THIS IS THE HOME PAGE OF GIUSEPPE BORZI'Curriculum Vitae of Giuseppe Borzi'.
I started to be interested in computational electromagnetics when I was at the Southern National Laboratory (LNS) of Catania. At the LNS I collaborated on the analysis and design of electromagnetic devices, and I realised that computational electromagnetics is a powerful tool for both tasks. I began my research work on computational electromagnetics as soon as I joined the electrical group at the University of Catania. The group had focused on the extension of FEM to unbounded static and quasi-static problems, such as electrostatics, eddy currents, etc. developing an iterative procedure called charge iteration to deal with such problems. In charge iteration the unbounded domain is truncated by means of an artificial boundary and a Dirichlet boundary condition is guessed on it; the bounded problem is solved and the solution used to refine the guess, employing the second Green's identity. It was proved that with a proper placement of the artificial boundary the algorithm converges to the true solution. This procedure has been applied to practical problems such as electromagnetic shielding [7] and VLSI parameter computation [11]. The first challenging problem I dealt with was the development of a procedure similar to charge iteration to solve unbounded time-harmonic problems such as scattering problems: the use of a Dirichlet boundary condition on the artificial boundary results in the same formulation as HFEM (Jin and Liepa, IEEE AP-36, n.1, pp. 50-54) with a different solution method for the resulting linear system. It can be shown that such a method can be non-convergent no matter how far the artificial boundary is placed; this has an intimate connection with the well-known problem of interior resonance, which is also a common problem for MoM and FEM/BEM. I solved the problem by using an appropriate Robin boundary condition on the artificial boundary: the resulting method is a new hybrid integral - FE one that completely avoids the well-known problem of interior resonance, and gives a linear system which is well suited for an iterative solution method. The Robin boundary condition used is an impedance-like one, or more generally an ABC-like one, so that it acts as an 'energy absorber' ensuring the unicity of the solution of the Helmholtz equation at all frequencies, thus setting up a well-conditioned system. The method has been also applied to scattering from a cavity recessed in a wedge [14]. The linear system arising from the discretization of the differential equation and the integral equation can be solved with a two-block Gauss-Seidel method, which can be interpreted as follows: the unknown boundary condition on the artificial boundary is first guessed, the corresponding bounded problem is solved and the field thus obtained is used to refine the initial guess. This procedure is repeated until it converges; numerical and theoretical results show that only a few steps are required to reach the final solution [1,4,8,10,14,16]. This procedure has been called the Robin Boundary Condition Iteration (RBCI) procedure. Owing to the form of the Robin condition used, the method can be viewed as a 'corrected' ABC. In [10] an elegant effective algorithm for computation of the Bistatic Radar Cross Section in post-processing is presented. In [2,12] the charge iteration procedure is modified employing a static ABC instead of a Dirichlet boundary condition on the artificial boundary; the number of iterations required to reach the solution reduces substantially, but this is counterbalanced by the increased size of the bounded system and a degradation in accuracy has been observed. Another interesting problem I have dealt with is acceleration of the convergence characteristic of charge iteration as well as of the Robin iterative procedure. Both methods can be rewritten in a form where the unknowns are the boundary conditions on the artificial boundary; in this form the iterative procedures outlined above resemble Richardson's method for linear systems, so they can be accelerated using some more effective scheme, such as the GMRES algorithm. In [3] the GMRES acceleration is applied to charge iteration, while the accelerated Robin iterative procedure is shown in [5]. The GMRES algorithm was chosen after a careful study of linear system solver algorithms, especially CG-like solvers. Thus, as a side effect, I acquired a good knowledge of this subject. In the near future I plan to study the convergence characteristic of GMRES-accelerated procedures and the application of the Fast Multipole Method (FMM) to reduce the computational effort needed in the construction of the integral part of the global system, which is a very expensive task.
Note: It is customary, in the FEM community, to check the accuracy of the algorithms developed by comparing the numerical solution with the analytical one. Obviously such a check can only be made with particular geometries for which the analytical solution is available. The use of a calculus program, such as Mathematica, Maple or Mathcad, is a convenient way to build the analytical solution. I learned to use Mathcad when I was a student: it was (and still is) the fastest, easiest and cheapest program of the three mentioned above. Unfortunately it only has a few special functions; to counter this I developed a dynamic linking library (DLL) which adds new special functions to the program. The first version of the library (for personal use only) added only Bessel and Neumann functions of fractional order; the first public release was based on the Cephes Math library by S.L. Moshier; almost all the special functions given in the Cephes library were added to Mathcad. The current release (version 1.2) adds about 70 special functions. The library is available from the program's homepage, Simtel and Winsite (mathlib.zip); it is completely free software.
