Prisims -- Hackathon 1

1. Using
the
PRISMS-­‐PF
Matrix-­‐Free
Finite
Element
Code
to
Solve
the
CHiMaD Test
Cases
Stephen
DeWitt
and
Shiva
Rudraraju
PRISMS
Center
University
of
Michigan

2. 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

3. Problem
1a:
Early
dynamics
Number of Iterations #104
0 1 2 3 4 5
FreeEnergy(arb)
-800
-600
-400
-200
0
200
400
600
A relatively
complex
structure
form
in
the
first
few
thousand
iterations

4. Problem
1a:
The
road
to
steady
state
Number of Iterations #105
0 2 4 6 8 10
FreeEnergy(arb)
-1000
-800
-600
-400
-200
0
200
400
600
100,000
time
units,
35
minutes
of
wall
time
for
16
processors
1,000,000
time
steps,
128x128
elements,
~16,000
DOF

5. Problem
1a:
Comparison
to
a
finer
mesh
Number of Iterations #105
0 1 2 3 4 5
FreeEnergy(arb)
-800
-600
-400
-200
0
200
400
600
128 mesh points per side
256 mesh points per side

6. Problem
1b:
No-­‐flux
BCs
50,000
time
units,
21
minutes
of
wall
time
for
16
processors
500,000
time
steps,
128x128
elements,
~16,000
DOF
Number of Iterations #106
0 1 2 3 4 5
FreeEnergy(arb)
-1200
-1000
-800
-600
-400
-200
0
200
400
600

7. Problem
1c:
T-­‐shaped
domain
50,000
time
units,
3minutes
of
wall
time
for
16
processors
500,000
time
steps,
T-­‐bars
are
14
elements
across,
2115
DOF
Number of Iterations #10
6
0 1 2 3 4 5
FreeEnergy(arb)
-100
-80
-60
-40
-20
0
20
40
60

8. Problem
1d:
Spinodal Decomposition
on
a
Surface
Manifold
(FENICS)
10,000
time
units,
216
minutes
of
wall
time
for
a
single
core
10,000
time
steps,
~41,000
DOF
(medium
mesh)

10. 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)

11. Problem
1
Recap
and
Impressions
§ In
our
experience
this
made
for
a
good
test
problem
− Spinodal decomposition
yields
well
understood
dynamics
● In
a
Hackathonsetting
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

12. Problem
2:
At
least
the
energy
is
decreasing
Number of Iterations #10
5
0 0.5 1 1.5 2 2.5 3 3.5 4FreeEnergy(arb)
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
1,000
time
units,
4h30m
of
wall
time
for
16
processors
1,000,000
time
steps,
128x128
elements,
200,000
DOF
Here,
we’re
less
confident
in
our
solution
Max
concentration
stabilizes
at
1.6,
rather
than
the
expected
0.95

13. Problem
2:
Order
parameter
evolution

14. 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