Fast integral equation solution for electric field shielding

Abstract

Purpose

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

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

The technique resides on the smotheness of kernel functions – which is no longer valid for big wave numbers.

Practical implications

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.

Originality/value

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

Citation

Cranganu‐Cretu, B., Ostrowski, J. and Andjelic, Z. (2005), "Fast integral equation solution for electric field shielding", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 2, pp. 639-647. https://doi.org/10.1108/03321640510586240