pTatin3D: High-performance methods for long-term lithospheric dynamics. Simulations of long-term lithospheric deformation involve post-failure analysis of high-contrast brittle materials driven by buoyancy and processes at the free surface. Geodynamic phenomena such as subduction and continental rifting take place over millions year time scales, thus require efficient solution methods. We present pTatin3D, a geodynamics modeling package utilising the material-point-method for tracking material composition, combined with a multigrid finite-element method to solve heterogeneous, incompressible visco-plastic Stokes problems. Here we analyze the performance and algorithmic tradeoffs of pTatin3D’s multigrid preconditioner. Our matrix-free geometric multigrid preconditioner trades flops for memory bandwidth to produce a time-to-solution > 2× faster than the best available methods utilising stored matrices (plagued by memory bandwidth limitations), exploits local element structure to achieve weak scaling at 30% of FPU peak on Cray XC-30, has improved dynamic range due to smaller memory footprint, and has more consistent timing and better intra-node scalability due to reduced memory-bus and cache pressure.

References in zbMATH (referenced in 9 articles )

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  1. Chang, Justin; Fabien, Maurice S.; Knepley, Matthew G.; Mills, Richard T.: Comparative study of finite element methods using the time-accuracy-size (TAS) spectrum analysis (2018)
  2. Kirby, Robert C.; Mitchell, Lawrence: Solver composition across the PDE/linear algebra barrier (2018)
  3. Borzacchiello, Domenico; Leriche, Emmanuel; Blottière, Benoît; Guillet, Jacques: Box-relaxation based multigrid solvers for the variable viscosity Stokes problem (2017)
  4. Chang, J.; Karra, S.; Nakshatrala, K. B.: Large-scale optimization-based non-negative computational framework for diffusion equations: parallel implementation and performance studies (2017)
  5. Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin: A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow (2017)
  6. Rudi, Johann; Stadler, Georg; Ghattas, Omar: Weighted BFBT preconditioner for Stokes flow problems with highly heterogeneous viscosity (2017)
  7. Mitchell, Lawrence; Müller, Eike Hermann: High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling (2016)
  8. May, D. A.; Brown, J.; Le Pourhiet, L.: A scalable, matrix-free multigrid preconditioner for finite element discretizations of heterogeneous Stokes flow (2015)
  9. Sundar, Hari; Stadler, Georg; Biros, George: Comparison of multigrid algorithms for high-order continuous finite element discretizations. (2015)