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An Efficient Geometric Multigrid Solver for Viscous Liquids

Published:26 July 2019Publication History
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Abstract

We present an efficient geometric Multigrid solver for simulating viscous liquids based on the variational approach of Batty and Bridson [2008]. Although the governing equations for viscosity are elliptic, the strong coupling between different velocity components in the discrete stencils mandates the use of more exotic smoothing techniques to achieve textbook Multigrid efficiency. Our key contribution is the design of a novel box smoother involving small and sparse systems (at most 9 x 9 in 2D and 15 x 15 in 3D), which yields excellent convergence rates and performance improvements of 3.5x - 13.8x over a naïve Multigrid approach. We employ a hybrid approach by using a direct solver only inside the box smoother and keeping the remaining pipeline assembly-free, allowing our solver to efficiently accommodate more than 194 million degrees of freedom, while occupying a memory footprint of less than 16 GB. To reduce the computational overhead of using the box smoother, we precompute the Cholesky factorization of the subdomain system matrix for all interior degrees of freedom. We describe how the variational formulation, which requires volume weights computed at the centers of cells, edges, and faces, can be naturally accommodated in the Multigrid hierarchy to properly enforce boundary conditions. Our proposed Multigrid solver serves as an excellent preconditioner for Conjugate Gradients, outperforming existing state-of-the-art alternatives. We demonstrate the efficacy of our method on several high resolution examples of viscous liquid motion including two-way coupled interactions with rigid bodies.

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    • Published in

      cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques
      Proceedings of the ACM on Computer Graphics and Interactive Techniques  Volume 2, Issue 2
      July 2019
      239 pages
      EISSN:2577-6193
      DOI:10.1145/3352480
      Issue’s Table of Contents

      Copyright © 2019 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 26 July 2019
      Published in pacmcgit Volume 2, Issue 2

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