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Computational Challenges In Electromagnetics Prof. N. Balakrishnan Associate Director Indian Institute of Science Bangalore ATIP 1 st HPC in India Workshop 2009 Supercomputing 2009 Portland, OR, USA November 20 th, 2009

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Traditional View of Computational Electromagnetics It is a technology for the defence It is more about waveguides, Circulators, cables, big antennas, radars The mathematics is tough and hence most of the people in microwaves are “hardcore” tinker/ mechanics You should be a plumber before you take up microwaves CEM are part of your life more than IT now

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CEM becomes quantitative and adds to Grand Challenges in Computer Science Numerical Circuit Simulations- EMI inside a chip EM Modelling Multitude of simulations encompassing PDEs and IEs in Frequency Domain and Time Domain- Birth of Compuatational Electromagnetics- even before CFD and FEM And now the new buzz words- TeraHetrz CEM drives the craving for more compute power

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Computational Techniques in EM Differential Equation FD FEM FDTD Asymptotic Techniques GO GTD UTD PO PTD SBR - Frequency domain - Time domain Integral Equation MOM MOT TLM T-Matrix FMM

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Finite Difference Time Domain (FDTD) 3D discretization Results in Sparse Matrix Gives excellent visualizaion Good for high resolution mapping of the aircraft Absorbing boundary condition Our contribution- PML and Lossy Media

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Discritisation Details for Representative Aircraft Frequency 1 GHz Total No. Layers in X 183 Total No. Layers in Y 379 Total No. Layers in Z 539 No. PML Layers used 18

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Discriminationof Radar Targets Radar Targetswith Minor Variations

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Triangular Patch modelling of an aircraft with stores missile length = 3.2 m A/c with stores modeled as 63 surfaces 48585 triangular patches

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Convolution Output Aircraft with missile: Te = 26 lm Aircraft with missile: Te = 30 lm Convolution output in late-time is minimum for the basic aircraft

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Radar Cross Section Estimation And Control

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Method of Moments (MOM) Hotspot Analysis

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Discritisation Details for Representative Aircraft Element type: Triangle No. of Edges 62202 (Unknowns) Criterion 4 cells /lambda On a 256 node Cluster 3 hrs Today we need to solve 15 million elements-

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RCS Prediction of a Model Aircraft Using Method of Moment (MoM)

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Surface Area of the Aircraft : 47.0135851 sq. meters Wing Span: 10.8 meters Aircraft is along the x-axis: Front angle of the wing w.r.t x-axis : Rear angle of the wing w.r.t x-axis : For all the frequencies the aircraft body is discretized with lambda by 5

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Complexity of Integral Eq. Techniques Surface Area of a typical Aircraft : 40 sq. meters Wing Span: 2.6 m (Approx) At 10 GHz the wave length is 3 cm Cell size at lambda/10 discretization is 0.04 Sq cm Number of cells = 10 Million At 3 GHz = 100,000 The matrix size at 10 GHz is 15M X 15M

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HARDWARE OVERVIEW IBM Bluegene: 4096 2-way SMP nodes (8192 processors) IBM PowerPC processors operating at 700 MHz 1 GB main memory per node with a total of 4 TB for the cluster. Gigabit network with Cisco 6500 Gigabit switch.

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NoFrequency (GHZ) Number of Nodes Number of Edges Number of Faces Number of unknowns Number of processors used Time 10.253417102456831102455123 min. 21216536495343304649535121.1 hrs 325223015668310445615668310245.5 hrs 42.577379232131154754232131102413.5 hrs Table for MoM Technique:

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Alternative Techniques Finite Element Method Physical Theory of Diffraction with Shooting and bouncing of Rays Multilayer Fast Multipole Method

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Machine Specification: Tyrone systems Two physical CPUs with a total of 8 cores. Intel® Xeon® CPU CPU GHz 2.88 Main Memory : 32GB Alternative- MLFMM

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FrequencyNumber of unknowns MethodNumber of processors Clock rate (MHz) Total CPU Time (hrs) 250 MHz14682MLFMM82883.5030.028

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FrequencyNumber of unknowns MethodNumber of processors Clock rate (MHz) Total CPU Time (hrs) 1 GHz55260MLFMM82833.5030.593

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FrequencyNumber of unknowns MethodNumber of processors Clock rate (MHz) Total CPU Time (hrs) 2 GHz223440MLFMM82833.5032.623

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FrequencyNumber of unknowns MethodNumber of processors Clock rate (MHz) Total CPU Time (hrs) 2.5 GHz345771MLFMM82833.5035.097

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Physical Theory of Diffraction with Shooting and Bouncing Rays Asymptotic technique Not rigourous Works well at high frequencies Not computationally expensive

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Discritisation Details Triangular Elements 104948 No. of Nodes 54365 No. of Edges 158318

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Others work – current state of the art

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Indian Institute of Science objectSizeFreq.TypeNo of unknownsMethod NASA Flamme 880λ440 GHzMetallic203,664,320MLFMM Polarization Θ Illumination90˚ No of Iteration154 Total Time(min.)2922 Computing platform Intel Xeon Dunnington processors with 2.40 GHz clock rate. 16 computing nodes, each node has 48 GB of memory and multiple processors, four cores per node (a total of 64 cores)

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Indian Institute of Science

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objectSizeFreq.TypeNo of unknownsMethod Aircraft carrier 128λ150 MHzMetallic415,316MoM Length256m Width66m Height47m Total Time(min.)946 Indian Institute of Science Computing platform One head node, 64 compute nodes and three Infiniband switches, head node has two quad- core Intel Xeon E5450 3.0 GHz processors, 16 GB of RAM, Each compute node has two quad- core Intel XeonE5450 3.0 GHz processors, 16 GB of RAM How do we scale to 10’s of GHz

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CEM: Present days Requirements * Electrically large in size Complex geometrical Shape High Frequency Analysis Multi-layered composite body Tera Hertz thru Human Body

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LAMENT Before an aircraft design is complete, we may need around 1000’s of runs at various frequencies of large complex objects- coated, penetrable etc Rigorous Methods such as MoM are not known to scale to the 15 M variables problems in accuracy nor do we have machines that can be used for computing RCS at > 10 GHz frequencies The Asymptotic Techniques require extensive validation with real measurements For Homeland Security applications and sensing for materials – it is high frequency, layered though small in size Large levels of validation needed More importantly new architectures, new physics and newer techniques are needed

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