376632-3-T E. Topsakal M. Carr J. L. Volakis CADRISA User Manual Sikorsky Aircraft Corp. 1201 South Ave Bridgeport, CT 06604 August 99 376632-3-T = RL-2522

CADRISA User Manual Table of Contents Table of Contents..............................................................................................2 Introduction....................................................................................................3 Compilation....................................................................................................3 Execution.......................................................................................................3 Interpreting Results............................................................................................6 Example Run...................................................................................................6 References......................................................................................................8 APPENDIX A - Cadrisa File Format Specification........................................................9 APPENDIX B - Problem Geometries...................................................................... 10 Case 0 - PEC Boundary................................................................................... 10 Case 1 - Bulk Dielectric................................................................................... 10 Case 2 - PEC/Dielectric................................................................................... 10 Case 3 - Dielectric Coated PEC.......................................................................... 10 Case 4 - Dielectric Boundary............................................................................. 10 Case 5 - Resistive Boundary............................................................................. 10 Case 6 -Impedance Boundary.........................................................................11. Case 7 - CABC (Circuit Analog Boundary)..........................................................11. Case 8 - Dielectric-Dielectric-PEC-PEC..............................................................11. Case 9 - Dielectric-Resistive-PEC-PEC...............................................................11.I Case 10 - Dielectric-CABC-PEC-PEC...............................................................11..I Case 11I - Dielectric-Dielectric-PEC-Impedance......................................................11.I Case 12 - Dielectric-Resistive-PEC-Impedance........................................................ 12 Case 13 - Dielectric-CABC-PEC-Impedance........................................................... 12 Case 14 - Dielectric-PEC-.PEC........................................................................... 12 Case 15 - Dielectric-PEC-Impedance................................................................... 13 Case 16 - Resistive-PEC-PEC........................................................................... 13 Case 15 - Dielectric-PEC-PEC........................................................................... 13 Case 16 - Resistive-PEC-PEC........................................................................... 13 Case 17 - Resistive-PEC-Impedance.................................................................... 13 Case 18 - CABC-PEC-PEC.............................................................................. 14 Case 19 - CABC-PEC-Impedance....................................................................... 14 Case 20 - PEC-Impedance................................................................................ 14 Case 21 - Impedance-PEC................................................................................ 14 APPENDIX C - Sphere Benchmark Test..................................................................1 5 Sphere Geometry Input File.............................................................................. 15 Incident Angle File........................................................................................ 16 MoM Results............................................................................................... 19 AIM Results................................................................................................. 22 Page 2 of 24

CADRISA User Manual Introduction CADRISA is a sophisticated code employing the very latest numerical methods. It is numerically intensive and in some situations can take a long time to run when dealing with complex material geometries. CADRISA models electromagnetic scattering from PEC, resistive, impedance, circuit-analog, and dielectric media. CADRISA can also simulate geometries made up of multiple layers of these mixed media. This manual will guide the user through compilation, execution, and data interpretation in such a way that CADRISA can be used most effectively. We will provide an example run, complete with results that can be used to verify the correct operation of the code. Compilation CADRISA is written in object-oriented, highly streamlined Fortran90 source code. A Fortran90 compiler is required to build the program. CADRISA relies heavily on the latest numerical techniques, including BLAS for matrix manipulation, LAPACK for LU decomposition subroutines, and FFTPACK for FFT transforms and inverse transforms. At this time, CADRISA implements its own iterative solvers. Because numerical optimization of the routines above varies from platform to platform, we suggest that the user obtain libraries of these functions for their specific operating system. Most hardware manufacturers such as Intel, Sun, and SGI supply such numerical libraries free of charge. Check with your supplier for the availability of these libraries. If a generic implementation is desired for compatibility between various machines, platform-independent versions of these libraries can be found at www.netlib.org. However, CADRISA's performance may suffer greatly without the benefit of optimized numerical libraries. In summary, the following items are required to compile CADRISA: * CADRISA FORTRAN 90 source files (*.f90) * FORTRAN 90 compiler * BLAS numerical routines library * LAPACK numerical routines library * FFTPACK numerical routines library Execution Before execution, the user must specify the incident angles of the plane wave excitation as well as the scattered-field look angles. These angles are all contained in the file INCIDENT.TXT, which must be located in the directory from which the program is executed. The first line of the INCIDENT.TXT file must contain the number of look angles. Each following line contains an angle specification for a single look angle. The syntax of the entire file is as follows, where the coordinate system is given in the diagram below: <N = number of look angles> <Oil> <(il> <al> <Osl> <(sl> <'i2> <'i2> <a2> <Os2> <(s2> <OiN> <(iN> <aN> <9sN> <(sN> Page 3 of 24

