng., 13, 2, 91-113, (2015)
[38] Shojaei, A.; Mudric, T.; Zaccariotto, M.; Galvanetto, U., A coupled meshless finite point/peridynamic method for 2D dynamic fracture analysis, Int. J. Mech. Sci., 119, 419-431, (2016)
[39] Shojaei, A.; Zaccariotto, M.; Galvanetto, U., Coupling of 2D discretized peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour, Eng. Comput., (2017), (in press)
[40] Mossaiby, F.; Rossi, R.; Dadvand, P.; Idelsohn, S., Opencl-based implementation of an unstructured edge-based finite element convection-diffusion solver on graphics hardware, Internat. J. Numer. Methods Engrg., 89, 13, 1635-1651, (2012) · Zbl 1242.76131
[41] Fan, H.; Li, S., Parallel peridynamics-SPH simulation of explosion induced soil fragmentation by using openmp, Comput. Parti. Mech., (2016)
[42] Kilic, B.; Madenci, E., Prediction of crack paths in a quenched Glass plate by using peridynamic theory, Int. J. Fract., 156, 2, 165-177, (2009) · Zbl 1273.74455
[43] Kilic, B.; Agwai, A.; Madenci, E., Peridynamic theory for progressive damage prediction in center-cracked composite laminates, Compos. Struct., 90, 2, 141-151, (2009)
[44] Kilic, B.; Madenci, E., Structural stability and failure analysis using peridynamic theory, Int. J. Non-Linear Mech., 44, 8, 845-854, (2009) · Zbl 1203.74045
[45] Diehl, P., Implementierung eines peridynamik -verfahrens auf GPU, 32, (2012), University of Stuttgart, Master’s thesis
[46] Diehl, P.; Schweitzer, M. A., Efficient neighbor search for particle methods on gpus, (Griebel, M.; Schweitzer, M. A., Meshfree Methods for Partial Differential Equations VII, (2015), Springer International Publishing Cham), 81-95 · Zbl 1342.76098
[47] Le, Q.; Chan, W.; Schwartz, J., A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids, Internat. J. Numer. Methods Engrg., 98, 8, 547-561, (2014) · Zbl 1352.74040
[48] Liu, W.; Hong, J.-W., Discretized peridynamics for brittle and ductile solids, Internat. J. Numer. Methods Engrg., 89, 8, 1028-1046, (2012) · Zbl 1242.74005
[49] Zhang, G.; Bobaru, F., Modeling the evolution of fatigue failure with peridynamics, Rom. J. Tech. Sci. Appl. Mech., 61, 1, 20-39, (2016)
[50] Rossi, R.; Mossaiby, F.; Idelsohn, S. R., A portable opencl-based unstructured edge-based finite element Navier-Stokes solver on graphics hardware, Comput. & Fluids, 81, 134-144, (2013) · Zbl 1285.76007
[51] Silling, S. A.; Epton, M.; Weckner, O.; Xu, J.; Askari, E., Peridynamic states and constitutive modeling, J. Elasticity, 88, 2, 151-184, (2007) · Zbl 1120.74003
[52] Warren, T. L.; Silling, S. A.; Askari, A.; Weckner, O.; Epton, M. A.; Xu, J., A non-ordinary state-based peridynamic method to model solid material deformation and fracture, Int. J. Solids Struct., 46, 5, 1186-1195, (2009) · Zbl 1236.74012
[53] Ha, Y. D.; Bobaru, F., Studies of dynamic crack propagation and crack branching with peridynamics, Int. J. Fract., 162, 1-2, 229-244, (2010) · Zbl 1425.74416
[54] Zaccariotto, M.; Luongo, F.; Sarego, G.; Galvanetto, U., Examples of applications of the peridynamic theory to the solution of static equilibrium problems, Aeronaut. J., 119, 1216, 677-700, (2015)
[55] Emmrich, E.; Weckner, O., The peridynamic equation and its spatial discretisation, Math. Model. Anal., 12, 1, 17-27, (2007) · Zbl 1121.65073
[56] K. Yu, X.J. Xin, K.B. Lease, A new method of adaptive integration with error control for bond-based peridynamics, in: Proceedings of the World Congress on Engineering and Computer Science, Vol. 2, 2010.
[57] Source code for OpenCL Peridynamics solver. http://dx.doi.org/10.6084/m9.figshare.5097385.
[58] OpenJDK. http://openjdk.java.net.
[59] McCalpin, J. D., Memory bandwidth and machine balance in current high performance computers, IEEE Comput. Soc. Tech. Comm. Comput. Archit. (TCCA) Newsl., 19-25, (1995)
[60] Silling, S.; Littlewood, D.; Seleson, P., Variable horizon in a peridynamic medium, J. Mech. Mater. Struct., 10, 5, 591-612, (2015)
[61] Ren, H.; Zhuang, X.; Cai, Y.; Rabczuk, T., Dual-horizon peridynamics, Internat. J. Numer. Methods Engrg., (2016)
[62] Ren, H.; Zhuang, X.; Rabczuk, T., Dual-horizon peridynamics: A stable solution to varying horizons, Comput. Methods Appl. Mech. Engrg., 318, 762-782, (2017)
[63] Belytschko, T.; Chen, H.; Xu, J.; Zi, G., Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment, Internat. J. Numer. Methods Engrg., 58, 12, 1873-1905, (2003) · Zbl 1032.74662
[64] Rabczuk, T.; Zi, G.; Bordas, S.; Nguyen-Xuan, H., A simple and robust three-dimensional cracking-particle method without enrichment, Comput. Methods Appl. Mech. Engrg., 199, 37-40, 2437-2455, (2010) · Zbl 1231.74493
[65] Song, J.-H.; Areias, P. M.A.; Belytschko, T., A method for dynamic crack and shear band propagation with phantom nodes, Internat. J. Numer. Methods Engrg., 67, 6, 868-893, (2006) · Zbl 1113.74078
[66] Kalthoff, J. F., Modes of dynamic shear failure in solids, Int. J. Fract., 101, 1/2, 1-31, (2000)
[67] Ravi-Chandar, K., Dynamic fracture of nominally brittle materials, Int. J. Fract., 90, 1-2, 83-102, (1998)
[68] Courtecuisse, H.; Jung, H.; Allard, J.; Duriez, C.; Lee, D. Y.; Cotin, S., GPU-based real-time soft tissue deformation with cutting and haptic feedback, Progr. Biophys. Mol. Biol., 103, 2, 159-168, (2010)
[69] Courtecuisse, H.; Allard, J.; Kerfriden, P.; Bordas, S. P.; Cotin, S.; Duriez, C., Real-time simulation of contact and cutting of heterogeneous soft-tissues, Med. Image Anal., 18, 2, 394-410, (2014)
[70] Bui, H. P.; Tomar, S.; Courtecuisse, H.; Cotin, S.; Bordas, S., Real-time error control for surgical simulation, IEEE Trans. Biomed. Eng., (2017)
[71] H.P. Bui, S. Tomar, H. Courtecuisse, M. Audette, S. Cotin, S. Bordas, Controlling the error on target motion through real-time mesh adaptation: Applications to deep brain stimulation, 2017. ArXiv Preprint arXiv:1704.07636.
[72] Faure, F.; Duriez, C.; Delingette, H.; Allard, J.; Gilles, B.; Marchesseau, S.; Talbot, H.; Courtecuisse, H.; Bousquet, G.; Peterlik, I., Sofa: A multi-model framework for interactive physical simulation, (Soft Tissue Biomechanical Modeling for Computer Assisted Surgery, (2012), Springer), 283-321
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.