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Education - European School of Antennas
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» The Method of Moments: From Basics to Large-Scale Applications
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The Method of Moments: From Basics to Large-Scale Applications
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The Fourth Doctoral School on selected topics in Electromagnetics,
organized by the Italian Society of Applied Electromagnetics (SIEm),
was held on September 16th and 17th, 2004, in Cagliari, on the
beautiful island of Sardinia.
This year the chosen topic was the Method of Moments (MoM), which was
presented in three half-day lectures given by Prof. Donald R. Wilton
from the University of Houston, USA, an indisputed world-class expert
on the MoM.
The School was held in the Cittadella dei Musei, the
museum quarter located inside the Arsenal, in the historical Citadel of
Cagliari. The Arsenal was built in 1552 under Spanish rule, but the
area was inhabited also during the Phoenician-Punic and Roman Eras, as
evidenced by two reservoirs. It was then transformed into the Cittadella dei Musei in 1979.
The event was the fourth in a series of annual international PhD
schools organised and financed by SIEm. This year the school was
co-financed by the Central and South Italy Section of IEEE and
supported by the Antenna Center of Excellence (ACE), a Network of
Excellence within the Sixth Framework Program (FP6) of the European
Union.
The members of the Steering Committee of the School were Prof. T.
Isernia (University of Naples), Prof. S. Maci (University of Siena),
Prof. G. Manara (University of Pisa), Prof. R. Sorrentino (University
of Perugia) and Prof. G. Vecchi (Polytechnic of Turin). The University
of Cagliari (Prof. G. Mazzarella) organized the school locally, in
connection with the Italian National Meeting of Applied
Electromagnetics (RiNEm). The ACE support was related to the Activity
3.1, Training and Education, and in particular to the Workpackage
3.1-1, namely the European School of Antennas. The school was actually
intended to be a first pilot course to test the future organization and
activation of short-term schools scattered all over Europe. In
particular, all the costs for the PhD students coming from ACE partners
were covered by the ACE budget; thus, the organization of the school
has also provided a first cost estimate for student travel grants.
The aim of the three half-day lectures given by Prof. Wilton was to
provide attendees with a working knowledge of the MoM and enough
information to understand the basics of its recent extensions to
large-scale problems.
Here follows a brief summary of the topics covered by the lectures:
- 1. Electric, Magnetic, and Combined Field Integral Equation Formulations,
- A. Scattering by cylinders - oblique incidence (2.5-D Formulation),
- B. Formulation for 3-D scattering and integral equation solution;
- 2. The Helmholtz Equation,
- A. 2.5- and 3-D formulations,
- B. Mesh termination-hybrid formulations;
- 3. Wires and Wire-to-Surface Junctions;
- 4. Formulation of Aperture Problems (Planar and Non-Planar);
- 5. Dielectric and Piecewise Homogeneous Scatterers (PMCHWT Formulation);
- 6. Introduction to Fast Methods,
- A. Principles of Fast Methods,
- B. Summary of AIM, polynomial interpolation, QR matrix compression, MLFMA, and MLFDA approaches.
The lectures introduced fundamental numerical methods, emphasizing
practical calculations for electromagnetic research problems. The
approach proposed by Prof. Wilton to introduce the key features of the
MoM started with the scattering by obliquely illuminated 2-D conducting
cylinders. This approach not only builds a solid foundation for
introducing a 3-D integral equation analysis, but also leads to
practical schemes for analyzing guided wave structures. The standard
electric, magnetic, and combined field integral equations were
presented and applied to 3D conducting surfaces and wire structures,
planar and non-planar apertures, and piecewise-homogeneous objects.
Moreover, he presented the finite element approach for solving the
Helmholtz equation. Notational consistency was maintained to emphasize
both similarities and differences between moment methods and finite
element formulations. Throughout the lectures, emphasis was given to
the philosophy behind the construction of the global system matrix,
which results by assembling the element matrix contributions: "Think
globally, act locally".
This 4th PhD course was very well attended, with more than 50 PhD
students and researchers, from several European countries who actively
participating in the lectures. Most of them are affiliated with ACE
partner institutions, both contractual (20) and non-contractual (8), as
sketched in the tables below. To this regard, it is worth noting that
the 2nd Doctoral School organized by SIEm in Ancona in 2002, which was
structured in three half-days like the one recently held in Sardinia,
had only about half the participants (27, still a considerable number),
who were all affiliated with Italian institutions.
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| Location: |
University of Cagliari - Cagliari, Italy |
| Date: |
16/09/2004 - 17/09/2004 |
| Contact Person: |
G. Mazzarella - University of Cagliari |
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