The main problems for applying boundary element methods (BEM) in computational electromagnetism are related to the large memory requirements of matrices and convergence iterative solver. In this paper, we solve a Laplace problem with mixed conditions by making use variational symmetric direct integral equation. Galerkin discretization results densely populated that here compressed adaptive cross approximation. This leads an approximation underlying BEM-operator means so-called hierarchical...

Expressions are presented for the calculation of magnetic field components due to toroidal current-carrying conductors rectangular cross section, with angular length equal 2 pi radians and constant current density. The expressions contain complete elliptic integrals orders I II. integral order III is avoided, allowing numerical integration be carried out more easily than in past treatments problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML"...

Abstract Starting from the time‐harmonic Maxwell equations at low‐frequency eddy current approximation H– ϕ formulation is presented. An equivalent system of boundary integral second kind on conductor surface (resp. conductor/dielectric) derived. Discretizing these with a element method (BEM) yields block linear equation \[ \left[\begin{array}{cc} A_{1} &amp; B_{1} \\ \tfrac{\mu}{\mu_{0}}\tilde{B}_{2} A_{2}\end{array} \right] \left( \begin{array}{c} j \sigma \end{array}...

This paper presents numerical experiments in applying a new technique for matrix compression and preconditioning to boundary element method (BEM)-based eddy-current analysis. Following these procedures, the classical problems of BEM approaches eddy-currents analysis industrial applications, such as large memory requirements solver instability (ill-conditioning), are significantly reduced. The algorithm, based on hierarchical arithmetic adaptive cross approximation techniques, efficiently...

Adopting the integral representation of scalar potential due to double layer charge, we derive a boundary equation with one unknown solve magnetostatic problems. The charge produces gap at air-material without disturbing continuity normal magnetic flux density and makes tangential component field continuous; accordingly, conditions are fully fulfilled even unknown. is capable solving edges corners. Once solved, it gives directly by Biot-Savart law. In this paper, investigate how evaluate vertex.

In this paper, we are concerned with eddy-current analysis based on fast boundary element methods (BEM). A novel compression and preconditioning technique, adaptive cross approximation, is used to benefit from several advantages when computing problems highly permeable materials. Several numerical experiments have been performed the aim investigate performance compared finite solvers. The results validated TEAM benchmark problem P21.

When using the indirect method in magnetostatic analysis, magnetic material is represented by double-layer charge on surface. The offers an integral form of scalar potential to give a boundary equation (BIE). A unified excitation has been derived, resulting BIE capable solving generic problems. we apply standard analyze shields thin shells with high permeability, usually cannot get accurate results shielded space. To accurately solve shielding problems rough meshes, this paper propose new...

A procedure is presented for investigating the optimal shape of electrodes and dielectrics. It based on 3-D calculation electrostatic fields. The mathematical model, treatment singular cases, optimization are described. program used numerical field a disconnecting element in SF/sub 6/-gas-insulated equipment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents a novel formulation for the analysis of dielectric problems appearing in engineering design. We emphasize main advantages this approach versus classical integral equation approaches and highlight them with reference to some from praxis. also demonstrate that all known bottlenecks currently used formulations can be removed using approach. Further, we point out bad modelling praxis sometimes lead inaccurate or even completely wrong results. At end, clearly that, taking into...

Since the magnetic permeability of steel is comparatively high, skin depth may be a few millimeters even at low frequency such as 50 Hz. And so, impedance boundary condition (IBC) works effectively in most eddy current analyses. However IBC originally defined on basis that material property linear, and order to apply nonlinear materials, we introduce IBC. With help IBC, lessen unknowns integral equations give value one derive an equation with loop state variable. In check adequacy...

The volume integral equation approach replaces the loop currents over elements in magnetic material with on surface to derive a boundary (BIE). current is equivalent double layer charge, which offers an form of scalar potential give BIE. Once BIE has been solved, gives flux density <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> by Biot-Savart law. many advantages such as giving accurate solutions and evaluating at edges corners. But it some...

Eddy currents induced in steel are analyzed by the boundary element method. As periodic electromagnetic quantities distorted due to nonlinear magnetization property, they expressed a Fourier series, whose fundamental and harmonic waves determined solving corresponding integral equations with surface magnetic fields given as values. In this paper, we introduce new combined integration scheme that enables efficient, volume-mesh-less treatment of practical problems typically characterized...

Since the line loop current is equivalent to double layer charge, it gives an integral form of scalar potential. The segmental on interface between magnetic materials produces a potential gap, which works give boundary equation (BIE). By virtue another gap due fictitious circulating along contour cut-surface in material, excitation becomes single valued and BIE applicable generic problems without any restriction. Regarding nonlinear material as composed with different values permeability, we...

A hybrid single and dual simple layer Boundary Integral (BIE) formulation is proposed in this paper. The number of unknowns per node can be reduced to minimum, i.e. one, three or four respectively depending on various kinds material interfaces. By using formulation, the computer storage greatly so that large complex application problem may numerically simulated. Numerical examples an are included.

The main purpose of numerical field calculation in high voltage engineering is the optimization electrode shape dielectrically stressed components. In design gas-insulated switchgear (GIS) components, several conflicting requirements must be satisfied simultaneously order to ensure success. For example, a compact reduce material costs and allow for modular, cost-effective layouts. At same time, electric stresses on active components low enough reliability compliance with international...

A set of new expressions is presented that provide an efficacious and simple calculation the magnetostatic field components in case current-carrying conductors. The are used to calculate a circular arc segment with transversal cross-section. They suitable for practical application various magnetic problems (tokamaks, transformers, reactors, etc.).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The scalar potential formulation by the boundary integral equation approach is attractive for numerical analysis but has fatal drawbacks due to a multi-valued function in current excitation. We derive an all-purpose with double layer charges as state variable and apply it nonlinear magnetostatic problems regarding magnetization fictitious volume charges. investigate two approaches how treat In discretization constant element, surface loop introduced charge. By linear are evaluated on...

New closed-form expressions are derived and presented to compute the three-dimensional magnetostatic field of a hollow cylinder finite thickness when current has longitudinal component. The results valid for problems with no magnetic materials. It is shown that solution can be written in terms complete incomplete Jacobian elliptic functions first second kind. Results specific configuration compared numerical solution.

The paper describes the procedure for reduction of breakdown appearance in HV apparatus by automatic geometry optimization. Such consists basically three main steps: field analysis, criteria evaluation and is briefly elaborated illustrated at some well-known "two-sphere" examples. As accurate analysis electrical complex engineering essential importance, we present an accelerated Boundary Element Method used a analysis. final step, optimization performed resulting end optimal with minimal...

The double-layer approach (DLA) possesses superior features for the analysis of static electromagnetic problems. In this article, dealing with magnetostatic analysis, we introduce two kinds double layers: first one on surface magnetic body and second cut-surface within exciting current loop. From layers cut-surface, were able to derive a novel, unified potential, which facilitates treatment any problem, including multiply connected Furthermore, in use time DLA forces acting bodies. law...

Purpose The purpose of this paper is to solve generic magnetostatic problems by BEM, studying how use a boundary integral equation (BIE) with the double layer charge as unknown derived from scalar potential. Design/methodology/approach Since produces only potential gap without disturbing normal magnetic flux density, field accurately formulated even one BIE unknown. Once determined, Biot‐Savart's law gives easily density. Findings using capable treating robustly geometrical singularities at...