CADRISA User Manual z Z XA Coordinate System Reference Please refer to the example below for a sample INCIDENT.TXT file. When CADRISA is executed, it will prompt for a series of parameters. These parameters are explained below. Geometry Input Filename This is the input file containing the geometry under test. The file must adhere to Tricode File Format 2 specifications, which are given in Appendix A RCS Output Filename This is the name of the output file that will be produced.. Please see the section "Interpreting Results" below for more details. Problem Type As of this writing CADRISA can solve 22 RCS simulation problems. The problem descriptions are given in Appendix B. Certain problem types may prompt for additional data concerning the geometry. The problem types are: 0 PEC 1 Bulk Dielectric 2 PEC/Dielectric 3 Dielectric Coated PEC 4 Dielectric 5 Resistive 6 Impedance 7 Circuit Analog 8 Dielectric-Dielectric-PEC-PEC 9 Dielectric-Resistive-PEC-PEC 10 Dielectric-CABC-PEC-PEC 11 Dielectric-Dielectric-PEC-Impedance 12 Dielectric-Resistive-PEC-Impedance 13 Dielectric-CABC-PEC-Impedance 14 Dielectric-PEC-PEC 15 Dielectric-PEC-Impedance 16 Resistive-PEC-PEC 17 Resistive-PEC-Impedance 18 CABC-PEC-PEC 19 CABC-PEC-Impedance 20 PEC-Impedance 21 Impedance-PEC Page 4 of 24

CADRISA User Manual Solver Type Enter 0 to use a LU-factorization solver. This is a direct solver and can only be used with Method of Moments (MoM) simulations. For smaller problems, the LU solver offers the best performance. However, its complexity increases by O(N3)-therefore, larger problems will require fast methods such as the Adaptive Integral Method (AIM). Enter 1 to use the conjugate-gradient-squared (CGS) method. This iterative method has an irregular convergence pattern, but often converges much faster than the benchmark BiCG iterative solver. If the AIM approach is to be employed, the user must select the iterative solver. The stopping residual sets the point at which the iterative solver considers its answer converged. For coarse results, a value of 0.03 is usually sufficient for fairly accurate co-pol terms. For more accurate cross-pol terms, use a value of 0.001. The maximum iterations sets the maximum number of iterations that the iterative solver will perform before aborting the procedure and proceeding to the following look angle. During iteration, the solver remembers the "best guess" based on the residual from each iteration. This best guess is then returned in the event that the number of iterations exceeds the maximum. The number of iterations actually required to converge to an answer varies depending on the condition of the Zmatrix, which is dictated by the geometry of the problem. The iterative solver implemented in CADRISA uses the converged answer from each look angle as the initial guess for the following look angle. This often reduces the number of iterations for the new look angle dramatically. It is well known that CGS may diverge when the initial guess is very close to the true answer-however, we have not observed this behavior in our tests and feel that the reduction of iterations outweighs the potential for divergence. Preconditioner Type Preconditioners can cause an iterative solver to converge more quickly and with a smoother convergence pattern. They may also help systems to converge to a smaller residual if very accurate results are required. A good preconditioning matrix [P] is measured by how closely [P] approximates [Z]-1. Generally speaking, the closer [P] approximates [Z]-', the longer [P] will take to generate. Therefore, the time required to generate [P] must be weighed against the time saved by performing fewer iterations. Entering 0 for this option uses no preconditioner. Mathematically speaking, [P] = [1] where [1] is the identity matrix. Entering I uses a diagonal preconditioner-a sparse matrix consisting of the inverses of the entries along the main diagonal of the Z-matrix. This type of preconditioner can be generated very quickly, but usually has little effect on convergence. The preconditioning matrix is then specified by Pm - {1/Zmn m=n m ~ n Entering 2 uses an approximate inverse preconditioner. This preconditioner often greatly accelerates convergence, but can require a large amount of time to generate. The preconditioning matrix approximates the inverse of the Z-matrix row-wise in a least-squares sense. Please refer to [2] for more information on this preconditioner. The minimizing iterations setting determines the number of iterations per row to generate the preconditioner. A good starting value for this parameter is 3. Larger numbers of minimizing iterations will consume large amounts of CPU time. The % of AIPC to keep setting determines the threshold for numerical dropping. This setting directly affects the sparsity of the AIPC matrix. A good starting value is 99-most terms are very small and even at this setting the AIPC will be less than 5% full. Page 5 of 24