List of publications |
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| 1) | G. Aiello, S. Alfonzetti, G. Borzì, S. Coco, N. Salerno, "Shape Optimization of the Magnetic Channel of a Superconducting Cyclotron", The International Journal for Computation and Mathemathics in Electrical and Electronic Engineering, vol. 17, n. 1-2-3, 1998, pp. 123-127. |
| 2) | S. Alfonzetti, G. Borzì, N. Salerno, "Accelerating the Robin Iteration Procedure by means of GMRES", The International Journal for Computation and Mathemathics in Electrical and Electronic Engineering, vol. 17, n. 1-2-3, 1998, pp. 49-54. |
| 3) | S. Alfonzetti, G. Borzì, N. Salerno, "Iteratively-Improved Robin Boundary Conditions for the Finite Element Solution of Scattering Problems in Unbounded Domains", International Journal for Numerical Methods in Engineering, vol. 42, 1998, pp. 601-629. |
| 4) | S. Alfonzetti, G. Borzì, N. Salerno, "An Iterative Solution to Scattering from Cavity-backed Apertures in a Perfectly Conducting Wedge", IEEE Transactions on Magnetics, vol. 34, n. 4, september, 1998. |
| 5) | G. Aiello, S. Alfonzetti, G. Borzì, N. Salerno, "Computing Spatially-Periodic Electrical Fields by Charge Iteration", IEEE Transactions on Magnetics, vol. 34, n. 4, september, 1998. |
| 6) | G. Aiello, S. Alfonzetti, G. Borzì, N. Salerno, "A Predictor-Corrector Scheme for Open Boundary Problems", IEEE Transactions on Magnetics, vol. 34, n. 4, september, 1998. |
| 7) | G. Aiello, S. Alfonzetti, G. Borzì, S. Coco, N. Salerno, "A Generalization of the Charge Iteration Procedure", IEEE Transactions on Magnetics, vol. 33, n. 2, march, 1997, pp. 1204-1207. |
| 8) | G. Aiello, S. Alfonzetti, G. Borzì, "A Generalized Minimal Residual Acceleration of the Charge Iteration Procedure", Journal de Physique III, vol. 7, n. 10, october, 1997, pp. 1955-1966. |
| 9) | S. Alfonzetti, G. Borzì, N. Salerno, "FEM Analysis of unbounded electro-magnetic scattering by the Robin iteration procedure", Electronic Letters, vol. 32, n. 19, september, 1996, pp. 1768-1769. |
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| 1) | G. Aiello, S. Alfonzetti, G. Borzì, N. Salerno, "Shape Optimization of Open-Boundary Axisymmetric Induction Devices", 8th Biennial IEEE Conference on Electromagnetic Field Computation, Tucson (USA), 1-3 june, 1998. |
| 2) | G. Aiello, S. Alfonzetti, G. Borzì, N. Salerno, "Applying GMRES to the Solution of FEM/DBCI Systems for Unbounded Skin Effect Problems", 8th Biennial IEEE Conference on Electromagnetic Field Computation, Tucson (USA), 1-3 june, 1998. |
| 3) | S. Alfonzetti, G. Borzì, "Three-Dimensional Electromagnetic Scattering Computation by means of the Robin Boundary Condition Iteration Method", 8th Biennial IEEE Conference on Electromagnetic Field Computation, Tucson (USA), 1-3 june, 1998. |
| 4) | S. Alfonzetti, G. Borzì, "Accuracy of the Robin Boundary Condition Iteration Method for the Finite Element Solution of Scattering Problems", International Workshop on Finite Elements for Microwave, Poitiers (France), 10-11 july, 1998. |
| 5) | G. Aiello, S. Alfonzetti, G. Borzì, N. Salerno, "Computation of MTL Parameters by means of a Finite Element Procedure", International Symposium on Electromagnetic Compatibility, Rome (Italy), 14-18 september, 1998. |
| 6) | S. Alfonzetti, G. Borzì, N. Salerno, "Robin Boundary Condition Iteration: a Method for Solving Scattering Problems in EMC Applications", International Symposium on Electromagnetic Compatibility, Rome (Italy), 14-18 september, 1998. |
| 7) | S. Alfonzetti, G. Borzì, N. Salerno, "Some Considerations about the Perfectly Matched Layer for Static Fields", 8th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, Graz (Austria), 21-23 september, 1998. |
| 8) | S. Alfonzetti, G. Borzì, N. Salerno, "Optimization of the Coating Layer of a Scattering", 8th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, Graz (Austria), 21-23 september, 1998. |
| 9) | S. Alfonzetti, G. Borzì, N. Salerno, "Scattering from Cavity-Backed Apertures in an Infinite Ground Plane by an Iterative Procedure", Conférence Européenne sur les Méthodes Numériques en Electromagnétisme, Lyon (France), 19-21 march, 1997. |
| 10) | G. Aiello, S. Alfonzetti, G. Borzì, S. Coco, N. Salerno, "Computation of Periodic Fields in Open Boundaries", Conférence Européenne sur les Méthodes Numériques en Electromagnétisme, Lyon (France), 19-21 march, 1997. |
| 11) | G. Aiello, S. Alfonzetti, G. Borzì, "Some Theoretical Aspects of the Generalized Charge Iteration Procedure", International Symposium on Theoretical Electrical Engineering, Palermo (Italy), 9-11 june, 1997. |
| 12) | G. Aiello, S. Alfonzetti, G. Borzì, S. Coco, N. Salerno, "Computation of Electrical Parameters for VLSI Circuit Design by means of the ELFIN", International Symposium on Theoretical Electrical Engineering, Palermo (Italy), 9-11 june, 1997. |
| 13) | G. Aiello, S. Alfonzetti, G. Borzì, S. Coco, N. Salerno, "An Iterative FEM Method for Analyzing Transmission Line Shielding Configurations", International Symposium on Electromagnetic Compatibility, Rome (Italy), 17-20 september, 1996. |
| 14) | S. Alfonzetti, G. Borzì, N. Salerno, "A method for the finite element solution of scattering problems in unbounded domains", 7th IGTE Symposium on Numerical Field Calculation in Electrical Engineering, Graz (Austria), 23-26 september, 1996. |
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| 1) | S. Alfonzetti, G. Borzì, "An iterative method for the solution of electromaagnetic scattering problems", SIMAI, Giardini-Naxos (Italy), 1-5 june, 1998. |
| 2) | G. Borzì, "Risoluzione Iterativa di Problemi di Diffrazione Elettromagnetica", Atti dell?11ma Riunione Nazionale di Elettromagnetismo, Florence (Italy), Oct. 1-4, 1996. |