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Acceleration of Two-Phase Flow Solvers on GPU Using Two-Level Preconditioning

This study explores an innovative approach to accelerate two-phase flow simulations using GPU technology. By applying two levels of preconditioning, namely Incomplete Poisson and Block Incomplete Cholesky, we achieve significant speed-up in solving Poisson-type matrices, particularly for large systems with millions of unknowns. Key factors affecting performance, including memory access patterns and the number of deflation vectors, are analyzed. Preliminary results indicate that double precision is essential for effective simulation of bubbly flows, showcasing the potential of deflation methods on many-core platforms.

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Acceleration of Two-Phase Flow Solvers on GPU Using Two-Level Preconditioning

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  1. Two Phase Flow using two levels of preconditioning on the GPU Prof. KeesVuik and Rohit Gupta Delft Institute of Applied Mathematics

  2. Problem Description Delft Institute of Applied Mathematics

  3. Computational Model ρ = 1 ρ = 1000 Boundary Conditions Delft Institute of Applied Mathematics

  4. Graphical Processing Unit • SIMD based Architecture: Army of Smaller Simpler Processors • Larger Memory Bandwidth • Programmer Managed Caches Delft Institute of Applied Mathematics

  5. Preconditioning Incomplete Poisson M-1=(I-LD-1)(I-D-1LT) Block Incomplete Cholesky Delft Institute of Applied Mathematics

  6. Deflation • Optimized Storage of AZ • Stripe-Wise Domains • Splitting Chosen • X = ( I – PT ) x + PT x • P=I-AQ • Q=ZE-1ZT • E=ZTAZ Delft Institute of Applied Mathematics

  7. Factors Affecting Speed-Up • Coalesced Memory Access • More Deflation Vectors • More preconditioning blocks Delft Institute of Applied Mathematics

  8. Results: Deflated Preconditioned CG BIC IP Poisson Type Matrix solved with Single Precision Math. ~1 Millions Unknowns (1024x1024). Precision Criteria 10e-04. Number of Blocks =512. Deflation Vectors=4096 Delft Institute of Applied Mathematics

  9. Two Phase (Double Precision) Preliminary Results Delft Institute of Applied Mathematics

  10. Conclusion • Deflation suits the many core platform • Two Phase requires double precision • Deflation with IP Preconditioning wins Delft Institute of Applied Mathematics

  11. References J. M. Tang and C. Vuik. Acceleration of preconditioned krylov solvers for bubbly ow problems. Lecture Notes in Computer Science, Parallel Processing and Applied Mathematics, 4967(1): 13231332, 2008. S.P. Van derPijl, A. Segal, C. Vuik, and P. Wesseling. A mass conserving level-set method for modelling of multi-phase ows. International Journal for Numerical Methods in Fluids, 47: 339361, 2005. M. Ament, G. Knittel, D. Weiskopf, and W. Strbaer. A parallel preconditioned conjugate gradient solver for the poisson problem on a multi-GPU platform. http://www.vis.unistuttgart.de/ amentmo/docs/ament-pcgip-PDP-2010.pdf, 2010. R. Gupta. Implementation of the Deated Preconditioned Conjugate Gradient Method for Bubbly Flow on the Graphical Processing Unit(GPU) . Master's thesis, Delft University of Technology, Delft, 2010. http://ta.twi.tudelft.nl/nw/users/vuik/numanal/gupta_afst.pdf. Delft Institute of Applied Mathematics

  12. Density of Oil = 1 Density of Water = 1000

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