Funded and Unfunded Research Projects in Scientific Computingin our group

Scientific Computing Research at UMDOne of the strongest groups anywhereDistributed across (Applied) Mathematics Computer ScienceDepartments (Physics, Engineering, Meteorology, etc.)Institutes (ESSIC, UMIACS, IPST, etc.)Because of the breadth students often are unaware of opportunitiesResearch can be more applied (more interesting in elucidating the science) or more fundamental (exploring analysis, or algorithms)

Applied Mathematics and Scientific CompuingFaculty in Mathematics doing Scientific Computing: John Osborn Ricardo Nochetto Tobias von Petersdorff Radu Balan Eitan Tadmor Jian-Guo Liu Eitan Tadmor Doron LevyOther 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 OLeary Pete Stewart

RecommendationExplore research opportunities that are of interest to you from all areasSeveral considerationsInterests, advisor, funding

My goal today: bring to your attention some projects that need graduate studentsBriefly talk about these, and invite you to meet me/others to discuss problems further if you are interested

Research AreasFast algorithms for acoustical and electromagnetic scatteringComputational Machine Learning Parallel Algorithms on Graphical ProcessorsPlasma SimulationTokamakSpace Plasma SimulationNumerical Weather Prediction

Gamer PowerSony Playstation 32.18 teraflops

GEFORCE 8880 GTXMulticore Intel box with 3 GPUs in Slots~ 1 Teraflop for < 3000(shown with 1 GPU)

Why are GPUs fast?Multicore stream processingSuccessor to SIMD SPMDSingle program multiple dataStream of data, same short kernel program runs on themExtremely large market sensitive to price. Wants performance Gaming and to a smaller extent personal computingStandardizationGPU programs execute well defined tasks (shaders) which are in OpenGL and DirectX => special purpose architecturePiggyback on the Moores law revolutionFaster memory and smaller die sizesA generation behind Intel/AMD (e.g., 90 nm vs. 45 nm), so they are likely to continue to speed up in the short termDistinguish GPUs from other similar technologiesCoprocessors, FPGAs, etc.Purpose built for smaller markets --- so likely more expensive

New parallel revolution?Been there, done thatArchitecture based parallel machinesConnection Machines, BBN Butterfly, CDC, SGI, After a few years became impressive doorstops and landfill material at national labsSo, current trend is towards cluster computingUse COTS processors But GPU is architecture basedHowever it is commodity3 million NVIDIA G80 series with 128 processors soldTotal connection machine market for CM5: 700 machines

General Purpose GPU ComputingUse GPUs to do something other than graphics/gamesFirst 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, CGSecond generation of GPGPU (2006-present)Lead by graphics board manufacturers who see a new marketAMD/ATI & NVIDIA have a graphics duopolyATIs GPGPU effort is called Close-to-the-metalProvides assembly type instructions to be captured by a 3rd party compilerNVIDIAs Compute Unified Device Architecture

Programming on the GPUGPU organized as 16 groups of multiprocessors (8 relatively slow 100 MHz processors) with small amount of own memory and access to common shared memoryFactor of 100s difference in speed as one goes up the memory hierarchyTo achieve gains problems must fit the SPMD paradigm and manage memoryCaveat: single precision only till Q4-2007Fortunately many practically important tasks do map well and we are working on converting othersImage and Audio ProcessingSome types of linear algebra coresMany machine learning algorithmsResearch issues: Identifying important tasks and mapping them to the architectureMaking it convenient for programmers to call GPU code from host codeLocal memory~50kBGPU shared memory ~1GBHost memory ~2-32 GB

Simulating Acoustic and Electromagnetic scatteringResearch in simulating acoustic scattering is related to human hearingHuman perception of a source location is aided by our modification of the received sound depending on direction of sound

HRTFs are very individualHumans have different sizes and shapesEar shapes are very individual as wellBefore 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 photographsIf ear shapes and body sizes are differentProperties of scattered wave are differentHRTFs will be very individualNeed individual HRTFs for creating virtual audio

HRTFs can be computedSound-hard boundaries:Sound-soft boundaries:Impedance conditions:Sommerfeld radiation conditionHelmholtz equation:Boundary conditions:Wave equation:Fourier Transform from Time to Frequency Domain

Idea for rapidly obtaining individual HRTFsDiscretize equation using surface meshes of individualsObtain these via computer visionBasis for an NSF ITR award in 2000Boundary Integral Formulations:Discretization

PapersNail 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, 29:18761899, 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, 43:14651468, 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, 225:206236, 2007.Nail A. Gumerov and Ramani Duraiswami. Fast multipole method for the biharmonic equation in three dimensions. Journal of Computational Physics, 215(1):363383, 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):17441761, 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):13441381, 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):26882701, 2002.

CURRENT RESEARCH ISSUESCreation of good meshes for scattering problemsUse of graphical processorsRedesigning algorithms for data-parallel and cluster architecturesHigh frequency acoustic/electromagnetic simulationsFunding: several proposals applied for

Numerical Weather/Disease ForecastingUniversity is a center for Earth Systems ScienceNational Oceanic and Atmospheric Administration is moving on campusESSIC, Geography, Applied Math, Computer Science, Physics, etc. all have faculty working on such problemsClimate Change is one of the biggest challenges facing humanity

GoalsDevelop/Use local models of climatePredict behavior of associated quantitiesCholera, other disease pathogensSea Nettles,Predict extreme events and their effectsStorm Surges, Cyclones, etc

ApproachDevelop validate modelsModels are a collection of equations (Navier-Stokes, Energy conservation)Historical data (observations) current observationsForecasts and Predictions need to assimilate dataModel Uncertainty in the predictions

Faculty teamRaghu Murtugudde, ESSIC and MeteorologyRita Colwell, CBCB and UMIACS Ramani Duraiswami, CSNail Gumerov, UMIACS

GoalsUse GPUs to aid forecastingEmploy methods for modeling uncertainty that are being developed in machine learning for problems in weather (and vice versa)Gaussian process regressionEnsemble Kalman filtersFunding: available for the next 18 months, and likely in the future

Simulating plasmaFusion: limitless cheap and clean powerProblem: very hard to confine and compress hydrogen and cause it to fuse and release energyLots of fluid mechanical instabilitiesConfine plasmaBig business in Physics around the worldProblem whose solution is always 50 years in the future :^)

Simulations + ExperimentsUMD again is a leaderNumerical simulation folks include Prof. Bill DorlandCollaborations between his group and mineFast and accurate simulation of plasmaUse GPUs/FMM/ GPU clustersFunding: several proposals pending, and some funding available over the next 4 years.

Space plasmasWork with Prof. Papadapoulos of Astronomy and Prof. GumerovSpace is almost entirely plasmaSatellites float in space in this plasmaIf plasma is disrupted so is communication, GPSLarge 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