Boundary Condition Iteration Research Articles

Optimization of Frequency Selective Surfaces for the Design of Electromagnetic Mantle Cloaks

A full optimization procedure that combines the parallel self-adaptive low-high evaluation-evolutionary algorithm with the finite element method-robin boundary condition iteration numerical method is proposed for the design of electromagnetic mantle cloaks enclosing arbitrary objects. The procedure is efficiently applied to optimize an ultrathin, conformal frequency selective surface (FSS), placed around an inhomogeneous dielectric cylinder to be made invisible. Two very different optimal solutions have been found, and this can be a great advantage for the designer using the proposed optimization strategy.

Optimization of the shape of an induction heating device in the presence of skin effect in the coils

Purpose The optimization of the cross section of an axisymmetric induction heating device is performed by means of genetic algorithms (GAs). Design/methodology/approach The hybrid finite element method–Dirichlet boundary condition iteration method is used to deal with the unbounded nature of the field. The formulation of the electromagnetic problems takes into account skin and proximity effects in the source currents. Findings The convergence of GAs towards the optimum is very fast, since less than a thousand analyses have been necessary. Originality/value A special derivation of the finite element global system is presented which allows us to save computing time.

Evaluation of Inflight Deicing Performance for Designed Electrothermal Systems with Experimental Verification

The deicing performance of an electrothermal system is critical to inflight safety; accordingly, a numerical study on dynamic deicing and the subsequent experimental verification are both performed. Different electrothermal systems are designed first; then, a coupling calculation method is developed by employing the equivalent heat transfer coefficient and the boundary condition iteration. The performance analysis is conducted by considering the variations of temperature and ice accretion, with their transient characteristics investigated. At the end of heating time, the minimum surface temperature ranges from 5.5 to 10°C, without the internal structure overheated. And, the maximum thickness of ice accretion is determined to be 1.39 mm, which is tolerable for the aerodynamic performance of the aircraft. Certain advantages of system B are found in the heating rate, whereas the cross-shaped parting strip installed on system A successfully prevents the leading edge from icing and divides the icing area. Furthermore, several effective deicing cycles of the two systems are observed during the wind-tunnel test, indicating the rationality of the preliminary design. The average and standard deviations of the experimental and numerical results are 13.2 and 0.79, respectively, which verify the accuracy of the dynamic simulation model.

Transient simulation and analysis of wing electrothermal ice protection system

The transient behaviour of electric heating and de-icing of the wing is studied by numerical method. The thermal convection coupling method based on the equivalent heat transfer coefficient and the boundary condition iteration is developed for the two designed schemes of the electric heating system. According to the surface temperature, the internal temperature, and the icing condition, the system transient performance is investigated. The purpose of this study is to establish the de-icing transient model of the wing ice protection system, simulate the transient de-icing process and form the method of performance estimation. The results under different working conditions show that the temperature distribution of the skin surface is not uniform, rather presents certain regularity. The rising rate of temperature decreases with the increase of the temperature. The trend is more obvious at lower ambient temperature, when the ambient temperature rises, the surface temperature rises rapidly in a short period. Scheme 2 has certain advantages in heating capability, while the hot knives structure of scheme 1 can narrow and split the icing area.

Solution of Open-Boundary Problems by Means of the Hybrid FEM-GDBCI Method

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.

Eddy Current Computation by the FEM-SDBCI Method

In this paper, the hybrid finite-element method (FEM) singular Dirichlet boundary condition iteration method, already developed for 2-D skin-effect problems, is extended to the 3-D solution of time-harmonic eddy current problems. The method is similar to the well-known FEM-boundary-element method (BEM), but it assumes a Dirichlet boundary condition on the truncation boundary instead of a Neumann one. Shorter solving times are obtained with respect to FEM-BEM.

FEM-DBCI Solution of Open-Boundary Electrostatic Problems in the Presence of Floating Potential Conductors

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.

Efficient Analysis of Grounding Systems by Means of the Hybrid FEM–DBCI Method

In the design of a grounding system, technical and normative constraints have to be met. Therefore, it is necessary to use a tool that is able to accurately estimate the values of the significant parameters of the grounding system, such as earth resistance and touch-and-step voltages. The computation of such quantities calls for the solution of a 3-D open-boundary static electromagnetic field problem, which should take into account the nonhomogeneous structure of soil. The hybrid finite-element method–Dirichlet boundary condition iteration method is applied to the solutions of such problems. A great advantage of this method is that it directly provides the electric potential distribution on the earth surface as part of the solution. Some grounding systems are analyzed, and the comparisons of the results with those obtained by other methods are made.

Electromagnetic Scattering Computation by Means of the Hybrid FEM-SRBCI Method

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.

