OVERVIEW OF THE SOFTWARE INTEGRATION ACTIVITIES WITHIN ACE

V. Volski(1), G. Vandenbosch

(1), J. Yang

(2), P.-S. Kildal

(2), F. Vipiana

(3), P. Pirinoli

(3), G. Vecchi

(3), P. de Vita

(4), F.

de Vita(4), A. Freni

(4), P. Baccarelli

(5), J.M. Rius

(6), H. Espinosa

(6), M. Mattes

(7), A. Valero

(8), P. Persson

(9), Z.

Sipus(10)

(1)Katholieke Universiteit Leuven,Kasteelpark Arenberg 10, 3001, Leuven, Belgium,

Email:vladimir.volski@esat.kuleuven.be (2)Chalmers University, Sweden, Email: jianyang@chalmers.se

(3) University of Torino, Italy, Email: francesca.vipiana@polito.it (4) University of Florence, Italy, Email: paolo.devita@unifi.it

(5) “La Sapienza” University of Rome, Italy, Email: baccarelli@mail.die.uniroma1.it

(6) UPC, Spain, Email: rius@tsc.upc.edu (7)EPFL, Switzerland, Email: michael.mattes@epfl.ch

(8) UPV, Spain, Email: avalero@dcom.upv.es

(9)KTH, Sweden, Email: patrik.persson@ee.kth.se

(10)UNIZAG – University of Zagreb, Croatia, Email: zvonimir.sipus@fer.hr

ABSTRACT

The ACE project initiated the start of several integration

activities between European institutions involved in

electromagnetic modeling of antennas with planar or

conformal topologies. The goal of the integration

activities was / is not to create a global software

package that integrates the software of all partners, but

to initiate a long term process for antenna software

integration activities within the European antenna

community. During the first two years of ACE the

integration activities were performed in several groups

with a rather small number of partners in each group.

The groups were formed by partners who wanted to

integrate a specific approach developed by one partner

into the software code of another partner.

This allows increasing the capability and efficiency of a

software code. In this paper a short overview of all

integration activities is given.

1. INTRODUCTION

The fast development of electronics in the last 20 years

triggered a new approach in the design and production

of electronic devices and antennas. This approach relies

heavily on CAD tools, which are becoming more

general, powerful and accurate. Meanwhile there are

still a lot of antenna problems that cannot be

investigated by available commercial software with

accuracy sufficient for practical needs. As a

consequence, at this moment, a lot of European

universities, research institutes and companies develop

their own antenna software. Although these codes show

a higher performance and accuracy for specific antenna

types than typical commercial codes, only a few people

efficiently use them.

During the first year of the ACE project a detailed

inventory was made of the software available among all

partners of the ACE network. From this inventory the

necessary information was extracted concerning all

possible integration activities. It was studied which

theoretical techniques and corresponding software of

different partners can collaborate or even be integrated

in a single entity. Several meetings among people who

have developed the software were organized to

investigate possible integration activities. The

integration activities to perform were selected based on

three criteria: feasibility, future usefulness and proven

excellence of the partner involved. The topics addressed

and the partners involved are listed below. There were 7

integration projects selected:

- on planar and cylindrical antennas, KUL and Chalmers

- on the Multi-Resolution (MR) Approach, POLITO and

UNIFI

- on the MR Approach, POLITO and KUL

- on Green’s function exchange, KUL and UNIFI

- on an efficient computation of periodic Green’s

function in layered dielectric media, SAPIENZA and

KUL

- on the fast UPC block LU-solver, UPC, EPFL and

UPV

- on conformal antenna software, KTH, UNIZAG and

Chalmers

One of the main problems that almost all groups

encountered was how to transfer information between

the different codes. This is due to the absence of

standardized ways to describe electromagnetic

quantities (currents, Green's functions, fields, and so

on). In practice, the information is stored in different

codes in a different way, and it is written to files using

incompatible formats. Although the groups worked

rather independently, the interaction between groups

was very noticeable and fruitful. The results of the on-

Proc. ‘EuCAP 2006’, Nice, France 6–10 November 2006 (ESA SP-626, October 2006)

going activities were reported to all partners during the

ASI meetings three times a year. For instance the format

for Green’s functions in planar media proposed by UPC

and EPFL was used as an example to construct the

format for other Green’s functions (2 dimensional and

spectral) used in the integration activities SAPIENZA-

KUL and UNIFI-KUL.

