Search

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, the hybrid finite-element method-Galerkin Dirichlet boundary condition iteration method is described for the finite-element solution of a variety of low-frequency electromagnetic field problems in open boundary domains. The method assumes a Dirichlet boundary condition on the truncation boundary and its imposition is made by means of a Galerkin integral equation over another surface strictly enclosed by the truncation boundary.

In this paper, the authors propose a modified version of the hybrid finite element method-Robin boundary condition iteration (FEM-RBCI) method to solve scalar scattering problems, such as 2-D electromagnetic and 3-D acoustic ones. In the modified method, called FEM-singular RBCI, the integration surface coincides with the truncation one, so that the integral equation becomes singular.

Purpose – The purpose of this paper is to present a modified version of the hybrid Finite Element Method-Dirichlet Boundary Condition Iteration method for the solution of open-boundary skin effect problems. Design/methodology/approach – The modification consists of overlapping the truncation and the integration boundaries of the standard method, so that the integral equation becomes singular as in the well-known Finite Element Method-Boundary Element Method (FEM-BEM) method. The new method is called FEM-SDBCI. Assuming an unknown Dirichlet condition on the truncation boundary, the global algebraic system is constituted by the sparse FEM equations and by the dense integral equations, in which singularities arise. Analytical formulas are provided to compute these singular integrals. The global system is solved by means of a Generalized Minimal Residual iterative procedure. Findings – The proposed method leads to slightly less accurate numerical results than FEM-BEM, but the latter requires much more computing time. Practical implications – Then FEM-SDBCI appears more appropriate than FEM-BEM for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices. Originality/value – Note that FEM-SDBCI assumes a Dirichlet condition on the truncation boundary, whereas FEM-BEM assumes a Neumann one.

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.

The Robin iteration procedure is a technique for the FEM computation of electromagnetic scattering fields in unbounded domains. It is based on the iterative improvement of the known term of a non‐homogeneous Robin condition on a fictitious boundary enclosing the scatterer. In this paper it is shown that the procedure is equivalent to the application of the Richardson method to a reduced system and that the use of GMRES significantly reduces the computational effort.

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 iterative procedure for the finite element computation of unbounded electrical fields, created by voltaged conductors. It makes use of a fictitious boundary, enclosing all the conductors, on which the electrical potential is first guessed and then iteratively improved according to the charge lying on the conductor surfaces. Highlights the theoretical foundations of the procedure outside any numerical context. From this useful insight, obtains a model which can aid the user in utilization of the numerical version of the procedure.

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. >

This paper presents a modified version of the hybrid FEM-DBCI method for the solution of time-harmonic skin effect problems in open boundaries. In this new version of the method the fictitious truncation boundary coincides with the integration one, as in the FEM-BEM method. The global algebraic system obtained is solved iteratively by means of the GMRES solver. Some validation examples are provided.

Purpose – The purpose of this paper is to improve the accuracy of the integral equation of the hybrid FEM‐RBCI (Finite Element Method‐Robin Boundary Condition Iteration) method for the numerical solution of two‐dimensional electromagnetic (or acoustic) scattering problems.Design/methodology/approach – This accuracy improvement is achieved by selecting the integration curve as straight segments lying in the middle of the triangular finite elements. An accuracy improvement is obtained as compared with selecting the integration curve as constituted by element sides.Findings – The improved FEM‐RBCI method described in this paper leads to accuracies of the numerical results which are better than those obtained by selecting the integration curve by element sides.Originality/value – The paper presents results for a simple two‐dimensional structure: a dielectric circular cylinder.

An improved placement of the integration surface for the integral equation in the hybrid FEM-RBCI method is achieved by selecting such surface as lying in the middle of tetrahedral finite elements. A better accuracy is obtained with respect to the case in which the integration surface lies along the finite element faces.

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. >

This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of open-boundary electrostatic field problems. Both methods couple a differential equation for the interior problem with an integral equation for the exterior one. The comparison shows that FEM-BEM is more accurate than FEM-DBCI but requires more computing time.

This paper extends an iterative method to efficiently solve the global algebraic system of equations obtained by applying the hybrid FEM-BEM method to cases in which the field is due to charge distributions only, that is, when conductors with assigned potential (Dirichlet conditions) are not present. In the proposed approach, a conjugate gradient solver is used to solve the singular FEM equations, whereas the BEM equations are modified.

