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This paper deals with the coupled mechanical‐electrostatic analysis of a shunt capacitive MEMS switch. The mechanical and electrostatic parts of the problem are modelled by the FE and BE methods, respectively. The fast multipole method is applied to reduce the storage requirements and the computational cost of the BE electrostatic model. An adaptive truncation expansion of the 3D Laplace Green function is employed. The strong interaction between the mechanical and electrostatic systems is considered iteratively.

The present paper deals with the fast multipole acceleration of the 2D finite element‐boundary element modelling of electromechanical devices. It is shown that the fast multipole method, usually applied to large 3D problems, can also lead to a reduction in computational time when dealing with relatively small 2D problems, provided that an adaptive truncation scheme for the expansion of the 2D Laplace Green function is used. As an application example, the 2D hybrid modelling of a linear actuator is studied, taking into account saturation, the voltage supply and the mechanical equation. The computational cost without and with fast multipole acceleration is discussed for both the linear and nonlinear case.

To develop a sub‐domain perturbation technique for efficiently modeling moving systems in magnetodynamics with a magnetic field h‐conform finite element (FE) formulation.

A reference problem is first solved in a global mesh excluding some moving regions and thus avoiding the inclusion of their meshes. Its solution gives the sources for a sequence of perturbation problems with the supplementary moving magnetic and conductive regions. Each of these sub‐problems requires an appropriate proper volume mesh of the associated moving region and its surrounding region, with no need of interconnection. The solutions are transferred from one problem to the other through projections of source fields between meshes.

The consideration of sub‐problems and associated sources, in a sequence of perturbation problems, leads to a significant speed‐up of the repetitive solutions in analyses of moving systems. A free movement in any direction can be considered with no need of remeshing.

When working with the perturbation fields, the volume sources can be limited to the moving regions, what allows for homogeneous perturbation boundary conditions and reduces the computational efforts for projecting and evaluating the sources. The curl‐conformity of the unknown magnetic field is preserved during the whole process thanks to the use of edge FEs for both the magnetic field and the intermediate source quantities. The sub‐problem approach also gives an easy way to directly express the time derivatives in moving frames.

The aim of the present paper is to compare the performances of a finite‐element perturbation technique applied either to the h‐ conform magnetodynamic formulation or to its b‐ conform counterpart in the frame of nondestructive eddy‐current testing problems.

In both complementary perturbation techniques, the computation is split into a computation without defect (unperturbed problem) and a computation of the field distorsion due to its presence (perturbation problem). The unperturbed problem is conventionally solved in the complete domain. The source of the perturbation problem is then determined by the projection of the unperturbed solution in a relatively small region surrounding the defect. The discretisation of this reduced domain is chosen independently of the dimensions of the excitation probe and the specimen under study and is thus well adapted to the size of the defect.

The accuracy of the perturbation model is evidenced by comparing the results of the two counterpart formulations to those achieved in the conventional way for different dimensions of the reduced domain. The size of the reduced domain increases with the size of the defect at hand. This proposed sub‐domain approach eases considerably the meshing process and speeds‐up the computation for different probe positions.

At a discrete level, the impedance change due to the defect is efficiently and accurately computed by integrating only over the defect itself and a layer of elements in the reduced domain that touches its boundary. Therefore, no integration of any flux variation in the coils is required.

The aim of this paper is the experimental validation of an original time‐domain thin‐shell formulation. The numerical results of a three‐dimensional thin‐shell model are compared with the measurements performed on a heating device at different working frequencies.

A time‐domain extension of the classical frequency‐domain thin‐shell approach is used for the finite‐element analysis of a shielded pulse‐current induction heater. The time‐domain interface conditions at the shell surface are expressed in terms of the average flux density vector in the shell, as well as in terms of a limited number of higher‐order components.

A very good agreement between measurements and simulations is observed. A clear advantage of the proposed thin‐shell approach is that the mesh of the computation domain does not depend on the working frequency anymore. It provides a good compromise between computational cost and accuracy. Indeed, adding a sufficient number of induction components, a very high accuracy can be achieved.

The method is based on the coupling of a time‐domain 1D thin‐shell model with a magnetic vector potential formulation via the surface integral term. A limited number of additional unknowns for the magnetic flux density are incorporated on the shell boundary.

