Implementation of a multigrid solver on a GPU for Stokes equations with strongly variable viscosity based on Matlab and CUDA. (February 2014)

• Record Type: Journal Article
• Authors: Zheng, Liang; Zhang, Huai; Gerya, Taras; Knepley, Matthew; Yuen, David A; Shi, Yaolin
• Is Part Of: International journal of high performance computing applications. Volume 28:Number 1(2014:Spring)
• Page Start: 50
• Page End: 60
• Publication Date: 2014-02
• Subjects: GPU -- Matlab -- multigrid -- Stokes flow -- strongly variable viscosity; High performance computing -- Periodicals; Supercomputers -- Periodicals; 004.1105
• DOI: 10.1177/1094342013478640
• Languages: English
• ISSNs: 1094-3420

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.