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Unformatted text preview: • Boundary value problem
• Finding the maximum
• The nbody problem Case Studies Algorithm Design Case Studies Ice water Rod Insulation Boundary Value Problem Foster’s Design Methodology CS6643 F'11 Lec05 2 • Identify communication pattern between primitive tasks
• Each interior primitive task has three incoming and three
outgoing channels Communication Partitioning • One data item per grid point
• Associate one primitive task with each grid point
• Twodimensional domain (data) decomposition Finite Difference Approximation Rod Cools as Time Progresses • p – number of processors
• O – message latency
• Parallel execution time n(F ªm/pº+2O) Parallel Execution Time Agglomeration Agglomeration and Mapping Reduction F – time to update element
m – number of elements
n – number of iterations (time steps)
Sequential execution time: m n F –
–
–
– Add
Multiply
And, Or
Maximum, Minimum • Given associative operator
• a0 a1 a2 … an1
• Examples •
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•
• Sequential execution time Binomial Trees Parallel Reduction Evolution Subgraph of hypercube Parallel Reduction Evolution Parallel Reduction Evolution 1 3 3 7 Finding Global Sum 6 10 4 4 2 9 1 8 6 2 5 3 0 8 2 4 Finding Global Sum 4 1 17 5 7 2 4 8 Finding Global Sum 8 6 Finding Global Sum sum sum sum sum Agglomeration 25 Binomial Tree Finding Global Sum • Total time: (ªn/pº 1)F + ªlg pº (O+ F) – Each step takes O+ F time • Local reduction time: (ªn/pº 1)F
• ªlg pº treebased reduction steps Parallel Execution Time Agglomeration CS 6643 F’11 Lec07 24 •
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•
• Gather Partitioning – Get positions of all other particles
– Compute new position, velocity Domain (data) partitioning
Assume one task per particle (body)
Task has particle’s position, velocity vector
Iteration The nbody Problem The nbody Problem E ) ( p 1)O n( p 1)
Ep
log p §
n( p 1)
2i1 n ·
¸ Ologp
¨O
¦ ¨ Ep ¸
Ep
i 1©
¹ Hypercube ( p 1)(O n/ p Communication Time Hypercube for Allgather Complete graph Complete Graph for Allgather Allgather ...
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This note was uploaded on 01/29/2012 for the course CS 6643 taught by Professor Staff during the Fall '08 term at The University of Texas at San Antonio San Antonio.
 Fall '08
 STAFF

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