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The purpose of this study is to demonstrate the novel approach in treating multiply connected problems in magnetostatic.

The new double layer approach (DLA) to be proposed is based on the use of the exciting double layer on the cut-surface. Applying Ampere’s circuital law to the circuital path along a toroidal core of M–C model, this paper derives unified exciting potential (UEP) from the common exciting potential. The UEP is applicable to the simply or M–C analysis. To check the effectiveness of the UEP, this paper analyze typical M–C problems and compares the results with those of other benchmark problems and also those obtained by surface charge method (SCM). Because the SCM encounters a cancellation error, this paper overcomes this problem by using the concept of direct boundary element method (BEM).

Using the improved DLA, this paper analyzed a typical multiply connected model and compared the results with those of the SCM, which has been improved to overcome cancellation errors. This paper has confirmed that the results obtained by the improved DLA are the same as those obtained by the improved SCM and Steklov–Poincaré operator formulation, tested at the well-known benchmark problems given in Andjelic et al. (2010). From these results, this paper concluded that the Improved DLA works well and that the improved SCM becomes available for analyzing both the simply and multiply connected problems.

Expanding a concept of the exciting double layer on the cut-surface, this paper improve the DLA to analyze the M–C problems. Applying Ampere’s circuital law to the full circuital path along the toroidal core of M–C problem, this paper derive UEP from the original exciting potential to get the governing BIE. The BIE is applicable to either simply or multiply connected analysis.

The purpose of this paper is to present a simple approach for calculation of the sensitivities in the free-form inverse design problems. The approach is based on the analogy with the similar tasks used in the signal-processing analysis. In the proposed case it is not required to solve an adjoint problem as in the most of the similar optimization tasks. The simulation engine used in the background is a Fast Boundary Element Method. The approach is validated on some known benchmark problems.

Inverse design is recognized nowadays as a crucial scientific grand challenge. Contrary to the conventional approach (“Given the structure, find the properties”) it purses a new paradigm (“Given the desired property, find the structure”). Inverse class of problems has a broad application area, from the material-, medical-, bio- to the engineering-class of problems. When dealing with the inverse design in free-form optimization of the engineering problems the typical approach is to calculate the adjoint problem. Calculation of the adjoint problem mostly requires the costly calculation of the gradients, which makes the whole optimization procedure rather expensive due to the high computational burden required for their solution.

In this paper it is proposed a novel Simple Sensitivity Approach to get in a fast way the response (sensitivity) function of the analyzed structure. The simulation engine used in the background is the Fast Boundary Element Method.

Novel approach for inverse design when performing the free-form optimization of engineering problems.

To provide first insight onto the application of hierarchical matrices and adaptive cross approximation (ACA) techniques for electromagnetic scattering problems.

The shielding effectiveness of metallic casings with apertures is analyzed via an electric field integral equation. To reduce the storage needs and the complexity of matrix equation solution, a technique combining the use of hierarchical matrices (H‐matrix) in conjunction with the ACA technique is used.

Provides first results for compression of a matrix resulting from a Helmholtz problem by means of hierarchical matrices and ACA techniques. Gives insight into the importance of obtaining a “cheap” preconditioner.

The technique resides on the smotheness of kernel functions – which is no longer valid for big wave numbers.

Gives means of solving problems of big dimensions in terms of number of unknowns – without the need to tailor the approach for the specific kernel function. The original integration functions used to fill the full matrix can be used here.

The paper represents one of the first attempts to use the above‐mentioned techniques for the high frequency domain.

The purpose of this paper is to solve generic magnetostatic problems by BEM, by studying how to use a boundary integral equation (BIE) with the double layer charge as unknown derived from the scalar potential.

Since the double layer charge produces only the potential gap without disturbing the normal magnetic flux density, the field is accurately formulated even by one BIE with one unknown. Once the double layer charge is determined, Biot‐Savart's law gives easily the magnetic flux density.

The BIE using double layer charge is capable of treating robustly geometrical singularities at edges and corners. It is also capable of solving the problems with extremely high magnetic permeability.

The proposed BIE contains only the double layer charge while the conventional equations derived from the scalar potential contain the single and double layer charges as unknowns. In the multiply connected problems, the excitation potential in the material is derived from the magnetomotive force to represent the circulating fields due to multiply connected exciting currents.