Journal of Applied Mathematics

TESLA GPUs versus MPI with OpenMP for the Forward Modeling of Gravity and Gravity Gradient of Large Prisms Ensemble

Carlos Couder-Castañeda, Carlos Ortiz-Alemán, Mauricio Gabriel Orozco-del-Castillo, and Mauricio Nava-Flores

Full-text: Open access


An implementation with the CUDA technology in a single and in several graphics processing units (GPUs) is presented for the calculation of the forward modeling of gravitational fields from a tridimensional volumetric ensemble composed by unitary prisms of constant density. We compared the performance results obtained with the GPUs against a previous version coded in OpenMP with MPI, and we analyzed the results on both platforms. Today, the use of GPUs represents a breakthrough in parallel computing, which has led to the development of several applications with various applications. Nevertheless, in some applications the decomposition of the tasks is not trivial, as can be appreciated in this paper. Unlike a trivial decomposition of the domain, we proposed to decompose the problem by sets of prisms and use different memory spaces per processing CUDA core, avoiding the performance decay as a result of the constant calls to kernels functions which would be needed in a parallelization by observations points. The design and implementation created are the main contributions of this work, because the parallelization scheme implemented is not trivial. The performance results obtained are comparable to those of a small processing cluster.

Article information

J. Appl. Math., Volume 2013 (2013), Article ID 437357, 15 pages.

First available in Project Euclid: 14 March 2014

Permanent link to this document

Digital Object Identifier


Couder-Castañeda, Carlos; Ortiz-Alemán, Carlos; Orozco-del-Castillo, Mauricio Gabriel; Nava-Flores, Mauricio. TESLA GPUs versus MPI with OpenMP for the Forward Modeling of Gravity and Gravity Gradient of Large Prisms Ensemble. J. Appl. Math. 2013 (2013), Article ID 437357, 15 pages. doi:10.1155/2013/437357.

Export citation


  • R. Vuduc and K. Czechowski, “What GPU computing means for high-end systems,” IEEE Micro, vol. 31, no. 4, pp. 74–78, 2011.
  • J. D. Owens, D. Luebke, N. Govindaraju et al., “A survey of general-purpose computation on graphics hardware,” Computer Graphics Forum, vol. 26, no. 1, pp. 80–113, 2007.
  • C. J. Webb and S. Bilbao, “Computing room acoustics with CUDA-3D FDTD schemes with boundary losses and viscosity,” in Proceedings of the 36th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '11), pp. 317–320, May 2011.
  • N. Nakata, T. Tsuji, and T. Matsuoka, “Acceleration of computation speed for elastic wave simulation using a Graphic Processing Unit,” Exploration Geophysics, vol. 42, no. 1, pp. 98–104, 2011.
  • R. Abdelkhalek, H. Calandra, O. Coulaud, J. Roman, and G. Latu, “Fast seismic modeling and reverse time migration on a GPU cluster,” in Proceedings of the International Conference on High Performance Computing and Simulation (HPCS '09), pp. 36–43, June 2009.
  • J. Yang, Y. Wang, and Y. Chen, “GPU accelerated molecular dynamics simulation of thermal conductivities,” Journal of Computational Physics, vol. 221, no. 2, pp. 799–804, 2007.
  • T. Brandvik and G. Pullan, “Acceleration of a two-dimensioanl Euler flow solver using commodity graphics hardware,” Journal of Mechanical Engineering Science, vol. 221, no. 12, pp. 1745–1748, 2007.
  • R. Capuzzo-Dolcetta, A. Mastrobuono-Battisti, and D. Maschietti, “NBSymple, a double parallel, symplectic N-body code running on graphic processing units,” New Astronomy, vol. 16, no. 4, pp. 284–295, 2011.
  • L.-G. Du, K. Li, F.-M. Kong, and Y. Hu, “Parallel 3D finite-difference time-domain method on multi-GPU systems,” International Journal of Modern Physics C, vol. 22, no. 2, pp. 107–121, 2011.
  • I. Foster, Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering, Addison-Wesley Longman, Boston, Mass, USA, 1995.
  • D. Michéa and D. Komatitsch, “Accelerating a three-dimensional finite-difference wave propagation code using GPU graphics cards,” Geophysical Journal International, vol. 182, no. 1, pp. 389–402, 2010.
  • M. Moorkamp, M. Jegen, A. Roberts, and R. Hobbs, “Massively parallel forward modeling of scalar and tensor gravimetry data,” Computers and Geosciences, vol. 36, no. 5, pp. 680–686, 2010.
  • L. Dagum and R. Menon, “Openmp: an industry-standard api for shared-memory programming,” IEEE Computing in Science and Engineering, vol. 5, no. 1, pp. 46–55, 1998.
  • T.-Y. Liang, H.-F. Li, and J.-Y. Chiu, “Enabling mixed openmp/mpi programming on hybrid cpu/gpu computing architecture,” in Proceedings of the IEEE 26th International Parallel and Distributed Processing Symposium Workshops (IPDPSW '12), pp. 2369–2377, 2012.
  • D. Komatitsch, “Fluid-solid coupling on a cluster of GPU graphics cards for seismic wave propagation,” Comptes Rendus Mécanique, vol. 339, no. 2-3, pp. 125–135, 2011.
  • B. Heck and K. Seitz, “A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling,” Journal of Geodesy, vol. 81, no. 2, pp. 121–136, 2007.
  • Z. Chen, X. Meng, and L. Guo, “Gicuda: a parallel program for 3d correlation imaging of large scale gravity and gravity gradiometry data on graphics processing units with cuda,” Computers and Geosciences, vol. 46, pp. 119–128, 2012.
  • K. L. Mickus and J. H. Hinojosa, “The complete gravity gradient tensor derived from the vertical component of gravity: a Fourier transform technique,” Journal of Applied Geophysics, vol. 46, no. 3, pp. 159–174, 2001.
  • C. Ortiz-Alemán and J. Urrutia-Fucugauchi, “Aeromagnetic anomaly modeling of central zone structure and magnetic sources in the Chicxulub crater,” Physics of the Earth and Planetary Interiors, vol. 179, no. 3-4, pp. 127–138, 2010.
  • M. G. Orozco-del Castillo, C. Ortiz-Alemán, J. Urrutia-Fucugauchi, R. Martin, A. Rodriguez-Castellanos, and P. E. Villase$\sim\,\!$nor-Rojas, “A genetic algorithm for filter design to enhance features in seismic images,” Geophysical Prospecting, 2013.
  • J. L. Rodríguez-Zúñiga, C. Ortiz-Alemán, G. Padilla, and R. Gaulon, “Application of genetic algorithms to constrain shallow elastic parameters using in situ ground inclination measurements,” Soil Dynamics and Earthquake Engineering, vol. 16, no. 3, pp. 223–234, 1997.