038954-10-T ANTENNA SIMULATIONS ON SHIPS FOR AMRFS APPLICATIONS Eighth Quarterly Report BAE SYSTEMS 95 Canal Street NCA1-6268 P.O. Box 868 Nashua, NH 030601-0868 Erdem Topsakal Rick Kindt Kubilay Sertel John Volakis September 2001:. sent Coo I~ 4 {;0r /'RL-1004 = RL-1004 1

PROJECT INFORMATION PROJECT TITLE: APPLICATIONS REPORT TITLE: U-M REPORT No.: CONTRACT START DATE: END DATE: DATE: SPONSOR: ANTENNA SIMULATIONS ON SHIPS FOR AMRFS 8th Quarterly Report 038954-10-T October 1999 March 2002 September, 2001 Art E. Dinbergs BAE SYSTEMS Mail Stop, MER 15-1351 PO Box 868 Nashua, NH 030601-0868 Phone: (603) 885-8690 Email: arturs.e.dinbergs@baesystems.com Quarterly Reports James F. Long BAE SYSTEMS MER 15-2516 130 DW Highway, North Merrimack, NH 03054 Phone:(603) 885-4460 Fax:(603) 885-4189 james.f.long@baesystems.com RF5443 John L. Volakis EECS Dept. University of Michigan 1301 Beal Ave Ann Arbor, MI 48109-2122 Phone: (313) 764-0500 FAX: (313) 747-2106 volakis@umich.edu http://www-personal.engin.umich.edu/~volakis/ Quarterly Reports SPONSOR CONTRACT No.: U-M PRINCIPAL INVESTIGATOR: CONTRIBUTORS TO THIS REPORT: Erdem Topsakal, John Volakis 2

TABLE OF CONTENTS TABLE OF CONTENTS............................................3 CHRONOLOGY of EVENTS..........................................4 QUARTERLY PROGRESS..............................................5 DETAILED SCHEDULE (October 1999-December 2000).........................7 DETAILED SCHEDULE (December 2000-December 2001)..........................................9 EXECUTIVE SUMMARY AND PROJECT STATUS...................... 10 AMFIA UPGRADES..................................................11 EXAMPLE LOADED PATCH..................................... 11 SOLVERS AND PRECONDITIONERS....................................... 13 LARGE FINITE LTSA ARRAYS....................................... 20 EXAMPLE 4x3 LTSA AARRAY.......................................20 EXAMPLE 6x6 LTSAA ARRAY..................................22 SHIP TOWER WITH ANTENNAS....................................24 COUPLING STUDIES..................................25 REFERENCES..................................................31 3

CHRONOLOGY of Events (Updated Every Quarter) * October 1998 Proposal Submission * December 1998 Oral Presentation to ONR * August 1999 Began Contract Negotiations * 26 August. 1999 Kickoff meeting at Sanders (attended by Sanders, UM, ONR) * 13 October 1999 Contract Signed between U-M and Sanders * 18 October 1999 MR_TETRA Code and the manual delivery * 15 December 1999 Submission of First Quarterly Report * 19 January 2000 AMRFS Review Meeting I (Lockheed Sanders - Nashua) * 19 January 2000 ARRAY-TETRA Code delivery * 1 April 2000 Submission of Second Quarterly Report * 15 June 2000 Submission of Third Quarterly Report * 27 July 2000 AMRFS Review Meeting II (Lockheed Sanders - Nashua) * 15 September 2000 Submission of Fourth Quarterly Report * 15 December 2000 Submission of Fifth Quarterly Report * 24 January 2001 AMRFS Review Meeting III (BAE Systems - Nashua) * 15 March 2001 Submission of Sixth Quarterly Report * 15 June 2001 Submission of Seventh Quarterly Report * 26 July 2001 AMRFS Review Meeting IV(BAE Systems - Nashua) * 15 September 2001 Submission of Eighth Quarterly Report 4