At the first stage the integration was performed using

the exchange of specific information between different

codes. This step did not require a large modification of

the existing codes but it allowed to produce very

noticeable results in a very short period of time. For

instance the efficiency of antenna software codes based

on the MoM method with RWG basis functions can be

greatly increased by implementing the MR approach

developed at POLITO. Two groups (KUL, UNIFI) have

successfully partially implemented these methods in

their codes.

A very significant increase of the capabilities of a

software code can be achieved using exchange of

Green’s functions. This type of exchange is not very

widespread because it requires the compatibility

between different codes on a rather low level. Several

groups have demonstrated that the exchange of Green’s

functions is a very simple way to implement dielectric

layers or periodicity in the codes that use a mixed-

potential formulation for electric fields. Moreover the

integration activity between Chalmers and KUL has

demonstrated that the exchange of Green’s functions

saves a lot of time in constructing the solution for very

complex problems like the finiteness of conformal

antennas.

A detailed overview of all integration activities

performed within the ACE project can be found in the

ACE-A1.1D3.4 report [1].

2. ON PLANAR AND CYLINDRICAL

ANTENNAS (CHALMERS-KUL)

This is one of the most complex and challenging

integration activities. The goal is to allow the analysis of

antennas located in the vicinity of cylindrical structures

of arbitrary cross sectional shape. The theoretical

background of this analysis is based on a combination

of solutions in the spectral and spatial domains [2]. This

combination required the integration between two codes

on a low level. Chalmers has developed a numerical

method for analyzing of cylindrical structures of

arbitrary cross sectional shape. The method is

implemented in software named G2DMULT [3]. This

code is able to calculate Green's functions of 2D multi

region structures, or in other words Green's functions of

composite cylindrical structures. The key feature of the

code is that it can very efficiently handle different cross

sectional shapes and complexity of the cylindrical

structure. However due to limited computer resources

finite metal antenna elements located in the cylindrical

structure cannot be large and have complex shapes.

KUL has developed methods and software named

MAGMAS for analysis of planar antennas in multilayer

structures. The analysis is done by the moment method

using subsectional basis functions on the conductive

parts, where the grounded dielectric slab is assumed to

be planar and of infinite extent and included via a pre-

calculated Green's function. A more detailed description

of the used techniques can be found in [4]. The basic

method used in MAGMAS cannot in principle account

for the case when the grounded dielectric slab is finite,

curved or truncated. However MAGMAS can very

efficiently handle different shapes of the metal

conducting antenna parts.

y

x

z

Figure 1. Example of a truncated structure

Thus, G2DMULT and MAGMAS have complementary

features that make it possible to get an improved

software tool by integration of the two software codes.

Integrated software will be able to handle planar

antennas on truncated layered cylindrical structures,

such as the geometry shown in Figure 1. It should also

be possible to analyze planar antennas on singly curved

multilayer structures. The cylindrical structures are still

assumed to be infinite in their axial z-direction, which is

a requirement to be able to use the G2DMULT

algorithm. Furthermore, all the user friendliness and

plotting capabilities of MAGMAS can be made

available in the integrated software.

The integration between the two methods uses a

generalized asymptote extraction technique. This is

described by the following formula for the mutual

impedance between two basis functions (current

segments) of the metal antenna parts,

( ) ( )[ ]

