Implementation of the Deflated Preconditioned Conjugate Gradient Method for Bubbly Flow on the Graphical Processing Unit (GPU)

In this work we have implemented the Iterative Method of Conjugate Gradients with two levels of Preconditioning to solve a System of Linear Equations on Graphical Processing Unit (GPU). This system represents the discretized Pressure equation resulting from the Level Set Method Solution of the Incompressible Navier Stokes Equation used to compute Bubbly Flows. We have tried to explore the problem space with different grid sizes, number of preconditioning blocks and deflation vectors. The results show that when the methods for preconditioning are chosen so that they can exhibit ample parallelism we can achieve considerable performance up to 20 times better than the CPU version. We show in our analysis that we are very close to maximum achievable speedup. We also report on the accuracy of our results and argue that GPUs can be beneficial in solving such problems efficiently.

Subject

GPU
conjugate gradient
deflation
preconditioning

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Student theses

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master thesis

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