A GPU accelerated discontinuous Galerkin approach to conservative level sets

Zechariah J. Jibben, Marcus Herrmann

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present a GPU-accelerated, arbitrary-order, nearly quadrature-free, Runge-Kutta (RK) discontinuous Galerkin (DG) approach to interface capturing for atomizing multiphase flows via the conservative level set (CLS) method [16, 17] An arbitrary-order DG numerical method is utilized for both advection and reinitialization, further developing the ideas of Czajkowski and Desjardins [3] by implementing a quadrature-free approach allowing for arbitrary polynomial degree, and treating the normal function in a DG sense. For effective use of processing power, the method is executed with the dual narrow band overset mesh approach of the refined level set grid method [11]. Computation is performed in parallel on either CPU or GPU architectures to make the method feasible at high order. Finally, by using normalized Legendre polynomial basis functions, we are able to pre-compute volume and surface integrals analytically. The resulting sparse integral arrays are stored in the compressed row storage format to take full advantage of parallelism on the GPU, where performance relies heavily on well-managed memory operations. The accuracy, consistency, and convergence of the resulting method is demonstrated using the method of manufactured solutions (MMS). Using MMS, we demonstrate k + 1 order spatial convergence for kth order normalized Legendre polynomial basis functions on both advection and reinitialization. MMS is also used to demonstrate the benefits of GPU hardware, where advection is found to provide a speedup factor >45x comparing a 2.0GHz Intel Xeon E5-2620 in serial against a NVIDIA Tesla K20c, with speedup increasing with polynomial degree. Arbitrarily high convergence rates combined with speedup factors that increase with polynomial degree motivate the development and use of a GPU accelerated, arbitrary-order DG method.

Original languageEnglish (US)
Title of host publication11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014
PublisherInternational Center for Numerical Methods in Engineering
Pages5625-5636
Number of pages12
ISBN (Print)9788494284472
StatePublished - Jul 1 2014
EventJoint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 - Barcelona, Spain
Duration: Jul 20 2014Jul 25 2014

Other

OtherJoint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014
CountrySpain
CityBarcelona
Period7/20/147/25/14

Fingerprint

Polynomials
Advection
Multiphase flow
Galerkin methods
Program processors
Numerical methods
Graphics processing unit
Hardware
Data storage equipment
Processing

Keywords

  • Discontinuous Galerkin
  • GPU
  • Level set
  • Multiphase

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Mechanical Engineering

Cite this

Jibben, Z. J., & Herrmann, M. (2014). A GPU accelerated discontinuous Galerkin approach to conservative level sets. In 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 (pp. 5625-5636). International Center for Numerical Methods in Engineering.

A GPU accelerated discontinuous Galerkin approach to conservative level sets. / Jibben, Zechariah J.; Herrmann, Marcus.

11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. International Center for Numerical Methods in Engineering, 2014. p. 5625-5636.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Jibben, ZJ & Herrmann, M 2014, A GPU accelerated discontinuous Galerkin approach to conservative level sets. in 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. International Center for Numerical Methods in Engineering, pp. 5625-5636, Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014, Barcelona, Spain, 7/20/14.
Jibben ZJ, Herrmann M. A GPU accelerated discontinuous Galerkin approach to conservative level sets. In 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. International Center for Numerical Methods in Engineering. 2014. p. 5625-5636
Jibben, Zechariah J. ; Herrmann, Marcus. / A GPU accelerated discontinuous Galerkin approach to conservative level sets. 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. International Center for Numerical Methods in Engineering, 2014. pp. 5625-5636
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