asympmnz

zjk

n

zasympzm

k

kmn

Zdke

kZkZZ

z

z

z

+

⋅−≈

−

−∫I

I

~

~~~

2

1 max

maxπ (1)

where asympmnZ is the impedance obtained from

MAGMAS in the infinite layered structure (also called

local approximating structure), ( )zkZ~

is the spectral

impedance in the z-spectral domain obtained from

G2DMULT in the actual truncated structure, and

( )zasymp kZ~

is the spectral impedance in the z-spectral

domain of the infinite layered structure. The calculation

of the latter ( )zasymp kZ~

is implemented in MAGMAS

as it can be calculated from the Green's functions of the

infinite grounded slab used there. In practice the integral

in (1) must be truncated and discretized to enable

numerical integration. The truncation limit will be much

lower in (1) than in the original inverse Fourier

transform without the asymptote extraction, because the

function in the square brackets in (1) decreases much

faster than the original ( )zkZ~

.

The integration activity has progressed very well. As

usual the partners have encountered a special problem

when transferring the spectral impedances of the

asymptotic problem obtained from MAGMAS. This

was different by a factor of about 40 from the actual

truncated problem analyzed by G2DMULT. The results

should of course be very similar, as the actual truncated

structure shall represent a correction to the infinite

asymptotic structure. The discrepancy was about

( ) 4022 ≈π and caused by different definitions of the

Fourier transforms.

Figure 2 Comparison between results with G2DMULT

and MAGMAS for ground planes of 0.4 and 4

wavelengths width with 2=rε .

The results of the integration of the second step were

presented at the ACE meeting in Dubrovnik in 2005-10-

10. In Fig. 2 the ( )zkZ~

and ( )zasymp kZ~

are plotted for

the coupling between two dipoles located on the top of a

grounded dielectric layer at the distance 0.2λ from each

other. In this calculation the size of the ground plane

used by G2DMULT is 0.4λ. The normalized difference

between two spectral couplings (3) is shown in Fig. 3.

)(~

)(~

)(~

)(

MAGMAS_

MAGMAS_G2DMULT

zasymp

zasympz

zkZ

kZkZk

−=∆ (3)

Figure 3 Normalized difference between results of

G2DMULT and MAGMAS

The calculated mutual impedance between two basis

functions calculated using the combination of

G2DMULT and MAGMAS and G2DMULT only is

shown in Tabl.1

Table 1. Mutual Impedance

Zmn

G2DMULT -290.54 – 50.21j

G2DMULT & MAGMAS -291.12 - 51.02j

It was shown that the integration of the codes

G2DMULT and MAGMAS can increase the

computational efficiency 3 to 4 times for the chosen test

problem when compared to using only G2DMULT, and

even more when compared to other standard

(commercial) numerical codes.

This integration activity will continue in ACE2, to

analyze a complete antenna. A complete planar antenna

is modeled by using several such basis functions in a

moment method procedure.

3. ON THE MULTI-RESOLUTION APPROACH

(KUL-POLITO)

The goal of this integration activity is the

implementation of the multi resolution approach (MR)

[5, 6], developed at POLITO, within the MAGMAS [4]

software, developed at KUL.

Nowadays, the method of moments (MoM) is a very

powerful tool for the electromagnetic analysis of

antennas formed by conducting surfaces. This method is

based on the description of the conducting surfaces in

terms of unknown equivalent electric currents. These

unknown electric currents are approximated using a

special set of basis functions. The Rao-Wilton-Glisson

(RWG) basis functions constructed using a triangular

2D mesh have gained huge popularity due to their

ability to describe conducting surfaces of arbitrary

shapes and forms. The application of the MoM reduces

the problem to the solution of a linear equations system.

The effectiveness of the whole MoM procedure depends

very much on the properties of the MoM matrix. These

properties depend to some extent on the choice of the

basis functions. The MR approach allows to construct a

new set of vector basis functions that are expressed as

linear combination of the RWG functions defined on an

existing 2D triangular mesh, with properties closed to

those of scalar. In particular, it is possible to reduce the

condition number of the resulting MoM matrix in the

MR basis by more than one order of magnitude, by

simply applying a diagonal preconditioner, with a

consequent increase in the convergence of the iterative

solvers used to solve the matrix equations and the

possibility of strongly “sparsifying” the MR MoM

matrix, without affecting the accuracy of the solution.

Although the integration activity looks rather

straightforward, there are a lot of hidden problems that

