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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 Applied Mathematics and Scientific CompuingCompuing
Faculty in Mathematics doing Scientific Computing:• John Osborn• Ricardo Nochetto• Tobias von Petersdorff• Radu Balan
• Eitan Tadmor• Jian-Guo Liu• Eitan Tadmor• Doron Levy
Other Faculty doing Scientific Computing:
• Nail A. Gumerov, UMIACS• Bill Dorland, Physics/IREAP/CSCAMM•….
Faculty in Computer Science doing Scientific Computing:• Ramani Duraiswami• Howard Elman
• Dianne O’Leary• Pete Stewart
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
Sony Playstation 3
2.18 teraflops <$500
Difficult to program
Microsoft X-Box 360
1.04 teraflops <$500
Difficult to program
Gamer Power
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
• Research issues: – Identifying important tasks and mapping them to the
architecture– Making it convenient for programmers to call GPU code from
host code
Local memory~50kB
GPU shared memory
~1GB
Host memory~2-32 GB
Simulating Acoustic and Electromagnetic scattering
• Research in simulating acoustic scattering is related to human hearing
frequency
amplitude
frequency
amplitude
• 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
Before fingerprints, Alphonse Bertillon used a system of identification of criminals that included 11 measurements of the ear
Even today ear shots are part of Mugshots & INS photographs
If ear shapes and body sizes are different Properties of scattered wave are different HRTFs will be very individual
Need individual HRTFs for creating virtual audio
HRTFs can be computed
0P
n
2 2 0P k P
Sound-hard boundaries:
Sound-soft boundaries: 0P
Impedance conditions:P
i P gn
Sommerfeld radiation condition lim 0
r
Pr ikP
r
Helmholtz equation:
Boundary conditions:
2 2 2 22 2 2
2 2 2 2
' ' ' ''
p p p pc c p
t x y z
Wave equation:
Fourier Transform from Time to Frequency Domain
dtetzyxpwzyxP ti
),,,('),,,(
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
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.
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
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