Transcript Generating Matlab-based 3D FDFD Computational Modeling by

The Improved 3D Matlab_based FDFD Model and Its Application
Qiuzhao Dong(NU), Carey Rapapport(NU) (contact: [email protected],[email protected])
This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging Systems, under the Engineering
Research Centers Program of the National Science Foundation (Award Number EEC-9986821)
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Abstract
Improvement
The forward 3D Matlab-based FDFD model is easily manipulated and powerfully
handles the complicated lossy, dispersive media by discretizing the Maxwell’s equations.
This modified Matlab-based FDFD model rids the high computational burden of the
traditional Fortran-based FDFD model (which is ~60 times as the new-version model) and
reduced the large memory requirement and the computational rate of the previous
preconditioning version Matlab-based FDFD model with the same grid size (the new
version needs less than half memory and 1/10 computational time as the previous). All this
computations are running on the Compaq Alpha supercomputer.
Several cases have been investigated and compared to other methods. The electrical
scattering fields of the spherical and elliptic TNT-material targets are simulated and
compared to SAMM solution.
The new modified model reduces the computational time (CPU time) to ~1/10 of the previous one.
For the grid size with 97x97x85 along x y and z axes and 161 total iterative number, the CPU time
of the previous model is around 15 hours, the modified one is only about 1.5 hours. The operative
memory decreases to less half (3/7) of the previous model, for example, with the restart=30 and the
same grid size as above, the memory is ~5 G for the modified one, but 12G for the old one.
Note: restart is the value of the inner iterative number in GMRES method, it is roughly linear to the
necessary memory and slightly relative to the CPU time.
Bio-Med
L3
Enviro-Civil
S2 S3
S1
S4
S5
Validating
L2 TestBEDs
Geometry and Applying parameters:
The TNT scatterer is buried 5cm under the surface with the shape of ellipse:
25x2 +25y 2+49z 2=(35/2cm)2;
The operating frequency is 960MHz;
Bosnian soil with relative dielectric constant =9.19(1+i0.014);
97x97x85 grid points along x, y & z axis;
The normally incident plane wave with x polarization;
Application
I.
Value Added to CenSSIS
II. Simulation of elliptic targets
Simulation for Sphere Targets
Geometry and Applied parameters:
The TNT scatterer is buried 5 cm under the surface with the shape of sphere: x2+y2+z2=(5cm)2;
The operating frequency is 960MHz;
Bosnian soil with relative dielectric constant =9.19(1+i0.014);
97x97x85 grid points along x, y & z axis;
The normally incident plane wave with x polarization;
R2
L1 Fundamental
Science
R1
R3
The magnitude and phase distribution of Ex components at plane x=0 ,y=0
and z=0 from FDFD and SAMM
State of the Art and Significance
•
State of the Art and Challenges
-Current SOA: 2D, scalar Helmholtz frequency domain modeling.; 3D, time-consuming Fortrand-based
FDFD modeling;
-Challenges: Computations in layered 3D inhomogeneous, dispersive media and high frequencies in
reasonable memory and computational time.
•
The magnitude and phase distribution of Ex components at plane x=0 ,y=0
and z=0 from FDFD and SAMM
Significance
The magnitude and phase distribution of Ey components at plane x=0 ,y=0
and z=0 from FDFD and SAMM
- Understanding the importance of optimizing the structure of Matrix and parallelizing in solving the
matrix equation
-3D Matlab-based FDFD method: Valuable tool for forward modeling in the frequency domain.
Conclusion:
3D FDFD Modeling
The magnitude and phase distribution of Ey at plane x=0,y=0 and z=0
from FDFD and SAMM
 3D matlab-based FDFD (finite difference frequency domain) method :
-- Based on the general Maxwell’s equations, the wave equation is



2
2
 E  (  E )  (   i ) E  0

The restart=20 and the total iterative number is 241; the memory is ~3.7 G, and the CPU time is 123
minutes or so; the comparison between FDFD and SAMM is acceptable.
In a word, the CPU time and memory used in the modified FDFD model are much less than these of the
previous model. It is practicable in some sort.
Future Plans
• Optimize the algorithm, parallelize the Matlab code to further reduce the CPU time, make it more
applicable;
• Apply the complicated geometry in the code, such as rough surface and simulate more realcases.
K k 2
where = 0.
-- Equipped with the popular PML (perfectly matched layer) ABC (absorbing boundary
conditions.
-- Employing the Yee cell geometry as the grid structure of finite difference method.
References
[1] J. Berenger, “A Perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys., vol. 114, pp.185-
The magnitude and phase distribution of Ez at plane x=0, y=0 and z=0
from FDFD and SAMM
 The applying mathematical method
The method finally leads to solving the problem of matrix equation: Ax=B; where A is the
coefficient matrix, B is the source column matrix and x is the unknown. A is a very large sparse
matrix. Therefore the problem is suitable for the Krylove subspace iterative methods. One of
them, GMRES (Generalized minimum residue method), is employed after optimalizing the
structure of matrix A by multiplying the assisted matrix and doing some permutations.
Analysis:
The comparison between modified FDFD method and SAMM method agree very well. In the modified
FDFD model, the restart=20, the total iterative number is 241, the CPU time is about 123 minutes (it is
around 20 hours previously) , the relative residue goes down to 0.07 (the previous one is around 0.12), the
operative memory is 3.7G (the previous is around 10G). Therefore, in this case, the modified FDFD method
is indeed improved considering the CPU time, the memory even the performance from the previous model..
200,Oct,1994;
[2] E. Marengo, C. Rappaport and E. Miller, “Optimum PML ABC Conductivity Profile in FDFD”,in review IEEE Transactions on
Magnetics, 35,1506-1509, (1999)
[3] S. Winton and C. Rappaport,”Specifying PML Conductivities by Considering Numerical Reflection Dependencies”, IEEE
Transactions on Antenna and Propogation, september,2000
[4] S. Winton and C. Rappaport,”Pfrofiling the Perfectly Matched Layer to Improve Large Angle Performance”, IEEE Transactions
on Antenna and Propogation, Vol 48,No. 7,July,2000
[5] C. Rappaport, M. Kilmer, and Eric Miller, “Accuracy considerations in using the PML ABC with FDFD Helmholtz equation
computation,” Int. J. Numer. Modeling, Vol 13, pp. 471-482,Sept. 2001.
[6] Morgenthaler A.W, Rappaport C.M, “Scattering from lossy dielectric objects buried beneath randomly rough ground:
validating the semi-analytic mode matching algorithm with 2-D FDFD “, IEEE Transactions on Geoscience and Remote Sensing, :
Volume: 39 page(s): 2421 - 2428 ,Nov. 2001