fast and efficient rcs computation over a wide frequency band using the universal characteristic...
DESCRIPTION
Fast and Efficient RCS Computation over a Wide Frequency Band Using the Universal Characteristic Basis Functions (UCBFs). Authors: Prof. Raj Mittra* Eugenio Lucente** Prof. Agostino Monorchio** * PennState University (PA) USA ** Pisa University (Pi) Italy. June 2007. - PowerPoint PPT PresentationTRANSCRIPT
Fast and Efficient RCS Computation over Fast and Efficient RCS Computation over a Wide Frequency Band Using the a Wide Frequency Band Using the
Universal Characteristic Basis Functions Universal Characteristic Basis Functions (UCBFs)(UCBFs)
June 2007June 2007
Authors: Prof. Raj Mittra* Eugenio Lucente** Prof. Agostino Monorchio**
* PennState University (PA) USA** Pisa University (Pi) Italy
22/17/17
Conventional MoM LimitationsConventional MoM Limitations
Long execution time Huge memory requirement Inefficient frequency analysis
Electrically large objects
33/17/17
What is the Characteristic Basis Function What is the Characteristic Basis Function Method ( CBFM ) ?Method ( CBFM ) ?
The CBF method is an iteration-free, highly parallelizable MoM
approach based on macro-domain basis functions, namely
Characteristic Basis Function (CBFs), for solving large
multiscale electromagnetic scattering and radiation problems.
44/17/17
How does CBFM work?How does CBFM work?
Step-1: Divide a complex structure into a number of smaller domains (blocks)
Geometry of a PEC plate divided into K blocks
55/17/17
Compute CBFs of the ith block
ith block
Step-2a: Determine characteristic basis functions (CBFs) for each block: - solve “isolated” smaller blocks for a wide range of incident angles- each block is meshed by using RWG or other sub-domain basis- each block is analyzed via MoM technique. This results in a dense impedance matrix
- determination of CBFs can be a time and memory demanding task
Step-2b: Construct a new set of basis functions via the SVD approach.
Step 2
66/17/17
Steps 3 - 4 - 5Steps 3 - 4 - 5 Step-3: Matrix reduction. Determine a reduced matrix, by using the
Galerkin method.
11 11 11 11 12 22 11 1
22 21 11 22 22 22 22 2
1 11 2 22
t t tM MM
t t tM MM
KM KM
t t tMM M MM M MM MM MM
J Z J J Z J J Z JJ Z J J Z J J Z J
Z
J Z J J Z J J Z J
Step-4: Solve the reduced linear system for the unknown weighting complex coefficients of CBFs
Step-5: Far field computation from the current distribution obtained in step-4.
Zred: reduced matrix, size KM by K M : unknown coefficient, b: new RHS J: current on the original geometry Jcbf: CBFs from each block
1
red
Mcbf
i ii
Z b
J J
77/17/17
FeaturesFeaturesSize of the reduced matrix is much smaller than the original MoM matrix of
all structure
Reduced matrix is independent of angle of incidence
Reduced matrix equation can be solved efficiently for many incident
angles. It can be stored in a file and re-used whenever the structure is
analyzed for a new incident angle
For frequency sweep, CBFs must be generated anew for each frequency in the
band on interest. This leads to a huge time requirement. Reduction in the CPU
time is achieved by using universal CBFs rather than regular ones.
The CBF Method is highly parallelizable. Each block can be analyzed
independently. MPI-based parallel version has been developed
88/17/17
Conventional Procedure for Generating CBFs on each block
Step-1: block is meshed by using a sub-domain scheme; typically triangular patch model.
Step-2: block is treated as an independent object illuminated by multiply incident Plane Waves (PWS)
Step-3: MoM technique is applied to the i-th block for obtaining the CBFs matrix equations
Step-4: Reducing number of initial CBFs via SVD by applying a thresholding procedure on Singular Values
Plane Wave Spectrum on Block
Individual Block
if /0
i Max ii
thresholdotherwise
i
99/17/17
Observations on Conventional Procedure for Generating CBFs
Conventional CBFs Generation is time-consuming and memory-demanding task since it requires an LU decomposition for each block whose size can range from 1k to 14k unknowns
CBFs depend upon the frequency
CBFs must be generated anew for each frequency
Inefficient frequency sweep analysis
1010/17/17
In order to eliminate the frequency dependency , a new version of the CBFs is introduced, the so-called Universal CBFs (UCBFs)
UCBFs are generated only once, at the highest frequency, in the band of interest
They are used at lower frequencies, without going trough the time-consuming task of generating them anew
They can be used over 2 : 1 frequency band
Universal CBFs
1111/17/17
Universal Characteristic Basis Functions UCBFs
Physical Understanding of the UCBFs:The following figures show the behaviors of post-SVD CBFs for a 4 strip illuminated by a TE- and TM-polarized plane waves
Fig. 1. Magnitude of CBFs for a flat surface for TM polarization.
Fig. 2. Magnitude of CBFs for a flat surface for TE polarization
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.2
0.4
0 1 2 3 40
0.2
0.4
0 1 2 3 40
0.2
0.4
0 1 2 3 40
0.2
0.4
0 1 2 3 40
0.2
0.4
0 1 2 3 40
0.2
0.4
0 1 2 3 40
0.1
0.2
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
0 1 2 3 40
0.05
0.1
1212/17/17
The UCBFs have all the desired features of wavelets, through in
contrast to the wavelets, they are tailored to the geometry of the
object
The UCBFs, generated at the highest frequency, embody all the
spatial behaviors we would need to capture the corresponding
behaviors of the CBFs at lower frequencies, because they are less
oscillatory as the physics would suggest
Important Observations:
1313/17/17
Numerical Results
Scattering problem by a PEC cone: - Frequency range: 0.6 – 1.0 GHz - UCBFs are generated at 1.0 GHz - RCS is obtained at 0.6 GHz - The cone has been dived into 3 blocks ( 4500 unknowns ) - Total Number of Unknowns 12201
Block I
Block II Block III
1414/17/17
Fig. 3 – Comparison of RCS of a PEC cone for =0° at 0.6GHz. Continuous line:present approach; markers: conventional CBMoM solution.
Fig. 4 – Comparison of RCS of a PEC cone for=90° at 0.6GHz. Continuous line: present approach; markers: conventional CBMoM solution.
Scattering by a PEC Cone ( RCS )
1515/17/17
Scattering problem by a PEC sphere of 2 Radius: - Frequency range: 0.3 – 0.6 GHz - UCBFs are generated at 0.6 GHz - RCS is obtained at 0.3 GHz - The cone has been dived into 4 blocks
Fig. 5 –.Comparison of RCS of a PEC sphere with radius 2 for =0° at 0.3 GHz. Continuous line: present approach; markers: Mie solution.
Fig. 6 – Comparison of RCS of a PEC sphere with radius 2 for =90° at 0.3 GHz. Continuous line: present approach; markers: Mie solution.
Scattering problem by a PEC sphere
1616/17/17
Final Remarks
Fast and efficient frequency sweep
The UCBFs have all the desired features of wavelets
The UCBFs embody all the spatial behaviors at lower frequencies
Reduced computational effort