Quarterly Progress Task 1st 2nd 3rd 4th Implementation of the Periodic Boundary - Conditions in MR-TETRA Fast Spectral Domain Algorithm Applied to MRTETRA (AIM delivered at this time) Finite Arrays / MRTETRA F Implementation and Formulation F77 to F90 code inversion for MR_TETRA_F And Code Optimization Coupling Studies between Elements and Array groups FMM FSS CUR E code initiation 5

Task 5th 6th 7th 8th ARRA Y_TETRA delivery Implementation of the Periodic _ _ __ Boundary Conditions in FSSCURVE - 3rd year) Implementation of Multilevel FMM in FSS-CURVE Coupling Implementation Elements and Array groups Code Optimization and Testing ___ FSS_CURVE delivery 6

DETAILED SCHEDULE (October 1999-December 2000) No. Description Due Date 1 FSSPRISM updated with Tetrahedral FEM(MR_TETRA) Accelerated with Adaptive Integral Method DELIVERED (1st) Code and the Manual 2 a) Periodic Boundary Conditions COMPLETE Implementation and validation DELIVERED (2nd) b) ARRAYTETRA Code COMPLETE c) Finite element approximation ___ d) Convert F77 to F90 (final modifications) ONGOING e) Array coupling formulation COMPLETE Added Task: f) Validations for patch and slot arrays COMPLETE IDEAS/PATRAN/GID interface 3 a) FSS-Curve updated with MLFMM BI and hexahedral COMPLETE FEM b) External field coupling (plane wave) COMPLETE 7

f) LTSA mesh driver COMPLETE e) LTSA and ETSA validations COMPLETE 4 September. 2000 a)Demonstrate fully documented ARRAY_ TETRA DELIVERED Version 2 ( all tasks except coupling to be completed (see manual for the code in this version of the code) information) b) Update FSS-Curve for tetrahedral elements -removed task c) Implement Periodic boundary conditions in FSS_CURVE (added task)-3d year 5 December. 2000 a) Coupling studies and realistic array analysis for FSS_CURVE (AMFIA) ONGOING (edge diffraction effects, element grouping etc) b) Demonstrate fully documented FSS-CURVE DELIVERED First Release 8

DETAILED SCHEDULE (December 2000-December 2001) No. Description Due Date 1 Remaining ARRAY TETRA modifications 1) BCs and Feeds in Patran 2) FSDA 3) Arbitrary external excitations 4) Pins and Loads 4) F90 version ARRAY -TETRA final release (F90) AMFIA Modifications 1) I/O modifications 2) Initial User's Manual 3) MLFMM implementation AMFIA first release (f77) 5) Coupling in a finite array environment COMPLETED ONGOING (July 2001) ONGOING (July 2001) ONGOING (July 2001) ONGOING (December 2001) December 2001 COMPLETED COMPLETED COMPLETED DELIVERED December 2001 - hI 9

Executive Summary and Project Status We continue to be on schedule with all activities and code development tasks. In the forth project review at Sanders (in July 2001), we presented results for finite arrays (patch, slot and TSAs (Tapered Slot Arrays)) using our AMFIA code. We also presented coupling results between antenna array elements and subarray-subarray. We also demonstrated some primary results using our newly developed, highly robust and exact AMFIA code. New code also upgraded from F77 to F90. Besides the coupling studies we demonstrated in the last review, this quarter we also focused on enriching the solver capabilities in AMFIA. A new solver BICGS(L) (Biconjugate gradient solver with respect to parameter L) has been shown to give better convergence characteristics compared to CGS, QMR and BICG for TSAs. An example of microstrip fed TSA antenna is given to demonstrate the performance of different solvers. Unother update in this quarter was the addition of a term to FE-BI formulation which is used when loads and shorting pins presents. A microstrip patch antenna has been choosen [1] to validate the results. During this quarter no changes were made to ARRAY TETRA. The final f77 version of ARRAY TETRA will be delivered to BAE December 20th after remaining modifications (outlined in the last report-Executive Summary and Project Status) are completed. F90 version of ARRAYTETRA will also be available by that time. In the last report, we also gave some coupling results using our newly developed AMFIA code. To summarize, the tasks carried out this quarter are; * Formulation and Implementation (Shorting pins and Loads for AMFIA) * Implementation of a new solver BICG(L) and comparison with the existing solvers for TSA * Coupling between array groups * Large finite arrays For the next quarter our goals are; * Formulation details and implementation outlines of Super Cell * FSDA for ARRAY TETRA with validations * F90 version of ARRAYTETRA 10

