Giuseppe Borzi

Finite-element solution to electromagnetic scattering problems by means of the Robin boundary condition iteration method

A new numerical method, called the Robin boundary condition iteration (RBCI), is proposed for the finite-element (FE) solution of electromagnetic scattering problems in open boundary domains. The unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous Robin (mixed) boundary condition is assumed for the Helmholtz equation in the bounded domain. The Robin condition is expressed by means of an integral formula (the second Green identity) in terms of the field in the interior of the bounded domain, with the integration surface being a surface strictly enclosed by the truncation boundary. The discretized differential and integral equations are then coupled together to solve the problem. The formulation is completely immune from the well-known interior resonance problems. A simple and effective iterative solving scheme is described. Examples are also provided to validate RBCI and compare it with other methods.

An improved solution scheme for open-boundary skin effect problems

FEM/DBCI (Dirichlet Boundary Condition Iteration) is a hybrid method which has been successfully applied to the finite element solution of static and quasistatic unbounded field problems. It is based on the iterative improvement of a Dirichlet condition on a fictitious boundary enclosing all the conductors, making use of the free-space Greens function. In this paper it is shown that for two-dimensional skin effect problems a more robust solving strategy can be pursued by means of GMRES, obtaining a reduction in both CPU and storage requirements.

An iterative solution to scattering from cavity-backed apertures in a perfectly conducting wedge

In this paper it is shown how the Robin iteration procedure, already proposed by the authors for the solution of electromagnetic scattering problems, can be easily adapted to scattering from cavities embedded in a perfectly-conducting wedge. The procedure couples a differential equation for the interior problem with an integral equation for the exterior one. A suitable choice of the Robin (mixed) boundary condition on the fictitious boundary dividing the interior and exterior domains avoids resonances.

An Algebraic Multigrid Method for a Class of Elliptic Differential Systems

The development, numerical investigation, and analysis of an algebraic multigrid (AMG) method for the numerical solution of a representative class of elliptic differential systems are presented. Our AMG scheme is based on the AMG strategy of Brandt, Ruge, and Stuben. However, the present approach may be implemented within other AMG schemes. By means of numerical experiments with model problems arising from some application areas, it is demonstrated that the computational performance of the proposed AMG scheme is comparable to that of AMG applied to a single scalar equation. An AMG convergence theory is presented that extends convergence results for AMG methods for scalar problems to the case of AMG applied to elliptic systems. Some details of our AMG implementation are given.

A fast solving strategy for two-dimensional skin effect problems

The authors show that the global matrix in the finite element integro-differential formulation of two-dimensional skin effect problems can be partitioned into the sum of a sparse matrix and a product of two equal arrays for each conductor of the multiconductor system. This partition allows both a great memory saving and a drastic reduction in the conjugate gradient solution time.

Numerical Computation of Antenna Parameters by Means of RBCI

A new numerical method, called Robin Boundary Condition Iteration (RBCI), recently devised by the authors for the finite element solution of electromagnetic scattering problems is adapted to the numerical computation of antenna parameters. In RBCI the unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the antenna and on which a suitable nonhomogeneous Robin (mixed) boundary condition is assumed for the Helmholtz equation in the bounded domain. The Robin condition is expressed by means of an integral formula (the 2nd Green identity) in terms of the field in the interior of the bounded domain, the integration surface being strictly enclosed by the truncation boundary. The discretized differential and integral equations are then coupled together to solve the problem. A simple and effective iterative solving scheme is described. The computation of the antenna impedance in postprocessing is discussed. Examples are also provided to explain the method.

Scattering from three-dimensional cavity-backed apertures in an infinite ground plane by RBCI

This paper describes an extension of the Robin boundary condition iteration (RBCI) method to solve the problem of scattering from three-dimensional cavities embedded in an infinite ground plane. The proposed method is a hybrid one since it combines a differential equation for the interior and the neighborhood of the cavities with an integral equation for the rest of the unbounded domain. A suitable choice of the boundary condition (of the nonhomogeneous mixed type) on the fictitious boundary dividing the two parts of the domain avoids resonances whatever the frequency. Moreover, an iterative solver is described for the efficient solution of the discretized global system of linear equations.

Some considerations about the perfectly matched layer for static fields

This paper discusses the perfectly matched layer method recently proposed for the computation of static or quasistatic fields in open boundaries. In particular it is shown how the method can be derived by means of a particular co‐ordinate transformation applied to a finite‐size isotropic domain surrounding the system of interest. The method is therefore equivalent to a trivial truncation from the point of view of both accuracy and computing time.

A GMRES iterative solution of FEM‐BEM global systems in skin effect problems

Purpose – This paper aims to extend an efficient method to solve the global system of linear algebraic equations in the hybrid finite element method – boundary element method (FEM‐BEM) solution of open‐boundary skin effect problems. The extension covers the cases in which the skin effect problem is set in a truncated domain in which no homogeneous Dirichlet conditions are imposed.Design/methodology/approach – The extended method is based on use of the generalized minimal residual (GMRES) solver, which is applied virtually to the reduced system of equations in which the unknowns are the nodal values of the normal derivative of the magnetic vector potential on the fictitious truncation boundary. In each step of the GMRES algorithm the FEM equations are solved by means of the standard complex conjugate gradient solver, whereas the BEM equations are not solved but used to perform fast matrix‐by‐vector multiplications. The BEM equations are written in a non‐conventional way, by making the nodes for the potenti...

Trigonometric approximations for the computation of Radar cross sections

Trigonometric approximation methods for the interpolation of the far field of a scatterer lit up by plane waves are presented. The Wacker method, commonly used to determine the far field of an antenna from spherical near field measurements, is adapted to decompose the scattered field in a finite series of vector spherical harmonics. The decomposition coefficients are used to assess the accuracy of the computed field and to efficiently store the far field profile. These coefficients are approximated by trigonometric functions up to a given order which can be estimated from the geometry of the scatterer. In this way an efficient procedure for the interpolation of monostatic and bistatic radar cross sections is obtained.