are able noticeably slow down the implementation. The

main reason is that there are no generally accepted

standards of how to describe currents and meshes. It

means that the first step of the integration activity was

to achieve the compatibility between different codes in

the description of meshes and currents. Several

meetings were organized to discuss this issue, which is

very far from being trivial. Finally, a rather simple

intermediate solution was selected. A special converter

was made to convert the mesh/current format used by

POLITO to the mesh/format format used by KUL. The

latter can be read by the standard KUL interface.

Several test structures have been analyzed to confirm

the compatibility of the POLITO mesh/ current format

with the KUL code. Then the MR approach can be

implemented rather straightforward because the RWG

mesh becomes compatible. However the MAGMAS

code uses additional basis functions to describe

excitations using a special deembeding procedure. This

requires a slight modification of the MR approach. As

an example, a square patch fed by a probe was

considered. The working frequency is 1 GHz (side of

the plate = λ0/2). The mesh file and the MR basis

change matrix were provided to KUL by POLITO. Two

geometries were considered. The first one is the patch

excited by an electric dipole. The electric dipole is

shifted 10 cm from the center of the patch. The whole

structure is located in air. The next geometry is a probe

fed patch. The patch is located on a grounded dielectric

slab with permittivity ε=2.2 and thickness 7.5 mm. In

the MAGMAS code a special attachment mode is used

to describe the smooth transition of the electric current

between the probe and the patch. The attachment mode

on the patch is shown in Fig. 4 by a yellow circle. This

attachment mode increases the size of the MAGMAS

MoM matrix in comparison with the POLITO MoM

matrix. The additional basis function requires a slightly

modified MR approach that takes into account the larger

size of the MoM matrix. The success of integration was

confirmed by the decrease of a condition number of the

MoM matrix after the application of the MR approach.

Figure 4. Square patch with an attachment mode.

The condition number was calculated before and after

the MR approach. The condition number was calculated

using the ccon routine from the NAPACK library. This

routine estimates the 1-norm condition of a general

complex matrix. The results are shown in Table.1.

Table. 1. Condition Number of the MoM matrix.

1-norm

condition

number

Air (dipole

excitation)

Dielectric

(probe fed,

ε=2.2)

[Z] 1429 23302

[ZMRPC

] 477 5901

These results show that the condition number decreases

noticeably in both cases. This confirms the effectiveness

of the MR approach.

During this integration activity between KUL and

POLITO the MR basis change was implemented in the

MAGMAS code. In order to use this MR basis change

matrix in the MAGMAS code, POLITO provided the

mesh file and the MR basis change matrix. The

application of the MR basis change matrix shows its

effectiveness in two new cases with respect to the

original setting of the MR technique. In the first place,

we have demonstrated that the MR approach remains

effective in the case where there is a dielectric in the

structure; this confirms the theoretical expectations

since the MR basis functions generated by POLITO are

independent from the dielectric media around the

metallic antenna. The second relevant results was that it

is possible to apply the MR basis change matrix to only

a part of the MoM matrix, as done here, while keeping

the positive effects of the MR basis; this latter result is

not obvious.

These obtained results are an excellent basis for future

cooperation between the two universities. This also sets

the stage for relevant activities to be carried out in the

framework of ACE-2. In addition to the already-

mentioned activity relevant to data exchange, it can be

foreseen that further improvement in the MR basis

formation algorithm could lead to a more flexible and

more far-reaching integration.

4. ON MULTI-RESOLUTION APPROACH

(UNIFI-POLITO)

This integration activity is about the use of the

MultiResolution (MR) technique, developed by

POLITO [5, 6], for the generation of an efficient

preconditioner that can be applied to the Banded Matrix

Iterative Approach/Adaptive Integral Method

(BMIA/AIM), named as Sparse Matrix/Adaptive

Integral Method (SM/AIM) in its latest version,

developed by UNIFI.

The SM/AIM is an iterative method, acting on the

efficiency of the Method of Moments (MoM) by

reducing the numerical complexity necessary for each

step of the iterative procedure, but not affecting its

