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The technique resides on the smotheness of kernel functions – which is no longer valid for big wave numbers.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

This paper seeks to deal with the computation of time‐harmonic electric potentials, currents, and surface charge distributions inside self‐healing metallized film capacitors in three dimensions. A 50 Hz exciting voltage is applied at contacts.

Extreme aspect ratios warrant dimensional reduction: the metallization is modelled as a 2D shell. This greatly reduces computational costs and makes possible an excellent resolution of the geometry. An integro‐differential equation for the complex amplitudes of the electric potential and surface charge densities on this shell is derived and discretized by means of boundary elements.

Adaptive cross approximation and H‐matrix technology is employed for matrix compression and preconditioning of iterative solvers. This permits one to use fine surface meshes and achieve satisfactory accuracy as demonstrated in numerical experiments.

The model is based on an electroquasistatic approach; thus it is valid for low frequencies only.

Numerical experiments of sophisticated real‐life capacitor‐designs show the efficacy of the method for industrial applications.

A novel model was developed and implemented for the 3D electric field computation inside metallized film capacitors in the frequency domain.