Michal Wiktor

Advances in computational electromagnetics

The paper presents a selection of techniques that are currently being investigated at the Technical University of Gdansk and can be used to accelerate CAD of microwave circuits and the computation of high and low frequency electromagnetic fields. Techniques for creating surrogate CAD models and their application to automated design of band pass filters are discussed. Different strategies of electromagnetic field representation for mesh based and meshless methods are introduced and their efficiency illustrated on examples involving structures with complex geometries.

Efficient material matrix generation for FDTD analyses using OpenGL

Application of OpenGL functions for fast and flexible generation of material matrix for finite difference mesh is presented. Application of graphical functions makes tessellation of complex objects efficient and flexible. Additionally, since most of computations is performed using a specialized hardware, presented technique is very fast. Two examples of tessellation of complex structures, including human head, are presented.

Study of interaction of pacemaker electrode with high frequency RF fields

The influence of radio-frequency fields on pacemaker operation is the object of numerous studies, both in technical and medical literature. The main point of interest is safety of MRI diagnostics and the influence of cellular phones on the device operation. In this article a wide band behavior of pacemaker lead is discussed, in order to categorize potentially dangerous frequency bands. Medical and engineering sciences use completely different methodology, so there is no unique answer if the malfunction of the pacemaker, even when occurred, brings potential risk to a patient. Tests of radiation from the pacemaker lead in wide frequency band, presented in this article show that interaction between the device and external RF field is possible, especially for frequencies over 1GHz. These tests could be potentially good background for further clinical tests. Other observation was, that the saline solution did not significantly change the radiation from the lead, compared to the measurements in air.

Efficient analysis of waveguide components using a hybrid PEE-FDFD algorithm

The partial eigenfunction expansion (PEE) method combined with the classical finite difference frequency domain (FDFD) algorithm is proposed to accelerate frequency domain analysis of waveguide components. Examples are shown validating the method both for eigenvalue and deterministic problems.

Exact modal absorbing boundary condition for waveguide simulations - discrete Green's function approach

A modal absorbing boundary condition (ABC) based on the discrete Greens function (DGF) is introduced and applied for termination of waveguides simulated by means of the finite-difference time-domain (FDTD) method. The differences between the developed approach and implementations already demonstrated in the literature are presented. By applying DGF, a consistent theoretical approach to modal ABC in the FDTD method is obtained. Developed ABC is applicable to propagating and evanescent modes yielding the reflection error below -250 dB. Because the perfect matching may be computationally expensive, results of investigations of the tradeoff between computational efficiency and accuracy of the developed method are presented.

Microwave imaging: Comparison of direct scattering problem solvers

Breast cancer detection has become one of the most emergent tasks these days. A microwave imaging for the breast cancer detection shows several advantages compared to the conventional X-ray mammography. If the test is carried out using the microwave imaging system a person is not exposed to a high dose of the radiation; the X-ray method is less sensitive to radio-graphically dense tissues, etc. A scattering solver is the most important part of the microwave imaging system. The scattering from an unknown object that exhibits a contrast in electric permittivity and conductivity has to be analyzed. There are several approaches for a numerical solution of the problem, e.g. Integral Equations (IE), Finite Differences (FD), Finite Elements (FE) and other methods.In the paper, the formulation of the scattering problem using IE, FD and FE methods is given. These methods are compared from the viewpoint of their suitability to model a scattering problem. Accuracy, computational time, and memory demands are the criteria for the method comparison.

Spatial discretization scheme based on Legendre polynomials for time and frequency domain analysis

The algorithm operating in time and frequency domain, similar to multiresolution analysis is presented. Instead of wavelets, orthogonal, compactly supported Legendre polynomials were used for discretization of curl operator. The resulting scheme has low numerical dispersion, compared to finite difference method, and implementation of perfect boundary conditions is easier, contrary to wavelet-based algorithms. The algorithm can be easily joined with finite difference method inside a single computational domain. This hybrid algorithm allow to reduce computational domain size and take advantage of different techniques developed for finite difference method.

Application of symmetry planes in finite difference analysis of coupled resonators

An efficient technique for calculation resonant frequencies and coupling coefficient of paired resonators using finite difference frequency domain algorithm is presented. Improvement in efficiency is obtained by utilizing symmetry planes, implemented in a new manner. Unlike well known solution, the symmetry planes are defined by modification of the original matrix problem using orthogonal matrix projection. Such a formulation allows, beside substantial reduction in number of variables and efficiency gain, precise alignment of electric and magnetic walls in the mesh.

Approximate analytical boundary conditions for efficient finite difference frequency domain simulations in cylindrical coordinates

A simple technique of numerical analysis of open resonator is presented. The technique combines a standard Finite Difference method with the Partial Eigenfunction Expansion. By doing this one gets a simple formulation of radiation boundary condition. The algorithm was tested for the dielectric resonator of different height placed in infinite radial waveguide and excellent agreement of the obtained results with other methods was achieved.

Increasing accuracy of finite difference methods in nonorthogonal irregular grids

This paper discusses a discrete form of wave equation applied to nonorthogonal and irregular grids. Modifications to the standard finite difference algorithm are introduced, preventing substantial loss of accuracy when the grid is deformed. The algorithm is used to find cutoff frequencies of rectangular waveguides rotated with respect to the mesh.