convergence rate, that is essentially the same as with the

standard MoM. The MR scheme manages to generate

``wavelet-like'' hierarchical multiscale vector functions

for any meshed geometry and well controls the MoM

condition number, by the simply application of a

diagonal preconditioner [5]. For this reason the MR

approach can be conveniently used to generate a low

cost and efficient preconditioner that can be used with

the SM/AIM.

The integration of the two techniques has required first

of all the “transfer of knowledge” from one Unit to the

other, in order to understand how the two methods work

and at what level the integration could be carried out.

For this reason the meetings listed in the following have

been organized: 17-18/03/05 Turin, 29/08/05 Florence,

22-23/09/05 Turin, 10-11/10/05 Dubrovnik, 15-

17/11/05 Turin.

The first and main problem was related to the fact that

the two codes used a different data format for the

description of the geometry mesh and of the subdomain

(RWG) functions defined on it. As explained in the

previous section, the MR scheme itself provides the

mesh at the finest level, and it is the one that has to be

used also by the SM/AIM approach. For this reason the

format of the geometry mesh file produced by the MR

scheme has to be compatible with the one used as input

by the SM/AIM scheme.

As an example, an array of bowtie dipoles (6x10) is

considered. Fig. 5 shows the number of iterations

necessary for the SM/AIM method to reach the set

tolerance on the frequency interval 1.8÷2.4GHz, with

and without the MR preconditioner.

Figure 5. Number of iterations for reaching the

tolerance of 10-4 versus the frequency

The use of MR reduces the number of iterations of

about a factor of 200. The slight increase in the number

of iterations around 2.3GHz can be connected to the

strong variation of the impedance around this frequency.

Fig.6 CPU for the whole arrays of dipoles

Fig. 6 reports the total CPU time needed to solve the

MoM linear system for increasing problem dimensions

(number N of unknowns). The three curves refer to the

use of the SM/AIM approach with the MR (circle) or of

the RWG (square) functions and of the standard MoM

(triangle). The marks correspond to computed values,

while the continuous curves are the interpolating

functions, which give the dependence of the CPU time

on N, whose expression is also reported in the figure.

The use of the SM/AIM instead of the classical MoM

reduces the numerical complexity from α·N2 to α·440N

log2 2N; in this case, α = 1.05·10-3

sec. This means that

starting from medium size problems (N ≥ 25,000) the

CPU time reduction achieved using the SM/AIM is

almost one order of magnitude. The introduction of the

MR functions within the SM/AIM frame has a further

strong effect on the numerical effort needed to solve the

linear system

5. ON GREEN’S FUNCTION EXCHANGE

(UNIFI-KUL)

This activity is based on the integration of the Green’s

functions for a multilayered structure, developed by

KUL [4], in the BMIA/AIM (Banded Matrix Iterative

Approach/Adaptive Integral Method) numerical code

formulated by UNIFI. At this stage the data have been

exchanged through a data file properly defined.

This activity has allowed the extension of the

BMIA/AIM code to the analysis of metallic patches in

multilayered structures.

In order to use the Green’s function data provided from

the MAGMAs code, it has been necessary to develop an

interpolation algorithm to better approximate the

Green’s function values required from the BMIA/AIM

code for the computation of the impedance matrix

elements.

Moreover, since the BMIA/AIM code was first

developed for structure in free space UNIFI had to add

in the evaluation of the right-hand-side term of the

MoM matrix system the case of multilayered dielectric

structure for a plane wave excitation, in order to

compare the accuracy of the integrated code with a

commercial one (Ensemble)).

The free space test has also been used to establish the

compatibility between codes since in the case of free

space the Green’s function are known in a closed form,

then to check the accuracy of the interpolated data.

These results encouraged the partners to continue in that

way and to perform advanced tests considering

dielectric structures.

Before implementing these cases, as in many integration

activities, an exchange of information on the

formulation used, in particular regarding the Green’s

function evaluation, has been necessary mostly to tune

the constant terms used.

In fact, UNIFI had to adjust the normalization factors

the partners used to evaluate the solution according to

those used to compute the Green’s function.

