Segregated Schur Complement Solvers for Fluid DFTs

Mike Heroux, Laura Frink, Andy Salinger

• New family of scalable solvers for complex fluid systems in Tramonto.
• Properties:
  • No tuning parameters.
  • 5-20 times memory use reduction over previous approaches.
  • O(10)-O(100) reduced implicit problem size.
  • Nearly linear scalability in: processor count, mesh density, polymer chain length.
  • Candidate for petascale class computing:
    • Super-linear speedup.
    • Applied for INCITE award

• Enables
  • Fundamentally new calculations for important bio problems.  Quotes from Physical Review Letters referees on computations using these solvers
    • “This is (to my knowledge) the first time [Fluid] DFT has been used to analyze the important problem of pore structure in biological membranes.”
    • “This appears to me to be a highly significant advance in theoretical biophyics, even by the high standards of Physical Review Letters. I suspect that this Sandia group is the only one in the world to have developed classical DFT methods sufficiently sophisticated to deal with such a remarkably complex problem in colloidal physics…”
    • “…I would then recommend at least a footnote that gives some introductory
      hint as to how they have managed to cope numerically with such
      complex structures; presumably a 3d finite element method with
      all manner of tricks?
• The “tricks” are the solvers.
• Solver work published in SIAM SISC.
• Tramonto first public release this year.

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