AMFIA UPGRADES Several upgrades have been carried out for AMFIA this quarter. We first modified the existing formulation to treat loads and shorting pins in the geometry. Below we provide a microstrip patch antenna example for validation of this implementation. Another modification was the inclusion of a new solver. We show here that the new solver has increased the convergence substantially. To demonstrate the solver, we analyzed a microstrip-fed LTSA and compared convergence with the other solvers EXAMPLE-Microstrip Patch Antenna As an example for the validation of the loads and shorting pins, we consider the microstrip patch antenna displayed in Fig.l. Input impedance characteristics of this antenna were computed from 1-4GHz. Figure 2 shows the input impedance for the antenna when a 50 Q resistor is placed at (x=-2,2 cm, y=-l.5cm). As seen our calculations compare well with measurements [1]. 4 7.5cm 0 5.10cm ---- A --- ------- ------- --- - NNMV m D.0519cm. I I. ------ ~ r:2.17 Figure 1. Microstrip Patch Antenna Geometry 11

25 20 ' r 10 - 2.5 Frequency (GHz) Figure 2. Input Impedance Validation (Real Part) 25 - I I I I 20k - Measurements [1] -- AMFIA - - - - - - - - - - - -- 15 10 l N' E -5 -10' I — I l l 1 l 1 1.5 2 2.5 3 3.5 4 Frequency (GHz) Figure 3. Input Impedance Validation (Imaginary Part) 12

SOLVERS AND PRECONDITIONERS This quarter we also investigated the convergence behavior of different solvers and preconditioners for TSAs. For this purpose 4 solvers and 2 preconditioners were analyzed. Solvers: * QMR (Quasi-Minimal Residual) * CGS (Conjugate Gradient Squared) " BICG (Bi-conjugate Gradient) * BICGS (L) (Bi-conjugate stabilized with respect to L) Preconditioners: * Diagonal * ILU (Incomplete LU) We are not going to go into details of these methods here. References can be found in the literature. (QMR,CGS,BICG and Preconditioners [2],[3], BICGS(L) [4]). To see the performance of those solvers and preconditioners, we consider a microstrip fed LTSA antenna operating at lOGHz (see fig 4). /, 0.078 ' I 3.0 I............................................................. - a) b) Figure 4. a) Microstrip-fed antenna geometry b) Field Distribution 13

Figs. 5&6 show the field patterns for E&H plane cuts from 8-12 GHz. As seen the data are not symmetric due to non-symmetric feeding (see fig.4a). 10 8GHz --- 9GHz 8 ---- - - - --- --- -- - ---- 10GHz 11GHz 8/ ' -.'I — 12GHz 61 - — _ __- - ' -- --- -r __ - 3-j_ _----- ------------ -- --------- --- --— t 6 t- I — - - - -- -r - ~L- - - - - - - - - - - -tZ- - I- - - - - - - - -- -r | I[I I -80 -60 -40 -20 0 20 40 60 80 10 - - - - -2- - - - - - - - - - - --- - I 68 ---------------- - - -- - --------- -, ---'- — 1 --- - -- L — I I I I I I I;I.s 2 — ------- ---------— W --- -8l Figure 5. Radiated Field versus observation angle-(E-plane) 10,....- 8GHz I _ _ _ 9GHz __ 12GHz o - _- - - -,- -- - -/- - - -. - - - - -..- - - - - - -- - - - -I -6 -- --- - -- - -- - ----- - - - - -- - - - - /1,I —/-I -10... ' - - -+-4- 4 —+ --- -- -I- -- A-80 -60 -40 -20 0 20 40 60 80 8 Figure 6. Radiated Field versus observation angle-(H-plane) 14