As an example, a square patch was considered. The

excitation is represented by a plane wave impinging

orthogonally on the structures. The agreement between

the results (Far Fields) of the integrated model and the

commercial software is good.

6. ON AN EFFICIENT COMPUTATION OF 2D

PERIODIC GREEN’S FUNCTIONS IN

LAYERED DIELECTRIC MEDIA

(SAPIENZA-KUL)

A software for the efficient computation of two-

dimensional (2-D) periodic vector and scalar Green’s

functions in layered dielectric media is here presented as

a result of an integration activity between SAPIENZA

and KUL. The obtained tool is devoted to the analysis

of infinite 2-D periodic structures printed on a

multilayered dielectric substrate, which is usually

performed by means of a mixed-potential integral

equation solved by the method of moments in the spatial

domain. 2-D periodic vector and scalar Green’s

functions in the spatial domain are needed and are

efficiently derived from their spectral domain

counterparts by using well-known acceleration

techniques. The non periodic spectral electric and

magnetic dyadic Green’s functions for current sources

embedded within planar stratified background media are

provided by KUL. A versatile approach for accelerating

the derivation of the 2-D periodic mixed-potential

Green’s functions in the space domain is then applied

from SAPIENZA. Numerical acceleration techniques

are performed by extracting asymptotic and slowly

converging terms, both in the on-plane and off-plane

cases. Kummer-Poisson’s formula and Ewald’s

transformations are then applied when the sum of the

extracted terms is added back. Results for a simple

reference 2D periodic structure are reported,

demonstrating how the integration of these rigorous

techniques provides a powerful and flexible tool for the

analysis of this kind of periodic structures. Furthermore,

comparisons among the various acceleration methods

are performed, thus making available fundamental

information on their actual efficiency in such canonical

problems. There is a special paper about this integration

activity at the conference.

7. ON INTEGRATION OF UPC BLOCK-LU

SOLVER INTO EPFL AND UPV ANTENNA

SIMULATION CODES (UPC, EPFL, UPV)

Actual and future telecommunication applications

require the use of array antennas with very demanding

specifications: large bandwidth, high efficiency, dual

polarization and low cost manufacturing techniques.

Excellent representative examples of the mentioned

design trends are Low Tolerance Arrays (LTAs), which

belong to the wide-band, dual-polarized ground and

space applications, including the satellite TVRO,

multimedia and VSAT terminals on board, large

bandwidth array panels and SAR antennas.

Integral equations (IE) discretised by Method of

Moments (MoM) are widely used for the numerical

simulation of antenna radiation. However, their

application to very complex or electrically large antenna

structures is limited due to the fact that the

computational requirements increase rapidly with the

electrical size and/or geometrical complexity of the

antenna. The cause for this is that the discretisation of

integral equations results in a full system of equations

that, in principle, requires storage memory proportional

the square of the number of unknowns N² and the

number of unknowns increases with the geometrical

complexity and the square of the electrical size of the

structure.

Consequently, the numerical simulation of most

problems of interest leads to systems of equations so

large that do not fit in the computer memory, and

special techniques are needed to compute the solution.

An integration of UPC’s Block-LU linear system solver

[7] with EPFL’s and UPV’s electromagnetic engines

has been performed. The result are combined codes

which have superior features than the original ones and

allow the exact simulation of large-scale structures that

previously EPFL and UPV could simulate only by

approximate methods.

Figure 7. Layout of 8x8 patch array

Figure 8 Measurements and simulation results of 8x8

patch array antenna in the E plane

Figure 9. Measurements and simulation results of 8x8

patch array antenna in the H plane

As an example, Fig. 7 shows an 8x8 patch array antenna

that has been used as a test case. Using the original

EPFL’s electromagnetic engine POLARIS, no exact

solution was possible, since 9947 unknowns were

necessary needing 1.5GB of memory. The structure

could only be simulated by an approximated method

called Sub-domain Multilevel Approach (SMA)

together with Macro Basis Functions (MBF). With the

integrated software POLARIS/ BLOCK-LU a direct

solution became possible.

The comparison of measurements with approximate and