CADRISA User Manual Solution Methods Entering 0 specifies the Moment Method (MoM). The complexity of this method is 0(N3), but for small problems it may be much faster than AIM due to its usage of the direct LUfactorization solver. Entering 1 specifies the Adaptive Integral Method (AIM). This method complexity is 0(N log N), but for small problems its iterative solver may take some time to converge. It is best used for larger geometries or monostatic simulations where the incident angle doesn't change. You must choose an iterative method for your solver in order to use AIM. The AIM grid spacing determines the spacing between the grid points used to surround the geometry. At this time, CADRISA uses the same spacing for the x-, y-, and z-spacing between points. A good starting value for this parameter is 0.05. The AIM threshold determines the boundary where two basis functions are considered to be "far" from each other. Any basis functions inside this threshold will be included in the Znear calculation, so making this parameter too small will increase fill time dramatically. A smaller value for this parameter will have little effect on the code since many terms will be dropped during the Znear correction phase. A good starting value for this parameter is 0.2. Interpreting Results The output file contains the description of the scattered far-field at each look angle. Each line of the output file contains the incident field angles, the scattered field angles, and the real and imaginary components of the vector field. The syntax of the file is as follows: <Oil> <.1> <al> <s 1> <sl1> <Re(Eo1)> <Im(Eol)> <Re(E41)> <Im(E4l)> <0i2> <0-2> <a2> <0s2> <(02> <Re(Eo2)> <Im(Eo2)> <Re(E42)> <Im(E42)> <ON> <AN> <aN> <OsN> <sN> <Re(EoN)> <Im(E oN)> <Re(EON)> <Im(EfN)> Therefore, the vector E-field can be expressed from the above data as follows: En = O((Re(En)) + j(Im(En)))+ ((Re(En)) + j(Im(E n))) Example Run The CADRISA distribution package contains the files necessary to reproduce a sphere test geometry. The files involved are: * Sphere_Geometry.txt: The CADRISA-format file describing the sphere geometry * Incident.txt: The incident angle file containing the bistatic view angles * Sphere-OutputMoM.txt: The output file produced by running an LU solution * Sphere-OutputAIM.txt: The output file produced by running an AIM solution * Sphere.pdf: A summary of results and visualization of the sphere geometry The calculated RCS patterns should appear as follows: Page 6 of 24