Figs. 7-9 show the convergence behavior of the solvers used in AMFIA for the microstrip fed LTSA antenna. In Fig. 7 no preconditioners are used. In Figs 8,9 diagonal and ILU preconditioners are used. As seen, BICGSTAB(L) has substantially better convergence behavior compared to the other solvers. It converges almost 10 times faster in all cases compared to the closest converged solver. 8 CGS BICG 7. QMR BICGSTAB(L) (13 1 I 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Iteration Number Figure 7. Solvers convergence behavior (no pc) 15

8 7 6 I I - CGS-diag - BICG-diag QMR-diag B- BICGSTAB(L)-diag l l- - - - - - - - - - 5 L.. c4 -a w 3 (D rlr 3 2 1 oL 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Iteration Number Figure 8. Solvers convergence behavior (Diagonal Preconditioner) 16

8 34 IIII O0 200 400 600 800 1000 1200 1400 1600 Iteration Number Figure 9. Solvers convergence behavior (ILU) 1800 2000 17

Figs. 10-12 show the effect of the "L" parameter for BICGSTAB(L) solver for various precinditioners. In all cases, iteration number decreases with increasing "L" value. However for values of "L" greater than "5", decrease in the iteration number slows down. o LIU -0 (a) 250 300 350 0 50 100 150 200 Iteration Number 400 Figure 10. Effect of L parameter (nopc) 18

1 0.8 L-:30.6 -o en 0.4 0.2 0 0 50 100 150 200 250 300 350 400 Iteration Number Figure 11. Effect of L parameter (Diagonal Preconditioner) 19

1 0.8 co LLJ:3 _0 CD cr 0.6 - n A U. - 0.2 to 5 I I I 2 5 50 100 150 200 250 300 400 350 Iteration Number Figure 12. Effect of L parameter (ILU) 20

Large Finite LTSA arrays a) 4x3 LTSA array Consider the 4x3 LTSA shown in fig. 13b. All array elements are identical and the dimensions are given in Figure 13a. The slotline feed is designed to be 100 ohms at 10GHz and the feed point is positioned 0.635cm from the slotline short. The antenna is 4.885cm in length.. 0.078 k 3 0 ^ Z 4............................. 1.5.............................. a) b) Figure 13 a) Element geometry b) 4x3 array 21

4x3 Anay-10Gz, " I 2 I " 1 C-O -- - -- - - -- - - - - t- - -I- - - - - - - - t- - - - - - - - -- I~ I, I I I I I I I I I I I I' -20 - - - - - - - - - -- - - - - - - - - - - _;- __ - - _ - - - - FI i I gure 1 I rectiv Figure 15. Field distribution on 4x3 array - -~ -40 -8 -60 -40 -20 0 20 40 60 80 Y X\Figure 15. Field distribution on 4x3 array 22

b) 6x6 LTSA array Consider the 6x6 LTSA array. All array elements are identical and the dimensions are given in Figure 13a. This prob;em was solved using 4 level FMM with 800 MB of memory. Without FMM 10 GB of memory is required and thus a parallel machine is required to carry out the analysis. '% ___ Ej.ane -5. ______H-.-Ic -------- ii -------- -102 -15- -/\ /A 201___I.III I I f!n 1 0 Alk i f Hk H M I M H Mi i i AN i 11/f I I' /1 / -30...... I -..........i A I I f I0 A 'I fq )IC ON! L l ie I. 1.. I I I I I I... -.... I I I - I ls - - 40C y '11 I r H I... v i i M.. a 4 --- li i i i --- I I -150 -100 -50 0 50 100 150 Figure 16. Radiated Fields as a function of observation angle 23

Figure 17. Field distribution 24

Ship Tower To demonstrate the capabilities of AMFIA we consider the geometry in Fig. 18a. LTSAs are the same ones used in our previous example (see Fig 13a). This problem required only 187Mbytes of memory with 6 level FMM. Without FMM the required memory was 4.3 GB (i.e. 23 times larger). a) 90 -1 I IC -15 -20 -30 -40 -200 -150 -100 -50 0 50 100 150 200 b) 180 0 270 c) Figure 18. a) Field distribution b) Radiated Field versus observation angle c) Radiated Field versus observation angle (polar coordinates) 25

