Funded and Unfunded Research
Projects in Scientific Computing
in our group
Scientific Computing Research at
UMD
• One of the strongest groups anywhere
• Distributed across
– (Applied) Mathematics
– Computer Science
– Departments (Physics, Engineering, Meteorology,
etc.)
– Institutes (ESSIC, UMIACS, IPST, etc.)
• Because of the breadth students often are
unaware of opportunities
• Research can be more applied (more interesting
in elucidating the “science”) or more
fundamental (exploring analysis, or algorithms)
Applied Mathematics and Scientific
Compuing
Faculty in Computer Science doing Scientific Computing:
• Ramani Duraiswami
• Dianne O’Leary
• Howard Elman
• Pete Stewart
Faculty in Mathematics doing Scientific Computing:
• John Osborn
• Eitan Tadmor
• Ricardo Nochetto
• Jian-Guo Liu
• Tobias von Petersdorff
• Eitan Tadmor
• Radu Balan
• Doron Levy
Other Faculty doing Scientific Computing:
• Nail A. Gumerov, UMIACS
• Bill Dorland, Physics/IREAP/CSCAMM
•….
Recommendation
• Explore research opportunities that are of
interest to you from all areas
• Several considerations
– Interests, advisor, funding
• My goal today: bring to your attention some
projects that need graduate students
• Briefly talk about these, and invite you to meet
me/others to discuss problems further if you are
interested
Research Areas
• Fast algorithms for acoustical and
electromagnetic scattering
• Computational Machine Learning
• Parallel Algorithms on Graphical
Processors
• Plasma Simulation
– Tokamak
– Space Plasma Simulation
• Numerical Weather Prediction
Gamer Power
Sony Playstation 3
Microsoft X-Box 360
2.18 teraflops
1.04 teraflops
<$500
Difficult to program
<$500
Difficult to program
GEFORCE 8880 GTX
Multicore Intel box with 3 GPUs
in Slots
~ 1 Teraflop for < 3000
(shown with 1 GPU)
Why are GPU’s fast?
• Multicore “stream” processing
• Successor to SIMD  SPMD
– Single program multiple data
– Stream of data, same short “kernel” program runs on them
• Extremely large market sensitive to price. Wants performance
– Gaming and to a smaller extent personal computing
• Standardization
– GPU programs execute well defined tasks (“shaders”) which
are in OpenGL and DirectX => special purpose architecture
• Piggyback on the Moore’s law revolution
– Faster memory and smaller die sizes
– A generation behind Intel/AMD (e.g., 90 nm vs. 45 nm), so they
are likely to continue to speed up in the short term
• Distinguish GPU’s from other similar technologies
– Coprocessors, FPGAs, etc.
– Purpose built for smaller markets --- so likely more expensive
New parallel revolution?
• Been there, done that
• Architecture based parallel machines
– Connection Machines, BBN Butterfly, CDC, SGI, …
– After a few years became impressive doorstops and
landfill material at national labs
• So, current trend is towards cluster computing
– Use COTS processors
• But GPU is architecture based
• However it is commodity
– 3 million NVIDIA G80 series with 128 processors sold
– Total connection machine market for CM5: 700 machines
General Purpose GPU Computing
• Use GPUs to do something other than graphics/games
• First Wave of GPGPU (till early 2006)
– Approach: Fool GPU in to thinking it is doing graphics by converting
general purpose calculation in to graphics metaphores
– Several successes and impressive speedups
– But programming GPUs was more curiosity
– Scientists found it hard to learn and properly use OpenGL, CG
• Second generation of GPGPU (2006-present)
• Lead by graphics board manufacturers who see a new
market
– AMD/ATI & NVIDIA have a graphics duopoly
• ATI’s GPGPU effort is called “Close-to-the-metal”
– Provides “assembly type instructions to be captured by a 3rd
party compiler
• NVIDIA’s “Compute Unified Device Architecture”
Programming on the GPU
• GPU organized as 16 groups of multiprocessors (8
relatively slow 100 MHz processors) with small
amount of own memory and access to common
shared memory
• Factor of 100s difference in speed as one goes up
the memory hierarchy
• To achieve gains problems must fit the SPMD
paradigm and manage memory
• Caveat: single precision only till Q4-2007
• Fortunately many practically important tasks do map
well and we are working on converting others
– Image and Audio Processing
– Some types of linear algebra cores
– Many machine learning algorithms
Local memory
~50kB
GPU shared
memory
~1GB
• Research issues:
– Identifying important tasks and mapping them to the
architecture
– Making it convenient for programmers to call GPU code from
host code
Host memory
~2-32 GB
Simulating Acoustic and
Electromagnetic scattering
• Research in simulating acoustic scattering
is related to human hearing
amplitude
amplitude
frequency
frequency
• Human perception of a source location is aided by our
modification of the received sound depending on direction of
sound
HRTFs are very individual


Humans have different sizes and
shapes
Ear shapes are very individual as well


Even today ear shots are part of


Mugshots & INS photographs
If ear shapes and body sizes are
different



Before fingerprints, Alphonse Bertillon
used a system of identification of criminals
that included 11 measurements of the ear
Properties of scattered wave are different
HRTFs will be very individual
Need individual HRTFs for
creating virtual audio
HRTFs can be computed
Wave equation:
Fourier Transform from
Time to Frequency Domain
Helmholtz equation:
2
2
2