CADRISA User Manual _.2X PEC Sphere - EFIE -5~ — ~"- jcc~~ — —! --- —---- ------------ ----- 0 -10 C --- ——: --- ——: — ----— I --- —-—: --- ------ -- -----— I --- —-- x AIM-# -15 0 20 40 60 80 100 120 140 160 180 e, (e=4=),=o) To reproduce these results, use the following inputs to the program: MoM Calculation CADRISA - Multiple Surface, Multiple BC MoM Solution with AIM Capability Written by Michael Carr, University of Michigan, Radiation Laboratory Erdem Topsakal, University of Michigan, Radiation Laboratory John Volakis, University of Michigan, Radiation Laboratory Geometry input filename? Sphere_ - Geometry.txt RCS output filename? SphereOutput MoM.txt 42 nodes requiring 0 Kbytes 80 faces requiring 4 Kbytes 240 edges requiring 718 Kbytes 120 unknowns in surface 1 Problem geometries: 0 - PEC 1 - Bulk Dielectric 2 - PEC/Dielectric 3 - Coated PEC 4 - Dielectric Problem type? 0 CFIE alpha? 1 Solver types: 0 - Direct LU Decomposition (MoM only) 1 - Conjugate Gradient Squared (CGS) Solver type? 0 AIM Calculation CADRISA - Multiple Surface, Multiple BC MoM Solution with AIM Capability Written by Michael Carr, University of Michigan, Radiation Laboratory Erdem Topsakal, University of Michigan, Radiation Laboratory John Volakis, University of Michigan, Radiation Laboratory Geometry input filename? SphereGeometry.txt RCS output filename? Sphere_Output AIM.txt RCS output filename? SphereOutputAIM.txt Page 7 of 24

CADRISA User Manual 42 nodes requiring 0 KBytes 80 faces requiring 4 KBytes 240 edges requiring 718 Kbytes 120 unknowns in surface 1 Problem geometries: 0 - PEC 1 - Bulk Dielectric 2 - PEC/Dielectric 3 - Coated PEC 4 - Dielectric Problem type? 0 CFIE alpha? 1 Solver types: 0 - Direct LU Decomposition (MoM only) 1 - Conjugate Gradient Squared (CGS) Solver type? 1 Stopping residual? le-3 Maximum iterations? 1000 Preconditioner types: 0 - No preconditioner 1 - Diagonal preconditioner (DPC) 2 - Approximate inverse preconditioner (AIPC) Preconditioner? 0 Solution methods: 0 - Method of Moments (MoM) 1 - Adaptive Integral Method (AIM) Solution method? 1 AIM threshold (lambda)?.2 AIM grid spacing?.05 References [1] E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale electromagnetics scattering and radiation problems," Radio Science, v 31, no 5, pp 1225-1251, Sept-Oct 1996. [2] Saad, Yousef. Iterative Methods for Sparse Linear Systems. 1996 PWS Publishing Co, Boston, MA. Page 8 of 24

CADRISA User Manual APPENDIX A - Cadrisa File Format Specification 1. The first line is a format identifier, "TFF2" for Tricode File Format version 2 2. The next line holds the number of nodes followed on the same same line by the number of triangles. 3. The list of nodes comes next, in X, Y, Z format where the units are wavelengths. 4. The list of triangles comes next, in N1, N2, N3, S format, where S is an integer identifying the surface. NOTE 1: The order in which the nodes are listed is very important. The surface normal is determined as such: (n2-n1)x(n3-n2) (n2 - n,)x (n3 -n NOTE 2: The surface numbering does not necessarily start with 1 and is not required to be numbered sequentially. <N=number of nodes> <T=number of triangles> <node #1 x coordinate> <node #1 y coordinate> <node #1 z coordinate> <node #2 x coordinate> <node #2 y coordinate> <node #2 z coordinate> <node #N x coordinate> <node #N y coordinate> <node #N z coordinate> <triangle #1 edgel> <triangle #1 edge2> <triangle #1 edge3> <triangle #1 surface> <triangle #2 edgel> <triangle #2 edge2> <triangle #2 edge3> <triangle #2 surface> <triangle #T nodel> <triangle #T node2> <triangle #T node3> <triangle #T surface> EXAMPLE: TFF2 N1 E9 N2 E11 N3 9 8 1.0 0.0 0.0 0.0 0.5 0.0 0.0 TI T3 1.0 0.0 0.0 0.0 0.5 0.0 E13 E5 0.5 0.5 0.0 E3 E14 1.0 0.5 0.0 0.o 1.0 0.o T2 T4 0.5 1.0 0.0 1.0 1.0 0.0 1 5 2 1 0.5 N4 E N5 E2 1 4 5 1 2 6 3 1 2 5 6 1 T5 T7 4 8 5 1 4 7 8 1 EE7 E8 5 9 6 1 E15 EE16 5 8 9 1 This example is for surface normals T6 T8 pointing out of the paper, with only _ \ one surface present. 0.0 N7 E10 N8 E12 N9 0.0 0.5 1.0 Page 9 of 24

