Spiral Interaction SPINT Analysis of changing the excitability of medium with C2

1
Spiral Interaction (SPINT)Analysis of changing
the excitability of medium with C2

• Presented by Group 2
• Juan Sandoval
• Kalpana Pal
• Hitesh Patel
• Pedro Perez
• CMPT 495 / 680 Parallel Architectures and
  AlgorithmsProf. Roman Zaritski

April 30, 2007
2
Outline

• Introduction
• Algorithm
• Implementation of the Galaxy MPI Cluster
• Snapshots
• Scalability/Speed-up Curves
• Snapshot Results Summary
• Summary Conclusions

3
To Do

• Pace C2 periodically (sinusoidally) around 0.75
  value.
• Use different frequencies and amplitudes to
  obtain different behaviors of spiral waves.
• Report any interesting changes in spiral wave
  behavior.

4
Introduction

• This project uses a Spiral Interaction (SPINT)
  code as the basis.
• Experiment by changing the excitability of the
  medium C2 (currently set to 0.75).
• To make the simulations faster, we reduced the
  domain size currently set to 1000x2000 to
  500x1000.
• A simple FitzHugh-Nagumo model is used to
  simulate the excitability of the medium.
• A parallel algorithm is used to distribute the
  task among nodes of Galaxy cluster because of
  large size of the domain, and the number of time
  steps.

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Introduction (cont.)

• The program is run on 15 CPUs.
• The program uses a domain slicing approach to
  distribute tasks among 14 CPU slaves.
• The grid is divided into 14 slices corresponding
  to 14 slave CPUs and one master.
• The Graphical window contains a grid of size N x
  M, NM100
• Each slave CPU computes values of the functions u
  and v for each grid point inside its slice, for
  every time step (dt .1), and for a total
  simulation time of DT 10000.

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Algorithm of the Problem

• The rectangular domain is sliced into rectangular
  strips.
• Each available processor takes care of one such
  strip
• For each time step, each processor updates
  unknown functions on the corresponding strip.
• The neighboring processors exchange the common
  boundary information using message passing (MPI)
• The entire rectangular domain gets updated.
• As result, when the program is running, the
  spiral shows the unique results at any given time
  on entire rectangular domain.

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Algorithm of the Problem (cont.)

• The spint.cc program was modified by using the
  below line of code in the main loop of the
  program.
• C2 0.75 A sin (w DiscrTime)
• a (C1C2)E1/C2
• E2 (C2aC3)/ (C2C3)
• This modification lead a change of C2 value
  periodically (sinusoidally) around the value of
  0.75 making it more excitable
• We experimented with amplitude (A) and frequency
  (wDiscrTime) value for several experiments.

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Algorithm of the Problem (cont.)

• By changing the code, and using the different
  values of A and w, we were able to get
  Excitability between the lowest value of C2
  0.60 and highest to C2. 0.90.
• That means that by having a higher amplitude
  value we will obtain a higher increase of waves
  on the spiral
• The same for the increase of frequency, by making
  the value of (w) higher, this will make the
  frequency (wt) values change more quickly with
  respect to time.

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Implementation on the Galaxy MPI Cluster

• Implementation in C
• 15 CPU Pentium based Cluster (located in RI 109)
• Red Hat Linux 6.2 Operating System
• MPI library (parallel communication)
• OpenGL library (data visualization)
• Pthread library (the graphical display functions)
• Xmanager Program (The graphical interface display)

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Implementation on the Galaxy MPI Cluster (cont.)

• 1000 x 2000 Rectangular Grid
• Cells on the edges of the grid are always
  unexcited (u 0, v 0)
• Using Vertical Domain Slicing to divide workload
  between the 15 CPUs
• Using MPI Send and Receive Functions to exchange
  cell values on borders between each chunk

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Task Distribution of each CPU (Slave)
CPU-1 . . . . . . . . .. . . CPU-14

• Master node splits the work among 14 CPUs
• 1 CPU acts as Master (has copy of whole array)
• 14 CPUs act as Slaves (handle parts of the array)
• Each Slave node sends screen updates to the
  Master node

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Classic Initial Conditions

• Grid Size 1000x2000
• DT 10000
• C2 0.75
• CPUs 15

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Classic Initial Spiral
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SNAPSHOTS
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Grid Size 500x1000, A0.18 W0.04, C2 0.60 at
DT10000
1.
4.
5.
2.
3.
6.
Figure 1
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Grid Size 500x1000, A0.12 W0.04, C2 0.65 at
DT10000
3.
1.
2.
4.
Figure 2
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Grid Size 500x1000, A0.16 W0.07, C2 0.60 at
DT10000
1.
3.
2.
4.
Figure 3
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Scalability/Speed-up
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Scalability/Speed-up

• Grid Size 500x1000
• DT 10000
• 2 np 15

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Scalability/Speed-up (contd)
Domain Size 500 x 1000
Graph 1
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Scalability/Speed-up (contd)
DT 10000
Graph 2
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Speed-up Results

• Speed-up was optimal at 15 CPUs
• Speed-up increases as DT increases for same
  number of CPUs (Graph 1)
• Speed-up is optimal at largest domain 1000x2000.
  (Graph 2)
• Speed-up tend to decrease for smallest domain
  after 9 CPUs e.g. 100x200 (Graph 2)

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Snapshot Results Analysis
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1. A 0.19 w 0.04
4. A 0.13 w 0.04
2. A 0.18 w 0.04
5. A 0.12 w 0.04
3. A 0.15 w 0.04
6. A 0.1 w 0.04
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1.
A 0.19, w 0.04 0.56 lt C2 lt 0.94
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2.
A 0.18, w 0.04 0.57 lt C2 lt 0.93
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3.
A 0.15, w 0.04 0.60 lt C2 lt 0.90
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4.
A 0.13, w 0.04 0.62 lt C2 lt0.88
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5.
A 0.12, w 0.04 0.63 lt C2 lt 0.87
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6.
A 0.1, w 0.04 0.65 lt C2 lt 0.85
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Summary Conclusions

• Classic spiral found for 0.65ltC2lt0.85
• Fully excited domain, but no spirals found for
  0.60ltC2lt0.90
• No excitation found for 0.56ltC2lt0.94
• Highest speed-up of 6.5 is observed for domain
  size 1000x2000 on 15 CPUs
• Speed-up increases with increase in DT value for
  same number of CPUs
• Speed-up decreases for smallest domain size
  100x200 after 9 CPUs

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Responsibility matrix for the contribution of
group members
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Thank You