S, Jin
(2013)
GPU Accelerated Three Dimensional Unstructured Geometric MultiGrid Solver.
Masters thesis, Indian Institute of Technology Hyderabad.
Abstract
Consider a set of points P in three dimensional euclidean space. For each point p, the neighbourhood
N(p), is defined as the set of points in P, which are voronoi neighbours. Each point in P represents
a variable and its value is dependent on the value of its neighbourhood. Its value is given by the sum
of the values of points in its neighbourhood scaled by predefined constants. The constants depend
on the spacing between the points. The problem is to solve all the variables. Such representations
arise naturally in solving flow equations in Computational Fluid Dynamics with domains represented
using unstructured meshes. The problem reduces to solve a system of linear equations. In this work
geometric multigrid method is implemented for solving the problem faster. Solving this problem on
very large input is a time consuming process. The inputs considered here are having size of the order
of millions. Graphics Processing Units(GPU) are dedicated parallel processors which serves both as
a programmable graphics processor and a scalable parallel computing platform. The parallelization
of this problem for GPUs is not straight forward because of the irregularity. The CFD problem used
for experiment is the steady and unsteady heat transfer problem in 3D unstructured meshes.The
combination of multigrid algorithm and GPU implementation for the steady problem on a 1.6 million
mesh gives 1630 times speed up compared to nonmultigrid CPU implementation.
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