CADRISA User Manual APPENDIX B - Problem Geometries This version of the code has the capability of solving 22 different types of problems. In the future the code will be generalized to treat any combination of the surfaces without restrictions to these combinations. At this time the user is permitted to only enter a case number from the list below. Case 0 - PEC Boundary Case 1 - Bulk Dielectric Eo,to SI S2 Case 2 - PEC/Dielectric S1(DIELECTRIC) \S4(PEC) S3(PEC) Case 3 - Dielectric Coated PEC %,Po sl Case 4 - Dielectric Boundary Case 5 - Resistive Boundary Subcase: 0 - Resistive Sheet in a free space Subcase: 1 - Sheet saparetes different mediums Page 10 of 24

CADRISA User Manual Case 6 - Impedance Boundary Case 7 - CABC (Circuit Analog Boundary) Case 8 - Dielectric-Dielectric-PEC-PEC go, S1(DIELECTRIC) / S3(PEC) S2(DIELECTRIC) Case 9 - Dielectric-Resistive-PEC-PEC E/ S1(DIELECTRIC) / S3(PEC) S2(RESISTIVE CARD) Case 10 - Dielectric-CABC-PEC-PEC co S1(DIELECTRIC)/ S3(PEC) S2(CA-BOUNDARY) Case 11 - Dielectric-Dielectric-PEC-Impedance S4(PEC) S4(PEC) S4(PEC) S4(PEC) Page 11 of 24

CADRISA User Manual S1(DIELECTRIC) S3(PEC) S2(DIELECTRIC) Case 12 - Dielectric-Resistive-PEC-Impedance Sl(DIELECTRIC) S3(PEC) S2(RESISTIVE CARD) Case 13 - Dielectric-CABC-PEC-Impedance Sl(DIELECTRIC) S3(PEC) S2(CA- BOUNDARY) Case 14 - Dielectric-PEC-PEC Sl(DIELECTRIC) S3(PEC) S4(IMPEDANCE) S4(IMPEDANCE) S4(IMPEDANCE) S4(PEC) I Page 12 of 24

CADRISA User Manual Case 15 - Dielectric-PEC-Impedance S1(DIELECTRIC) S3(F Case 16 - Resistive-PEC-PEC S2(RESISTVE) S3( Case 15 - Dielectric-PEC-PEC S2(DIELECTRIC) S3( Case 16 - Resistive-PEC-PEC S2(RESIS nVE) S3( Case 17 - Resistive-PEC-Impedance S4(IMPEDANCE) PEC) S4(PEC) PEC) S4(PEC) PEC) S4(PEC) PEC) Page 13 of 24

CADRISA User Manual S2(RESISTIVE) Case 18 - CABC-PEC-PEC S2(CA-BOUNDARY) Case 19 - CABC-PEC-Impedance \S44(IMPEDANCE) S3(PEC) -— V S4(PEC) S3(PEC) S2(CA-BOUNDARY) Case 20 - PEC-Impedance S4(IMPEDANCE) S3(PEC) S3(PEC) Case 21 - Impedance-PEC S4(IMPEDANCE) S3(IMPEDANCE) S4(PEC) Page 14 of 24

