Implementation of a multigrid solver on a GPU for Stokes equations with strongly variable viscosity based on Matlab and CUDA

Liang Zheng, Huai Zhang, Taras Gerya, Matthew Knepley, David A Yuen, Yaolin Shi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The Stokes equations are frequently used to simulate geodynamic processes, including mantle convection, lithospheric dynamics, lava flow, and among others. In this study, the multigrid (MG) method is adopted to solve Stokes and continuity equations with strongly temperature-dependent viscosity. By taking advantage of the enhanced computing power of graphics processing units (GPUs) and the new version of Matlab 2010b, MG codes are optimized through Compute Unified Device Architecture (CUDA). Herein, we illustrate the approach that implements a GPU-based MG solver with Red-Black Gauss-Seidel (RBGS) smoother for the three-dimensional Stokes and continuity equations, in a hope that it helps solve the synthetic incompressible sinking problem in a cubic domain with strongly variable viscosity, and finally analyze our solver's efficiency on a GPU.

Original languageEnglish (US)
Pages (from-to)50-60
Number of pages11
JournalInternational Journal of High Performance Computing Applications
Volume28
Issue number1
DOIs
StatePublished - Feb 2014

Bibliographical note

Funding Information:
This work was supported by the National High Technology Research and Development Program of China (863 Program), ‘Rapid visualization and diagnosis techniques of earth system model output data’ (grant number 2010AA012402), the NSF CMG Program and the Project SinoProbe-07 of China.

Keywords

  • GPU
  • Matlab
  • Stokes flow
  • multigrid
  • strongly variable viscosity

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