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The tensor complex permeability of a multi-turn coil with elliptic cross-section is analytically expressed. In field analysis, a multi-turn coil can be modeled by the uniform material that has the present tensor complex permeability. It is shown that the frequency characteristic of the present tensor complex permeability is in good agreement with that evaluated by finite element method applied to a unit cell of the multi-turn coil region.

The authors introduce a new method to evaluate the complex permeability of a multi-turn rectangular coil. To obtain the complex permeability of a rectangular coil in a closed form, it is approximated as an elliptic coil. Because the rectangular coil has different complex permeabilities in the vertical and horizontal directions, the complex permeability have to be defined in a tensor form. It suffices to discretize the coil region into rather coarse finite elements without considering the skin depth in contrast to the conventional finite element method.

The proposed method is shown to give the impedance of multi-turn coils which is in good agreement with results obtained by the conventional finite element (FE) analysis. By extending the proposed approach, the authors can easily perform 3D FE analysis without difficulty in discretization of the coil region with fairly fine finite elements. Moreover, they found that the approximation of rectangular coils as the elliptic coils is valid for analysis of quasi-static fields using this homogenization method.

The novelty of this study is in the approximation of the rectangular coils with elliptic coils, and the complex permeability for them is formulated here in a closed form. The proposed formula includes that for the round coils. Using the present method, the authors analyze the rectangular coils without fine discretization.

The purpose of this paper is to determine the broadband frequency response of the impedance matrix of wireless power transfer (WPT) systems comprising litz wire coils.

A finite-element (FE)-based method is proposed which treats the microstructure of litz wires by an auxiliary cell problem. In the macroscopic model, litz wires are represented by a block with a homogeneous, artificial material whose properties are derived from the cell problem. As the frequency characteristics of the material closely resemble a Debye relaxation, it is possible to convert the macroscopic model to polynomial form, which enables the application of model reduction techniques of moment-matching type.

FE-based model-order reduction using litz wire homogenization provides an efficient approach to the broadband analysis of WPT systems. The error of the reduced-order model (ROM) is comparable to that of the underlying original model and can be controlled by varying the ROM dimension.

Since the present model does not account for displacement currents, the operating frequency of the system must lie well below its first self-resonance frequency.

The proposed method is well-suited for the computer-aided design of WPT systems. It outperforms traditional FE analysis in computational efficiency.

The presented homogenization method employs a new formulation for the cell problem which combines the benefits of several existing approaches. Its incorporation into an order-reduction method enables the fast computation of broadband frequency sweeps.

Understanding the fluid flow through rock masses, which commonly consist of rock matrix and fractures, is a fundamental issue in many application areas of rock engineering. As the equivalent porous medium approach is the dominant approach for engineering applications, it is of great significance to estimate the equivalent permeability tensor of rock masses. This study aims to develop a novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses.

The radial point interpolation method (RPIM) and finite element method (FEM) are coupled to simulate the seepage flow in fractured porous rock masses. The rock matrix is modeled by the RPIM, and the fractures are modeled explicitly by the FEM. A procedure for numerical experiments is then designed to determinate the equivalent permeability tensor directly on the basis of Darcy’s law.

The coupled RPIM-FEM method is a reliable numerical method to analyze the seepage flow in fractured porous rock masses, which can consider simultaneously the influences of fractures and rock matrix. As the meshes of rock matrix and fracture network are generated separately without considering the topology relationship between them, the mesh generation process can be greatly facilitated. Using the proposed procedure for numerical experiments, which is designed directly on the basis of Darcy’s law, the representative elementary volume and equivalent permeability tensor of fractured porous rock masses can be identified conveniently.

A novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses is proposed. In the approach, the RPIM and FEM are coupled to simulate the seepage flow in fractured porous rock masses, and then a numerical experiment procedure directly based on Darcy’s law is introduced to estimate the equivalent permeability tensor.

The purpose of this paper is to present a fully automated numerical tool for computing the effective permeability of porous media from digital images which come from the modern imagery technique.

The permeability is obtained by the homogenization process applied to a periodic rigid solid in which the fluid flow is described by the Stokes equations. The unit cell problem is solved by using the Fast Fourier Transform (FFT) algorithm, well adapted for the microstructures defined by voxels.

Various 3-D examples are considered to show the capacity of the method. First, the case of flow through regular arrays of aligned cylinders or spheres are considered as benchmark problems. Next, the method is applied to some more complex and realistic porous solids obtained with assemblies of overlapping spherical pores having identical or different radii, regularly or randomly distributed within the unit cell.

The use of FFT allows the resolution of high-dimension problems and open various possibilities for computing the permeability of porous microstructures coming from X-ray microtomography.