CADRISA User Manual APPENDIX C - Sphere Benchmark Test Sphere Geometry Input File TFF2 42 o 11755700E+00 0. 19021100E+00 o0.19021100E+00 0. 11755700E+00 0. 95105700E-01 o0.15388399E+00 o0.15388399E+00 o0.95105700E-01 o0.36327101E-01 0.587784 98E-01 o0.58778498E-01 o0.36327101E-01 -0. 36327101E-01 -0. 58778498E-01 -0. 58778498E-01 -0. 36327101E-01 -0. 95105700E-01 -'0.153883 99E+00 -0. 15388399E+00 -0. 95105700E-01 -0. 11755700E+00 -0. 19021100E+00 -0. 19021100E+00 -0. 11755700E+00 -0. 95105603E-01 -0. 15388399E~00 -0. 15388399E+00 -0. 95105603E-01 -0. 36327101E-01 -0. 58778599E-01 -0. 58778498E-01 -0. 36327101E-01 0. 36327101E-01 0. 58778599E-01 0. 58778599E-01 0. 36327101E-01 0. 95105700E-01 0. 15388399E+00 o.15388399E+00 0. 95105700E-01 0D.OOOOOOOOE+00 0. OOOOOOOOE+00 2 6 1 6 3 7 2 7 4 8 3 8 6 10 5 10 7 11 6 11 8 12 7 12 10 14 9 14 11 15 10 15 12 16 11 16 14 18 13 18 15 19 14 19 8 0 0. OOOOOOOOE+00 0.OOOOOOOOE+00 0. OOOOOOOOE+00 0. OOOOOOOOE+00 0. 69098003E-01 0. 11180300E+00 0.1118030OOE+00 0. 69098003E-01 0.1118030OOE+00 0. 18090200E+00 0. 18090200E+00 0. 11180300E+00 0.1118030OOE+00 0. 18090200E+00 0. 18090200E+00 0. 11180300E+00 0. 69098003E-01 0.1118030OOE+00 0.1118030OOE+00 0.69098003E-01 0. OOOOOOOOE+00 0. OOOOOOOOE~00 0. OOOOOOOOE+00 0. OOOOOOOOE+00 -0. 69098003E-01 -0. 11180300E+00 -0. 1118030OOE+00 -0. 69098003E-01 -0. 11180300E+00 -0. 18090200E+00 -0. 18090200E+00 -0. 11180300E+00 -0. 1118030OOE+00 -0. 18090200E+00 -0. 18090200E+00 -0. 11180300E+00 -0. 69098003E-01 -0. 11180300E+00 -0. 1118030OOE+00 -0. 69098003E-01 0. OOOOOOOOE+00 0. OOOOOOOOE+00 0. 16180301E+00 0. 61803401E-01 -0. 61803401E-01 -0.1618030O1E+00 0. 16180301E+00 0. 61803401E-01 -0.61803401E-01 -0.1618030OlE+00 0.1618030O1E+00 0. 61803401E-01 -0. 61803401E-01 -0. 16180301E+00 0. 16180301E+00 0. 61803401E-01 -0. 61803401E-01 -0. 16180301E+00 0.1618030OlE+00 0.6180340OlE-01 -0.618 03401E-01 -0. 16180301E+00 0.1618030O1E+00 0. 61803401E-01 -0.6180340OlE-01 -0.1618030O1E+00 0. 16180301E+00 0. 61803401E-01 -0. 61803401E-01 -0. 16180301E+00 0.1618030O1E+00 0. 61803401E-01 -0. 61803401E-01 -0. 16180301E+00 0.1618030O1E+00 0.6180340OlE-01 -0. 61803401E-01 -0. 16180301E+00 0.1618030O1E+00 0. 61803401E-01 -0. 61803401E-01 -0. 1618030O1E+00 0. 20000000E+00 -0. 20000000E+00 1 5 2 6 3 7 5 9 6 10 7 11 9 13 10 14 11 15 13 17 14 18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Page 15 of 24

CADRISA User Manual 16 15 18 17 19 18 20 19 22 21 23 22 24 23 26 25 27 26 28 27 30 29 31 30 32 31 34 33 35 34 36 35 38 37 39 38 40 39 1 5 9 13 17 21 25 29 33 37 42 42 42 42 42 42 42 42 42 42 20 20 22 22 23 23 24 24 26 26 27 27 28 28 30 30 31 31 32 32 34 34 35 35 36 36 38 38 39 39 40 40 2 2 3 3 4 4 5 9 13 17 21 25 29 33 37 1 8 12 16 20 24 28 32 36 40 4 15 19 17 21 18 22 19 23 21 25 22 26 23 27 25 29 26 30 27 31 29 33 30 34 31 35 33 37 34 38 35 39 37 1 38 2 39 3 41 41 41 41 41 41 41 41 41 41 4 8 12 16 20 24 28 32 36 40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Incident Angle File 182 00000 00020 00040 00060 00080 00 0 10 0 00 0 12 0 00 0 14 0 Page 16 of 24