The purpose of this paper is to develop a sub‐domain perturbation technique for refining magnetic circuit models with finite element (FE) models of different dimensions.

A simplified problem considering ideal flux tubes is first solved, as either a 1D magnetic circuit or a simplified FE problem. Its solution is then corrected via FE perturbation problems considering the actual flux tube geometry and the exterior regions, that allow first 2D and then 3D leakage fluxes. Each of these sub‐problems requires an appropriate proper volume mesh, with no need of interconnection. The solutions are transferred from one problem to the other through projections of source fields between meshes.

The developed perturbation FE method allows to split magnetic circuit analyses into subproblems of lower complexity with regard to meshing operations and computational aspects. A natural progression from simple to more elaborate models, from 1D to 3D geometries, is thus possible, while quantifying the gain given by each model refinement and justifying its utility.

Approximate problems with ideal flux tubes are accurately corrected when accounting for leakage fluxes via surface sources of perturbations. The constraints involved in the subproblems are carefully defined in the resulting FE formulations, respecting their inherent strong and weak nature. As a result, an efficient and accurate computation of local fields and global quantities, i.e. flux, MMF, reluctance, is obtained. The method is naturally adapted to parameterized analyses on geometrical and material data.

The purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors.

An approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields.

The results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost.

Limitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor.

The efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

To develop a subdomain perturbation technique to calculate skin and proximity effects in inductors within frequency and time domain finite element (FE) analyses.

A reference limit eddy current FE problem is first solved by considering perfect conductors via appropriate boundary conditions. Its solution gives the source for eddy current FE perturbation subproblems in each conductor with its actual conductivity. Each of these problems requires an appropriate mesh of the associated conductor and its surrounding region.

The skin and proximity effects in inductors can be accurately determined in a wide frequency range, allowing for a precise consideration of inductive phenomena as well as Joule losses calculations in thermal coupling.

The developed subdomain method allows to accurately determine the current density distributions and ensuing Joule losses in conductors of any shape, not only in the frequency domain but also in the time domain. It extends the domain of validity and applicability of impedance boundary condition techniques. It also allows the solution process to be lightened, as well as efficient parameterized analyses on signal forms and conductor characteristics.

This paper aims to apply the non-linear impedance boundary condition (IBC) for a linear piecewise B–H curve in frequency domain simulations to find the equivalent impedance of a simple induction heating system model.

An electromagnetic description of the inductor system is performed to substitute the effects of the induction load, for a mathematical condition, the so-called IBC. This is suitable to be used in electromagnetic systems involving high conductive materials at medium frequencies, as it occurs in an induction heating system.

A reduction of the computational cost of electromagnetic simulation through the application of the IBC. The model based on linear piecewise B–H curve simplifies the electromagnetic description, and it can facilitate the identification of the induction load characteristics from experimental measurements.

This work is performed to assess the feasibility of using the non-linear boundary impedance condition of materials with linear piecewise B–H curve to simulate in the frequency domain with a reduced computational cost compared to time domain simulations.

In this paper, the use of the non-linear boundary impedance condition to describe materials with B–H curve by segments, which can approximate any dependence without hysteresis, has been studied. The results are compared with computationally more expensive time domain simulations.

This paper seeks to develop a sub‐domain perturbation technique to efficiently calculate strong skin and proximity effects in conductors within frequency and time domain finite element (FE) analyses.

A reference eddy current FE problem is first solved by considering perfect conductors. This is done via appropriate boundary conditions (BCs) on the conductors. Next the solution of the reference problem gives the source for eddy current FE perturbation sub‐problems in each conductor then considered with a finite conductivity. Each of these problems requires an appropriate volume mesh of the associated conductor and its surrounding region.

The skin and proximity effects in both active and passive conductors can be accurately determined in a wide frequency range, allowing for precise losses calculations in inductors as well as in external conducting pieces.

The developed method allows one to accurately determine the current density distributions and ensuing losses in conductors of any shape, not only in the frequency domain but also in the time domain. Therefore, it extends the domain of validity and applicability of impedance‐type BC techniques. It also offers an original way to uncouple FE regions that allows the solution process to be lightened, as well as efficient parameterized analyses on the signal form and the conductor characteristics.