COUPLING STUDIES In the previous reports we studied element to element coupling within the same array environment this quarter we are expanding our analysis to subarray/subarray coupling. For demonstration we consider the slot to patch array coupling in Fig. 19. Slot-Patch array system considered for this purpose( see fig. 19). Slot array consists of 18 identical slots with 0.4XxO.1. The patch array to the right consists of 9 identical patches with dimensions 0.4Xx0.2k (inner rectangle) and 0.6Xx0.4k (outer rectangle). Solution of this problem required 116 Mbytes of Memory without FMM but only 11Mbytes with FMM. All slots are excited ( active). Our goal is to observe the coupling as a function of array separation between two array systems. Fig. 20-22 show the field distribution for different separation distances. As you can see that the coupling decreases as "d" increases. 1.8X ' — 2.4 X - Ed ' ' 2.4 X Figure 19. Geometry of the array system 26

MSC/PA11AN Vemon 9.0 2SdJuIAO1 035 Frhpg: bisttW MAX( DEFLECilON = 0.OE.0, DISPLACEMENT, ROTKT1ON - MA(~ (NON-LAYERED) z 9.47+01 8.51+01 7.75+01 5.03+01 5.17+01 4.31+01 2.58+01 1.72+01 8.51+00 3.05-05 dehuL Fringe: max 5.32-42 @Nd 1595 Min 0.@~Nd I z I Ii y L-1 --- I ". — x Figure 20. Field distribution d=O.1IX 27

MSCIPATRAN Version 9.0 23-Jul-01 03:04:356 Fringe: baisttx, MAX DEFLECTION =.00E+00 DISPLACEMENT, ROTATION - Magnituda, (NON-LAYERED) z 9.47-i01 8.51401 7.755.01 5.8940 5.17401 4.30.0 p3.44.01 2.58..0 1.72401 8.51-4X 3.0505 default Frnnge: Max 5.29402 (~Nd %3Q Min 0.~Nd I z Y z7 Figure 21. Field distribution d=O.5X 28

MSC/PATRAN Verlon 9.0 2Ju-01 14:10X9 Frngo: bisti, MAX DEFLECTION =.00E+O3, DISPLACEMENT, ROTATION - MAG, (NON-LAYERED) 9.47401 8.61401 7.75401 6.89401 6.o0301 5.17401 4.3001 p 3.44-01 25&801 1.72401 8.614. 3.0505 dulIFnngo: Max 6.32.02 (@Nd 591 Mm O.@Ndl z Y — -— X Figure 22. Field distribution d=lX 29

Fig. 23-25 show the coupling from slot array to patch array elements. Element 1 is the upper left patch, element 2 is the middle left patch and 3 is the lower left patch. -20.,.... -30 -40 cr CD T-.. U3 -50 \ -70 - -80 -w4 I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Separation in terms of X 0.8 0.9 1 Figure 23. Coupling (array to element) -ZU. I -30 -40 c CN -50 <60 -60 -70 -An -mu 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Separation in terms of X 0.8 0.9 1 Figure 24. Coupling (array to element) 30

m.50 'I c:. -60 - O \ -70 -80 -90 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Separation in terms of X Figure 25. Coupling (array to element) 31

REFERENCES [1] Jian-Ming Jin, John Volakis, "A hybrid Finite Element Method for Scattering and Radiation by Microstrip Patch Antennas and Arrays Residing in a Cavity", IEEE Antennas and Propagat. Vol.39., no. 11, November 1991 [2] Yousef Saad, "Iterative Methods for Sparse Linear Systems", http://wwwusers.cs.umn.edu/-saad/books.html [31 John Volakis, Arindam Chatterjee, Leo Kempel, "Finite Element Method for Electromagnetics", IEE press, 1998 141 Gerard L.G.Sleijpen, Diederik R. Fokkema, "BICGSTAB(L) for Linear Equations Involving Unsymmetric matrices with Complex Spectrum", Electronic Transactions on Numerical Analysis, vol., pp. 11-32, Septmber 1993 32