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

Liang Zheng, Taras Gerya, Matthew Knepley, David A. Yuen, Huai Zhang, Yaolin Shi
Laboratory of Computational Geodynamics, Chinese Academy of Sciences, China
University of Minnesota Supercomputing Institute Research Report UMSI 2011/33, 2011

@article{zheng2011implementation,

   title={Implementation of a multigrid solver on GPU for Stokes equations with strongly variable viscosity based on Matlab and CUDA},

   author={ZHENG, L. and Gerya, T. and Knepley, M. and Yuen, D.A. and ZHANG, H. and SHI, Y.},

   year={2011}

}

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Stokes equations have been used in numerical simulations of geodynamic processes such as mantle convection , lithospheric deformation and lava flow, etc. In order to implement a solver for these equations, multigrid method is introduced to our solve. Multigrid method is commonly used in reducing the iteration steps for solving the elliptic partial differential equation with the ill-conditioned matrix due to the saddle points in the matrix system coupling mass and momentum equations and strongly variable viscosity due to rheology. Taking the advantages of the current Graphic Processing Units’ (GPU) computing ability and the new Matlab 2010b we utilize the massive programming method to speed up the original Matlab codes with Compute Unified Device Architecture (CUDA). In this paper we will introduce the implementation of a Matlab based multigrid solver for three dimensional Stokes equations with strongly variable viscosity using Red-Black Gauss-Seidel method on GPU.
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