Solution of skin-effect problems by means of the hybrid SDBCI method

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.

Improving the integral equation in the hybrid FEM‐RBCI method for scalar electromagnetic scattering problems

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.

A Novel Parallelization Method for the Edge-Elements-Based Integral Equation

This letter introduces a new parallelization method for the computation of the discrete integral equation where edge elements are used as the discretization base. This new method does not need traditional mesh partitions and can be implemented with minimal programming efforts. The new method has been implemented using OpenMP for the robin boundary condition iteration (RBCI), but it applies to the method of moments as well. It is based on the subdivision of the discrete surface's elements into groups in such a way that elements belonging to the same group can be treated in parallel.

A Modified FEM-DBCI Method for Static and Quasi-Static Electromagnetic Field Problems

This paper presents a modified version of the hybrid FEM-DBCI (Finite Element Method-Dirichlet Boundary Condition Iteration) method to solve static and quasi-static electromagnetic field problems in open boundary domains. The modification consists of overlapping the fictitious truncation boundary with the integration one, as in the FEM-BEM (Boundary Element Method) method. The global algebraic system obtained is solved iteratively by means of the GMRES (Generalized Minimal Residual) solver, applied virtually to a reduced system in which the unknowns are those relative to the potential on the truncation boundary only. Some validation examples are provided.

Improved Selection of the Integration Surface in the Hybrid FEM-DBCI Method

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.

Stochastic Optimization of Magnetic Shields in Induction Heating Applications by Means of the FEM-DBCI Method and the SALHE Evolutionary Algorithm

In this paper, stochastic optimization of the shielding of an axisymmetric induction heating system is performed by means of the self-adaptive low-high evaluations evolutionary algorithm (SALHE-EA). The finite element formulation of the electromagnetic problem is based on the magnetic vector potential. The hybrid finite element method Dirichlet boundary condition iteration (FEM-DBCI) method is used to deal with the unbounded nature of the field problem and to reduce the computing effort required for optimization.

Thermal analysis of an eddy‐current heated piece by means of the FEM‐DBCI method

PurposeThis paper aims to propose a hybrid method, called finite element method‐Dirichlet boundary condition iteration (FEM‐DBCI), for the computation of time‐harmonic eddy current problems inside a conductor heated by coils in 3D open‐boundary geometry.Design/methodology/approachThe method assumes the electrical field as unknown on a mesh of tetrahedral edge elements. The heating power density inside the conductor is then computed and a steady‐state thermal analysis is performed on the same mesh of nodal tetrahedra to calculate the temperature distribution inside the heated piece, taking radiation and convection into account. A numerical example is also provided.FindingsThe method couples a differential equation for the interior problem in terms of the electric fields with an integral equation for the exterior one. The global algebraic system is efficiently solved in an iterative way.Originality/valueThe paper illustrates the computation of time‐harmonic eddy current problems inside a conductor heated by coils.

Analysis of the Nonconcentric Reflector Antenna-in-radome System by the Iterative Reflector Antenna and Radome Interaction

Nonconcentric reflector antenna-in-radome systems are used in applications especially requiring smaller radome coverages. The analysis of this two-dimensional geometry is performed for the E-polarization case. Here the geometry is decomposed into two parts and the analysis is performed by imposing the boundary conditions on each part as an iterative manner. This is known as the iterative boundary condition method in the literature. Convergence and accuracy are established numerically and it is seen that the expectations are really verified in reasonable CPU times. Also various numerical results are obtained for the description of the radiation characteristics.

Improving the accuracy of the integral equation in the hybrid FEM-DBCI method for open boundary electrostatic problems

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

DBCI Solution of Helical Scalar Potential Problems in Unbounded Domains

Dirichlet boundary condition iteration (DBCI) is a hybrid method to solve electromagnetic problems in unbounded domains in conjunction with the standard finite-element method. The purpose of the paper is to extend the capabilities of DBCI to compute open-boundary electrical and magnetic scalar potentials exhibiting helical symmetry. The potential values obtained with DBCI agree well with those derived from an analytical solution used to validate the method. The DBCI is also applied to the study of a capacitance sensor used to measure the concentration of phases in a fluid mixture.

Finite-element solution of eddy-current problems in unbounded domains by means of the hybrid FEM-DBCI method

A hybrid method, called finite-element method-Dirichlet boundary-condition iteration (FEM-DBCI), is described for the finite-element solution of time-harmonic eddy current problems in three-dimensional unbounded domains. The procedure couples a differential equation for the interior problem in terms of the electric field with an integral equation for the exterior one, which expresses the Dirichlet condition on the truncation boundary. The global algebraic system is efficiently solved in an iterative way. FEM-DBCI leads to shorter solving times and not much higher memory requirements with respect to the FEM-boundary-element method.