This paper describes a new family of axisymmetric nodal boundary elements to be used in the hybrid FE-BE method to deal with unbounded static and quasi-static electromagnetic field problems. The scalar field is developed by means of classical polynomial shape functions of a given order, whereas its normal derivative is developed with lower-order shape functions.

This paper reviews some solving procedures for unbounded electromagnetic field problems, based on the integral representation of the unknown boundary condition on the truncation fictitious boundary. Three problems are considered: electrostatic, time-harmonic skin effect, and time-harmonic scattering in unbounded domains. These problems are formulated, respectively, by means of the hybrid FEM-BEM, FEM-DBCI and FEM-RBCI methods, which in all cases lead to global algebraic systems which are partly sparse and partly dense. The paper shows that a very good solving strategy is based on the use of the GMRES solver, virtually applied to a suitably reduced algebraic system, in which the unknowns are only the truncation boundary ones.

This paper presents a novel family of nodal boundary elements to be used in the context of the hybrid FEM-BEM method to deal with unbounded static and quasi-static electromagnetic field problems. In this new type of boundary elements the scalar field is developed by means of classical polynomial shape functions of a given order, whereas its normal derivative is developed with lower-order shape functions.

This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of open-boundary electrostatic field problems. Both methods couple a differential equation for the interior problem with an integral equation for the exterior one. The comparison shows that FEM-BEM is more accurate than FEM-DBCI but requires more computing time.

This paper presents a novel family of nodal boundary elements to be used in the context of the hybrid FEM-BEM method to deal with unbounded static and quasi-static electromagnetic field problems. In this new type of boundary elements the field variable is developed by means of classical polynomial shape functions of a given order, whereas its normal derivative is developed with lower-order shape functions. A numerical example is provided regarding a simple electrostatic problem.

This paper describes an iterative method to solve efficiently the global algebraic system of equations obtained by applying the hybrid finite element method-boundary element method (FEM-BEM) to the solution of open-boundary electrostatic problems. In the proposed approach, a conjugate gradient (CG) solver is used to solve the FEM equations, whereas the BEM equations are solved by making use of the direct LU solver. To do so, it is convenient to implement the BEM equations in a nonconventional way, by choosing the nodes of the potential as not coinciding with those of its normal derivative

In this paper, the accuracy of the integral equation of the hybrid finite-element-method-Dirichlet boundary condition iteration method is improved for the computation of open boundary electrostatic fields. This is achieved by selecting the integration curve (or surface) as lying in the middle of the triangular (or tetrahedral) elements. A notable improvement in accuracy is obtained compared with selecting the integration curve (or surface) as constituted by element sides

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.

An iterative procedure is described for the finite-element solution of scalar scattering problems in unbounded domains. The scattering objects may have multiple connectivity, may be of different materials or with different boundary conditions. A fictitious boundary enclosing all the objects involved is introduced. An appropriate Robin (mixed) condition is initially guessed on this boundary and is iteratively improved making use of Green's formula. It will be seen that the best choice for the Robin boundary condition is an absorbing-like one. A theorem about the theoretical convergence of the procedure is demonstrated. An analytical study of the special case of a circular cylindrical scatterer is made. Comparisons are made with other methods. Some numerical examples are provided in order to illustrate and validate the procedure and to show its applicability whatever the frequency of the incident wave. Although particular emphasis is laid in the paper on electromagnetic problems, the procedure is fully applicable to other kinds of physical phenomena such as acoustic ones. © 1998 John Wiley & Sons, Ltd.

A new accurate procedure for the FEM solution of unbounded electromagnetic scattering problems is described. The scatterers are enclosed in a fictitious boundary on which a Robin condition is initially guessed, and then iteratively improved using the Green formula. The method does not present interior resonances and is easy to implement.

Charge iteration is an iterative finite-element procedure to deal with unbounded electrical field problems 1,2,3. In the procedure a fictitious boundary BF enclosing all the conductors, defines a bounded domain. By assuming an initial guess for the potential on BF a standard FEM solution can be carried out. Starting from this first-step solution one can compute the charge density lying on the conductor surfaces and from it a new estimate (closer to the true one) of the potential on BF, by means of an appropriate free-space Green’s function. The procedure is iterated until a convergence test is satisfied.