CADRISA User Manual o 0 0 16 0 o0 0018 0 o0 0020 0 0 0 022 0 0 0 024 0 0 0 026 0 0 002 280 0 0030 00 0 003 320 0 0 034 0 0 0 036 0 0 003 380 0 0040 00 0 0 042 0 0 0 044 0 0 0 046 0 0 004 480 0 0 050 0 0 00 52 0 0 0 054 0 0 0 056 0 0 00 58 0 0 0 060 0 0 0 062 0 0 0 064 0 0 0 066 0 0 0 068 0 0 00 70 0 0 0 072 0 0 0 074 0 0 0 076 0 0 0 078 0 0 0 080 0 0 0 082 0 0 0 084 0 0 0 086 0 0 0 088 0 0 0 090 0 0 0 092 0 0 0 094 0 0 0 096 0 0 0 098 0 000100 0 000102 0 000104 0 000106 0 000108 0 000110 0 000112 0 000114 0 000116 0 000118 0 000120 0 000122 0 000124 0 000126 0 000128 0 000130 0 000132 0 000134 0 000136 0 000138 0 000140 0 000142 0 000144 0 000146 0 000.148 0 000150 0 000152 0 000154 0 000156 0 Page 17 of 24

CADRISA User Manual 0 0 0 158 0 000 160 0 0 00 162 0 0 00 164 0 0 00 166 0 0 00 168 0 000 170 0 000172 0 000174 0 000 176 0 000 178 0 0 00 180 0 0 0 90 0 0 0 0 90 2 0 0 0 90 4 0 0 0 90 6 0 0 0 90 8 0 0 0 90 10 0 0 0 90 12 0 0 0 90 14 0 0 0 90 16 0 0 0 90 18 0 0 0 90 20 0 0 0 90 22 0 0 0 90 24 0 0 0 90 26 0 0 0 90 28 0 0 0 90 30 0 0 0 90 32 0 0 0 90 34 0 0 0 90 36 0 0 0 90 38 0 0 0 90 40 0 0 0 90 42 0 0 0 90 44 0 0 0 90 46 0 0 0 90 48 0 0 0 90 50 0 0 0 90 52 0 0 0 90 54 0 0 0 90 56 0 0 0 90 58 0 0 0 90 60 0 0 0 90 62 0 0 0 90 64 0 0 0 90 66 0 0 0 90 68 0 0 0 90 70 0 0 0 90 72 0 0 0 90 74 0 0 0 90 76 0 0 0 90 78 0 0 0 90 80 0 00 90 82 0 0 90 84 0 0 0 90 86 0 0 0 90 88 0 0 0 90 90 0 0 0 90 92 0 0 0 90 94 0 0 0 90 96 0 0 0 90 98 0 0 0 90 100 0 0 0 90 102 0 0 0 90 104 0 0 0 90 106 0 0 090 108 0 0 0 90 110 0 0 0 90 112 0 0 0 90 114 0 0 0 90 116 0 Page 18 of 24

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CADRISA User Manual 0. 0 0. 0 0. 0 0. 0 0. 0 90. 0 174.0 0. 0 90. 0 176. 0 0.0 90.0 178. 0 0. 0 90.0 18 0. 0 AIM Results 0. 0 0.0 0.0 0.0 0. 0 0.0 0.0 0. 0 0. 0 0.0 0.0 0.0 0. 0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0.0 0. 0 0. 0 0.0 0.0 0. 0 0.0 0.0 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 0. 0 0.0 0. 0 0.0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0.0 0.0 0. 0 0.0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 0.0 0. 0 0. 0 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0.0 0. 0 0.0 0. 0 0.0 0.0 0.0 0. 0 0.0 0.0 0. 0 0. 0 0.0 0.0 0.0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 0. 0 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