The ability to characterise highly conducting objects, that may also be highly magnetic, by the complex symmetric rank–2 magnetic polarizability tensor (MPT) is important for metal detection applications including discriminating between threat and non-threat objects in security screening, identifying unexploded anti-personnel landmines and ordnance and identifying metals of high commercial value in scrap sorting. Many everyday non-threat items have both a large electrical conductivity and a magnetic behaviour, which, for sufficiently weak fields and the frequencies of interest, can be modelled by a high relative magnetic permeability. This paper aims to discuss the aforementioned idea.

The numerical simulation of the MPT for everyday non-threat highly conducting magnetic objects over a broad range of frequencies is challenging due to the resulting thin skin depths. The authors address this by employing higher order edge finite element discretisations based on unstructured meshes of tetrahedral elements with the addition of thin layers of prismatic elements. Furthermore, computer aided design (CAD) geometrical models of the non-threat and threat object are often not available and, instead, the authors extract the geometrical features of an object from an imaging procedure.

The authors obtain accurate numerical MPT characterisations that are in close agreement with experimental measurements for realistic physical objects. The assessment of uncertainty shows the impact of geometrical and material parameter uncertainties on the computational results.

The authors present novel computations and measurements of MPT characterisations of realistic objects made of magnetic materials. A novel assessment of uncertainty in the numerical predictions of MPT characterisations for uncertain geometry and material parameters is included.

The resin transfer molding process for composites manufacturing consists of either of two considerations, namely, the fluid flow analysis through a porous fiber preform where the location of the flow front is of fundamental importance, and the combined flow/heat transfer/cure analysis. In this paper, the continuous sensitivity formulations are developed for the process modeling of composites manufactured by RTM to predict, analyze, and optimize the manufacturing process. Attention is focused here on developments for isothermal flow simulations, and various illustrative examples are presented for sensitivity analysis of practical applications which help serve as a design tool in the process modeling stages.

This paper aims at the problem of surrounding rock excavation damage zone of tunneling in the rich water region, this paper aims to propose a new seepage-stress-damage coupling model and studied the numerical algorithm. This reflects the characteristics of rock damage evolution, accompanied by plastic flow deformation and multi-field interaction.

First of all, rock elastoplastic damage constitutive model based on the Drucker–Prager criterion is established, the fully implicit return mapping algorithm is adopted to realize the numerical solution. Second, based on the relation between damage variation and permeability coefficient, the rock stress-seepage-damage model and multi-field coupling solving iterative method are presented. Finally, using the C++ language compiled the corresponding programs and simulated tunnel engineering in the rich water region.

Results show that difference evolution-based back analysis inversed damage parameters well, at the same time the established coupling model and calculating program have more advantages than general conventional methods. Multiple field coupling effects should be more considered for the design of tunnel support.

The proposed method provides an effective numerical simulation method for the construction of the tunnel and other geotechnical engineering involved underground water problems.

The purpose of this paper is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters like the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution.

The Fourier transform method is used to solve frequency-dependent heat transfer problems. The periodic Lippmann–Schwinger integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors, which can then be solved by iteration schemes.

Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems.

The formulation of the method is constructed using static and dynamic Green operators and can be applied to pixelized microstructure issued from tomography images.

Perfectly matched layers (PMLs) are used for reflectionless truncation of the problem boundaries in finite element methods applications. In this paper, the method of PMLs is extended to truncate any lossless medium and the method is implemented for the T formulation.

The basic concept behind PMLs is to create an artificial material with a complex and diagonal anisotropic permittivity and permeability. For the A, V formulation PMLs are well known.

It is shown that it is possible to truncate any linear lossless material with PML layers, and if the material has small losses the PML works fine.

In the present paper, an artificial anisotropic lossy material is applied to a 3D edge finite‐element T, formulation to form perfectly matched layers.

The purpose of this paper is to study the microwave behaviour of effective magnetic permeability for two‐component ferrite like metamaterial medium in the direction of a biasing magnetic field. The metamaterial medium is presented as an infinite host dielectric material (air) with periodically embedded ferric cylindrical and spherical inclusions saturated with an external dc magnetic field. The study is based on the effective medium theory developed for polycrystalline metaferrites. The simulations show that the presented metamaterial can exhibit the ultra‐low refractive index (ULI) phenomenon and the phenomenon of negative magnetic permeability for the case of microwave propagation in the direction of bias.

The obtained results are based on the wave long approximation of permeability tensor of the presented metamaterial media obtained earlier by the first author. Using the standard approach, the authors apply the above expressions for the microwave propagation in direction of biasing dc magnetic field considering different polarization of the incident microwave.

The considered artificial material media can become either material with a ULI or with negative values in the GHz frequencies.

The paper is concerned with part of the theory of a new generation of artificial ferrites.