Using  the  PRISMS-­‐PF  Matrix-­‐Free  Finite  Element  Code  to  Solve  the  CHiMaD Test  Cases

Stephen  DeWitt  and  Shiva  RudrarajuPRISMS  Center

University  of  Michigan

Problem  1:  Spinodal Decomposition

§ We  investigated  both  explicit  and  implicit  time  stepping§ Unsurprisingly,  with  backward  Euler  we  were  able  to  obtain  faster-­‐running  simulations  that  still  captured  the  morphology  evolution

§ Full  disclosure:  implicit  time  stepping  isn’t  in  the  public  PRISMS  code  quite  yet

§ Our  standard  mesh  was  128  nodes  by  128  nodes§ Used  a  fixed  mesh  and  a  constant  time  step

− Planning  to  implement  adaptivity in  time  and  space  in  the  PRISMS  code  in  the  near  future

Problem  1a:  Early  dynamics

Number of Iterations #1040 1 2 3 4 5

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A relatively  complex  structure  form  in  the  first  few  thousand  iterations  

Problem  1a:  The  road  to  steady  state

Number of Iterations #1050 2 4 6 8 10

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100,000  time  units,  35  minutes  of  wall  time  for  16  processors1,000,000  time  steps,  128x128  elements,  ~16,000  DOF

Problem  1a:  Comparison  to  a  finer  mesh

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600128 mesh points per side256 mesh points per side

Problem  1b:  No-­‐flux  BCs

50,000  time  units,  21  minutes  of  wall  time  for  16  processors500,000  time  steps,  128x128  elements,  ~16,000  DOF

Number of Iterations #1060 1 2 3 4 5

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Problem  1c:  T-­‐shaped  domain

50,000  time  units,  3minutes  of  wall  time  for  16  processors500,000  time  steps,  T-­‐bars  are  14  elements  across,  2115  DOF

Number of Iterations #1060 1 2 3 4 5

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Problem  1d:  Spinodal Decomposition  on  a  Surface  Manifold  (FENICS)

10,000  time  units,  216  minutes  of  wall  time  for  a  single  core10,000  time  steps,  ~41,000  DOF  (medium  mesh)

Problem  1d:  Free  Energies

Zooming  in  to  the  first  few  iterations

Energy  at  the  middle  level  of  grid  refinement  (red)  matches  that  at  the  highest  level  of  refinement  (green)

Problem  1  Recap  and  Impressions

§ In  our  experience  this  made  for  a  good  test  problem− Spinodal decomposition  yields  well  understood  dynamics● In  a  Hackathon setting  it  is  important  to  know  easily  that  your  simulations  are  behaving  as  they  should

− Initial  condition  yields  interesting  structure  without  relying  on  noise− Problem  was  computationally  manageable,  allowing  us  to  get  

results  relatively  quickly

§ Suggestion:  Associate  a  desired  end  time  for  the  problem− Most  of  the  “interesting”  morphology  evolution  is  early− It’s  hard  to  compare  wall  times  to  steady  state,  since  the  threshold  

to  steady  state  is  not  clearly  defined

Problem  2:  At  least  the  energy  is  decreasing

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1,000  time  units,  4h30m  of  wall  time  for  16  processors1,000,000  time  steps,  128x128  elements,  200,000  DOF

Here,  we’re  less  confident  in  our  solutionMax  concentration  stabilizes  at  1.6,  rather  than  the  expected  0.95

Problem  2:  Order  parameter  evolution

Conclusions

§ Problem  1  worked  well  as  a  benchmark  problem§ It’s  harder  for  us  to  judge  problem  2,  since  we  didn’t  get  a  reasonable  answer

§Overall,  we’re  happy  with  the  performance  of  the  PRISMS  code− Looking  forward  to  re-­‐running  these  benchmarks  as  features  are  added  to  the  code

§ Please  let  us  know  if  you  want  to  use  the  PRISMS  code− http://www.prisms-­‐center.org/− https://github.com/prisms-­‐center