computational challenges in electromagnetics prof. n. balakrishnan associate director indian...
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Computational ChallengesIn
Electromagnetics
Computational ChallengesIn
Electromagnetics
Prof. N. BalakrishnanAssociate Director
Indian Institute of ScienceBangalore
Prof. N. BalakrishnanAssociate Director
Indian Institute of ScienceBangalore
ATIP 1st HPC in India Workshop 2009Supercomputing 2009
Portland, OR, USANovember 20th, 2009
ATIP 1st HPC in India Workshop 2009Supercomputing 2009
Portland, OR, USANovember 20th, 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
DifferentialEquation
FD
FEMFEM
FDTD
AsymptoticTechniques
GO
GTD
UTD
PO
PTD
SBR- Frequency domain- Time domain
IntegralEquation
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 GHzTotal 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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Discrimination Discrimination
ofof
Radar Targets Radar Targets
with with
Minor VariationsMinor 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 OutputConvolution Output
Aircraft with missile: Te = 26 lmAircraft with missile: Te = 26 lm
Aircraft with missile: Te = 30 lmAircraft with missile: Te = 30 lm
Convolution output
in late-time
is minimum
for the basic aircraft
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Radar Cross Section EstimationAnd
Control
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Method of Moments(MOM)
Hotspot Analysis
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Discritisation Details forRepresentative Aircraft
Element type: TriangleNo. 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 metersAircraft 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
deg122deg142
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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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No Frequency
(GHZ)
Number of Nodes
Number of Edges
Number of Faces
Number of unknowns
Number of processors
used
Time
1 0.25 3417 10245 6831 10245 512 3 min.
2 1 21653 64953 43304 64953 512 1.1 hrs
3 2 52230 156683 104456 156683 1024 5.5 hrs
4 2.5 77379 232131 154754 232131 1024 13.5 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- MLFMMAlternative- MLFMM
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Frequency Number of unknowns
Method Number of processors
Clock rate
(MHz)
Total CPU Time (hrs)
250 MHz 14682 MLFMM 8 2883.503 0.028
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Frequency Number of unknowns
Method Number of processors
Clock rate
(MHz)
Total CPU Time (hrs)
1 GHz 55260 MLFMM 8 2833.503 0.593
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Frequency Number of unknowns
Method Number of processors
Clock rate
(MHz)
Total CPU Time (hrs)
2 GHz 223440 MLFMM 8 2833.503 2.623
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Frequency Number of unknowns
Method Number of processors
Clock rate
(MHz)
Total CPU Time (hrs)
2.5 GHz 345771 MLFMM 8 2833.503 5.097
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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
object Size Freq. Type No of unknowns Method
NASA Flamme
880λ 440 GHz Metallic 203,664,320 MLFMM
Polarization Θ
Illumination 90˚
No of Iteration 154
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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object Size Freq. Type No of unknowns Method
Aircraft carrier
128λ 150 MHz Metallic 415,316 MoM
Length 256m
Width 66m
Height 47m
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 GHzHow 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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