Transcript Erosion parallel project final slides (Powerpoint)

Landscape Erosion
Kirsten Meeker
[email protected]
Outline
Plan
Progress
Verification
Performance
Plan
Analyze sequential code
Select parallel tools and partitioning
Convert in stages, preserving functioning of whole
simulation
Stochastic PDE’s, individual results are a function of
random parameters including numerical noise
Success of results are measured by statistical
parameters
“Clean” maintainable, portable code
Improve performance, currently hours to days
Decisions
Maintainability:
Use MPI for portability on clusters
Investigate solver libraries: PETSc
Modify functions to use only needed input parameters,
to try to eliminate use of global Params struct
Performance:
Use row-wise partitioning
Consider writing data to disk from each processor then
reassembling result off-line
Try to eliminate multiple passes over grid
Progress
Converted main and water surface routines
Created a set of utility functions:
scatter, gather
comm_to_local, local_to_comm
print_grid
Verification of Initial Elevation
17.47
parallel
sequential
17.468
17.466
17.464
17.462
17.46
17.458
17.456
0
50
100
150
200
250
300
350
400
450
500
Verification of Initial Water
Verification of Final Elevation
Performance Vs. Grid Size
7
6
Time (s)
5
4
3
2
1
0
50000
150000 250000 350000 450000
Grid Size
Performance Vs. Number of
Processors
10
9
8
Time (s)
7
6
5
4
3
2
1
0
2
4
6
8
Number of Processors
10
Conclusions
Too much unnecessary data messaging
Cell structure has 17 values, only 3 needed!
Reduce message size and cache hits
Water algorithm is fine-grained
4 passes over grid means 4 border exchanges
Landscape erosion is a SOC
www.cs.ucsb/~kmeeker/erosion.html
Landscape Erosion
Kirsten Meeker
[email protected]
Outline
Model
Behavior
Conclusions
Model Equations
Ill-Posed
Results vary widely with initial conditions
Noise driven
Initial surface randomly perturbed
Substrate and rainfall constant
Shocks develop in water flow
Singularities in sediment flow: waterfalls
or rapids
Dynamic Behavior
Large Fourier components (smallest spatial
scale) grow fastest, all modes grow
exponentially
Nonlinearities saturate, producing colored
noise
Invariant statistical measures
Width function
Statistically self-similar if there exists a scaling
c = 0.5 during channel formation
c = 0.7 mature landscape
Agrees with data from Ethiopia, Somalia, Saudi
Arabia (badland conditions)
Conclusion
Bridge between stochastic and deterministic
modeling
physically-based PDE model
random walk models
Channel formation is a Brownian process
Mature landscape is diffusion driven by
quenched noise - driven interface in a random
media
Combination is analogous to directed
percolation networks