2 p '

p
'

p
'

p'  2 2
2

c


 c  p'
 2
2
2
2 
t
y
z 
 x

P( x, y, z, w)   p' ( x, y, z, t )eit dt

2 P  k 2 P  0
Boundary conditions:
Sound-hard boundaries:
Sound-soft boundaries:
Impedance conditions:
Sommerfeld radiation
condition
P
0
n
P0
P
 i P  g
n
 P

lim r 
 ikP   0
r 
 r

Idea for rapidly obtaining individual HRTFs



Discretize equation using surface meshes of individuals
Obtain these via computer vision
Basis for an NSF ITR award in 2000
Boundary Integral Formulations:
Discretization
Papers

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
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Nail A. Gumerov and Ramani Duraiswami. Fast Multipole
Methods for the Helmholtz Equation in Three Dimensions. The
Elsevier Electromagnetism Series. Elsevier Science, Amsterdam,
2005. ISBN: 0080443710.
Nail A. Gumerov and Ramani Duraiswami. Fast multipole methods
on graphical processors. Submitted, 2008.
Nail A. Gumerov and Ramani Duraiswami. Fast radial basis
function interpolation via preconditioned Krylov iteration. SIAM
Journal on Scientific Computing, 29:1876–1899, 2007.
Zhenyu Zhang, Isaak D. Mayergoyz, Nail A. Gumerov†, and
Ramani Duraiswami. Numerical analysis of plasmon resonances in
nanoparticles based on fast multipole method. IEEE Transactions
on Magnetics, 43:1465–1468, April 2007.
Ramani Duraiswami, Dmitry N. Zotkin, and Nail A. Gumerov†.
Fast evaluation of the room transfer function using multipole
expansion. IEEE Transactions on Speech and Audio Processing,
15:565– 576, 2007.
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Nail A. Gumerov and Ramani Duraiswami. A scalar potential formulation and
translation theory for the time-harmonic Maxwell equations. Journal of
Computational Physics, 225:206–236, 2007.
Nail A. Gumerov and Ramani Duraiswami. Fast multipole method for the
biharmonic equation in three dimensions. Journal of Computational Physics,
215(1):363–383, Jun 2006.
Nail A. Gumerov and Ramani Duraiswami. Computation of scattering from
clusters of spheres using the fast multipole method. The Journal of the
Acoustical Society of America, 117(4):1744–1761, 2005.
Nail A. Gumerov and Ramani Duraiswami. Recursions for the computation of
multipole translation and rotation coefficients for the 3-D Helmholtz equation.
SIAM Journal on Scientific Computing, 25(4):1344–1381, 2003.
Nail A. Gumerov and Ramani Duraiswami. Computation of scattering from N
spheres using multipole reexpansion. The Journal of the Acoustical Society of
America, 112(6):2688–2701, 2002.
CURRENT RESEARCH ISSUES
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Creation of good meshes for scattering problems
Use of graphical processors
Redesigning algorithms for data-parallel and cluster
architectures
High frequency acoustic/electromagnetic simulations
Funding: several proposals applied for
Numerical Weather/Disease
Forecasting
• University is a center for “Earth Systems”
Science
• National Oceanic and Atmospheric
Administration is moving on campus
• ESSIC, Geography, Applied Math,
Computer Science, Physics, etc. all have
faculty working on such problems
• Climate Change is one of the biggest
challenges facing humanity
Goals
• Develop/Use local models of climate
• Predict behavior of associated quantities
– Cholera, other disease pathogens
– Sea Nettles,
• Predict extreme events and their effects
– Storm Surges, Cyclones, etc
Approach
• Develop validate models
• Models are a collection of
– equations (Navier-Stokes, Energy
conservation)
– Historical data (observations)
– current observations
• Forecasts and Predictions need to
assimilate data
• Model Uncertainty in the predictions
Faculty team
• Raghu Murtugudde, ESSIC and
Meteorology
• Rita Colwell, CBCB and UMIACS
• Ramani Duraiswami, CS
• Nail Gumerov, UMIACS
Goals
• Use GPUs to aid forecasting
• Employ methods for modeling uncertainty
that are being developed in machine
learning for problems in weather (and vice
versa)
– Gaussian process regression
– Ensemble Kalman filters
• Funding: available for the next 18 months,
and likely in the future
Simulating plasma
• Fusion: limitless cheap and clean power
• Problem: very hard to confine and
compress hydrogen and cause it to fuse
and release energy
• Lots of fluid mechanical instabilities
• Confine plasma
• Big business in Physics around the world
• Problem whose solution is always 50
years in the future :^)
Simulations + Experiments
• UMD again is a leader
• Numerical simulation folks include Prof. Bill
Dorland
• Collaborations between his group and mine
• Fast and accurate simulation of plasma
• Use GPUs/FMM/ GPU clusters
• Funding: several proposals pending, and some
funding available over the next 4 years.
Space plasmas
• Work with Prof. Papadapoulos of Astronomy
and Prof. Gumerov
• Space is almost entirely plasma
• Satellites float in space in this plasma
• If plasma is disrupted so is communication, GPS
• Large five year project to simulate what happens
when there is a disturbance in plasma (e.g. via
natural means or nuclear explosions)
• Physics and Numerical simulation