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This paper extends the hybrid finite-element method–Dirichlet boundary condition iteration method for the solution of open-boundary electrostatic problems to the case, in which some floating potential conductors are present in the system. The iterative solution scheme of the basic method is modified in order to deal with the unknown values of the potential of these conductors.

In this paper, we optimize the size and position of silver hemispherical nanoparticles arranged in a regular array embedded in a thin-film heterojunction solar cell. The metallic nanoparticles are added in order to improve solar cell efficiency by exploiting the phenomenon of plasmon resonance. A finite-element code has been employed to compute the light scattered from the device and the optimization was performed at first by means of a genetic algorithm and then by means of the parallel self-adaptive low–high evaluation evolutionary algorithm.

The self-adaptive low-high evaluation evolutionary-algorithm (SALHE-EA) is used to solve multimodal optimization problems. SALHE-EA is able to find the multiple optima of a single objective function (OF) and to give an idea of the fitness landscape in the neighborhood of these optima. This aspect is of crucial importance when the single OF is obtained using the weighted sum of the OFs, each related to a different goal of the optimization problem. This paper presents an improved version of SALHE-EA. This new version has several new features and, mainly, the suitability for parallelization.

In this paper an improved placement of the integration surface for the integral equation in the hybrid finite element method-Dirichlet boundary condition iteration (FEM-DBCI) method is achieved by selecting it as lying in the middle of the tetrahedral or hexahedral finite elements. A better accuracy is obtained with respect to the case in which the integration surface lies along the element faces. Some numerical examples are provided.

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 Green's 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.

Genetic algorithms (GAs) are widely used in the optimization of electromagnetic devices. However, if finite element analyses are needed for the evaluation of the objective function, GAs require a long computation time. They also need a difficult tuning session before starting optimization, to select the best configuration of the parameters that control the algorithm. This paper proposes a universal choice of the GA parameters in order to spare the designer the tuning session and to reduce the computing time for the whole procedure.

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.

In this paper the charge iteration procedure is extended to cover the computation of spatially-periodic electrostatic fields. A fictitious boundary which encloses all the conductors is introduced inside the basic space period. The unknown electric potential on the fictitious boundary is initially guessed and then iteratively improved making use of a suitable periodic Green's function.

Charge iteration is an FEM procedure, devised by the authors for the computation of electrical fields in open boundary domains. In the procedure, a closed fictitious boundary is introduced enclosing all the conductors. On this boundary the electrical potential is first guessed and then iteratively improved according to the current solution by means of the free-space Green's function until convergence takes place. In this paper the procedure is generalized by allowing not only Dirichlet conditions, but also Neumann and Robin ones to he imposed on the fictitious boundary. Some reduction in computational effort comes from this generalization as pointed out by theoretical and numerical examples.

Current iteration is a purely FEM iterative procedure devised by the authors to deal with boundless skin-effect problems in terms of the magnetic vector potential. If material non-linearities occur, a Newton-Raphson solver, nested inside the current iteration, has to be used. A computing strategy is described which allows us to achieve overall computational efficiency in carrying out the two nested iterations.

This paper presents an iterative FEM procedure for the solution of unbounded non-linear transient magnetic field problems. The boundlessness of the domain is dealt with by introducing a fictitious boundary defining a bounded region. At each discrete time, by assuming a first guess for the Dirichlet condition on such a boundary a standard FEM solution for the bounded non-linear transient problem is carried out; the results of the FEM analysis are used to update the Dirichlet condition on the fictitious boundary; the above steps are then iterated until a solution to the unbounded problem is reached. The procedure is rapidly convergent, accurate and easy to implement.

Charge iteration is an N-dimensional (N=1,2,3) FEM procedure for the solution of unbounded electrostatic fields created by voltaged conductors. In the procedure a fictitious boundary enclosing all the conductors defines a bounded region where the unbounded problem is solved iteratively using the charge lying on conductors to improve the Dirichlet condition on the fictitious boundary. The convergence properties of charge iteration in the presence of overrelaxation are investigated. A remarkable reduction in computational effort is obtained due to the reduction in the number of iterations and the restriction of the bounded domain to the vicinity of the conductors where the unrelaxed procedure exhibits a divergent behaviour. The above advantages are illustrated by an analytical verification and by a numerical example.

An iterative finite-element procedure is described for the solution of skin-effect problems, under the assumption of quasi-static TEM conditions. The systems considered consist of parallel straight conductors of arbitrary cross section, with inhomogeneous conductivity and permeability, embedded in an unbounded homogeneous dielectric medium. A fictitious boundary enclosing all the conductors is introduced; an initial guess for the magnetic vector potential is assumed on this boundary and is iteratively improved according to the Laplacian behaviour of the potential outside the conductors. An example of application to a simple transmission line is given. >

The numerical treatment of unbounded electrostatic field problems can be conveniently integrated in standard FE codes for bounded problems, by using charge iteration, an efficient, N-dimensional FE procedure recently presented by the authors. In this paper its convergence characteristics (accuracy and number of iteration steps) are investigated. Comparisons with known analytical solutions are used in order to assess the precision achievable. >

An iterative procedure is presented for the finite-element computation of axisymmetric electrostatic fields in unbounded domains. In the procedure the original unbounded problem is solved by using successive evaluations of the potential on a fictitious boundary enclosing all the conductors of the problem, according to the charge lying on their surface. For simplex Lagrangian elements universal matrices are used for a fast and efficient computation of this charge. The main advantage of this procedure lies in its ease of implementation in a standard bounded problem finite-element code and in the accuracy of the computed results. >