exact solutions is shown in Fig. 8 and Fig.9 showing a

good agreement between both measurements and

simulations and exact and approximate simulation

results. (Solid lines: measurements; dashed lines:

approximate solution using SMA+MBF; circles: exact

solution of integrated software POLARIS/BLOCK-LU).

Additional data of the simulation can be found in Tabl.

2.

Table 2. Simulation data of 8x8 patch array antenna

Matrix dimensions 9947x9947

Memory size 1510MB

Reading from file + Matrix formatting +

Storing MoM sub-matrix (2 blocks,

0MB/block)

3498s

Block LU decomposition time 8242s

Block LU solution time 155.8s

8. ON A CONFORMAL ANTENNA SOFTWARE

(CHALMERS, KTH, UNIV. OF ZAGREB)

One of the goals of the WP 2.4-3 “Structuring Research

on Conformal Antennas” was to join research activities

of different groups in Europe working with conformal

antennas. In the past, KTH, UNIZAG and Chalmers

have independently developed methods for analysis of

array antennas on cylindrical structures. Chalmers and

UNIZAG has been using a spectral-domain approach

[8], while an UTD based approach was adopted at KTH

[9] (UTD is Uniform Theory of Diffraction).

However, a single method is seldom useful when

analyzing conformal antennas. The UTD method is

advantageous when large metal structures of any convex

shape are analysed. The spectral-domain method is

advantageous when multilayer cylindrical or spherical

structures are analysed. On the other hand, the spectral-

domain method has numerical difficulties when it is

applied for analysing large structures, and the UTD

method is not suitable for structures with small radius

and for structures that include multilayer dielectric

layers.

By joining the research activities at KTH, UNIZAG and

Chalmers a "hybrid spectral domain–UTD" method for

analyzing conformal antennas has been developed. In

this work, Persson and Sipus have integrated their

methods and software’s to take advantage of the two

methods discussed above. This makes it possible to

develop a general software useful for multilayered,

electrically large, singly curved convex surfaces.

The spectral-domain method and UTD have been

combined by an asymptote extraction approach in which

the advantages of both methods are combined. The goal

with the approach was to reduce the number of terms in

the Fourier series and to reduce the length of integration

in the Fourier transformation (the Fourier series and

transformation are part of the spectral domain method).

The work was mainly done by interchanging formulas

and verification data, and the integrated software was

finally verified as shown below. The ACE network

made the integration possible in a smooth and

convenient way.

To shortly illustrate the method we will consider a

waveguide array embedded in multilayer dielectric

structure (Fig. 10).

Figure 10. Circular-cylindrical array of waveguide

elements covered with a radome. Note, the radome is

not shown in the picture. See [10] for details about the

geometry.

Figure 11. Mutual coupling in the E-plane.

The accuracy of the proposed method is illustrated in

Fig. 11, where the developed hybrid method has been

verified against both measurements and calculated

results obtained with the spectral domain approach

where no acceleration techniques were used. The

comparison of the calculated and measured S-

parameters is shown for the first row of waveguide

elements, i.e. we plotted Sn,1 , n=2,18. It needs to be

mentioned that the hybrid program gave a reduction in

computation time by a factor 10.

Currently, we are working on developing the method

further to include other types of singly curved surfaces

than just the circular cylinder. Just recently some

radiation pattern calculations were shown [10] due to an

aperture antenna on an elliptic surface (with and without

a radome), additional results including mutual coupling

analysis will be shown at the EuCAP conference in

Nice.

9. REFERENCES

1. ACE-A1.1D3.4 Report

2. Kildal P.S., et al., IEEE Antennas and Propagation,

Vol. 44, 1183-1192, 1996

3. Yang J., et al., Microwave and Optical Technology

Letters, Vol 32, 108-112, January 2002

4. Vandenbosch G.A.E, et al., IEEE Antennas and

Propagation, Vol. 40, 806-817, 1992

5. Pirinoli P., et al., IEEE Antennas and Propagation,

Vol.49, 858-874, 2001

6. Vipiana F., et al., IEEE Antennas and Propagation,

Vol. 53, 2247-2258, 2005

7. Heldring A., et al., IEEE Magnetics, Vol.38, 337-340,

2002

8. Sipus Z., et al., Applied Computational

Electromagnetics Society Journal, Vol. 13, 243-

254, 1998.

9. Persson P., et al., IEEE Antennas Propagation., Vol.

49, 672-677, 2001.

10. Sipus Z., et al., Nordic Antenna Symposium

(Antenn06), Linköping, Sweden, May 2006.