The Improved 3D Matlab_based FDFD Model and Its Application Qiuzhao Dong(NU), Carey Rapapport(NU) (contact: 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 ) Abstract 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. 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. Significance - 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. 3D FDFD Modeling  3D matlab-based FDFD (finite difference frequency domain) method : -- Based on the general Maxwell’s equations, the wave equation is where  =  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.  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. R1 R2 Value Added to CenSSIS Fundamental Science Fundamental Science Validating TestBEDs Validating TestBEDs L1 L2 L3 R3 S1S4S5 S3 S2 Bio-MedEnviro-Civil Improvement 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. Application Simulation for Sphere Targets I. Simulation for Sphere Targets Geometry and Applied parameters: The TNT scatterer is buried 5 cm under the surface with the shape of sphere: x 2 +y 2 +z 2 =(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; 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.. II.Simulation of elliptic targets Geometry and Applying parameters: The TNT scatterer is buried 5cm under the surface with the shape of ellipse: 25x 2 +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; Conclusion: 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. References [1 ] J. Berenger, “A Perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys., vol. 114, pp ,Oct,1994; [2] E. Marengo, C. Rappaport and E. Miller, “Optimum PML ABC Conductivity Profile in FDFD”,in review IEEE Transactions on Magnetics, 35, , (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 ,Sept [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): ,Nov The magnitude and phase distribution of Ex components at plane x=0,y=0 and z=0 from FDFD and SAMM The magnitude and phase distribution of Ey at plane x=0,y=0 and z=0 from FDFD and SAMM The magnitude and phase distribution of Ez at plane x=0, y=0 and z=0 from FDFD and SAMM The magnitude and phase distribution of Ex components at plane x=0,y=0 and z=0 from FDFD and SAMM The magnitude and phase distribution of Ey components at plane x=0,y=0 and z=0 from FDFD and SAMM