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A parallel multigrid Poisson solver for fluids simulation on large grids

Aleka McAdams, Eftychios Sifakis, Joseph Teran
ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) — 2010
    Download the publication : mgpcg_poisson.pdf [2.5Mo]  
    We present a highly efficient numerical solver for the Poisson equation on irregular voxelized domains supporting an arbitrary mix of Neumann and Dirichlet boundary conditions. Our approach employs a multigrid cycle as a preconditioner for the conjugate gradient method, which enables the use of a lightweight, purely geometric multigrid scheme while drastically improving convergence and robustness on irregular domains. Our method is designed for parallel execution on shared-memory platforms and poses modest requirements in terms of bandwidth and memory footprint. Our solver will accommodate as many as 768×768×1152 voxels with a memory footprint less than 16GB, while a full smoke simulation at this resolution fits in 32GB of RAM. Our preconditioned conjugate gradient solver typically reduces the residual by one order of magnitude every 2 iterations, while each PCG iteration requires approximately 6.1sec on a 16-core SMP at 768^3 resolution. We demonstrate the efficacy of our method on animations of smoke flow past solid objects and free surface water animations using Poisson pressure projection at unprecedented resolutions.

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    BibTex references

      author       = "McAdams, Aleka and Sifakis, Eftychios and Teran, Joseph",
      title        = "A parallel multigrid Poisson solver for fluids simulation on large grids",
      booktitle    = "ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA)",
      year         = "2010",
      editor       = "M. Otaduy and Z. Popovic",
      url          = "http://graphics.cs.wisc.edu/Papers/2010/MST10"

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