Funded and Unfunded Research Projects in Scientific Computing in our group.

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