Lukasz Kulas

Reduced order models of refined Yee's cells

This letter introduces a new approach to increasing the accuracy of Finite Difference (FD) methods by means of local mesh refinement. The area slightly larger than single Yees cell is covered by dense mesh and its macromodel is created by the Model Order Reduction (MOR) of state equations in the frequency domain. Such macromodels are subsequently used in the Finite Difference Time Domain (FDTD) or the Finite Difference Frequency Domain (FDFD) analysis of the entire structure. Unlike a popular subgridding technique, the model order reduction approach does not affect the stability or convergence properties of underlying numerical schemes.

A fast high-resolution 3-D finite-difference time-domain scheme with macromodels

A fast three-dimensional (3-D) finite-difference time-domain (FD-TD) scheme of high spatial resolution is presented. Increased resolution is obtained by combining the standard FD-TD algorithm with macromodels of highly refined volumes created by a model-order reduction technique. New updated equations for macromodels are derived and the numerical costs involved in using 3-D macromodels are estimated. Excellent performance has been observed during numerical tests for high-refinement factors.

Low-reflection subgridding

The paper presents a novel three-dimensional subgridding scheme applicable to the finite-difference technique in the time and frequency domains. Transfer of fields between a main grid and a refined volume is performed using a simple linear interpolation. Very low-reflection levels from the main to local grid interface are obtained by co-location of fields used in the interpolation process. The technique allows material traverse without any special boundary treatment. The accuracy of the scheme is verified in numerical tests showing excellent performance even for high refinement factors.

Multilevel model order reduction

We present a multilevel Model Order Reduction scheme for enhancing numerical analysis of electromagnetic fields by means of grid based techniques. The scheme allows one to create nested macromodels and combine macromodels with the Fast Frequency Sweep. The implementation of the method is illustrated on the Finite Difference Frequency Domain technique and efficient nodal order reduction algorithm (ENOR) but the concept can easily be applied also for other mesh based methods and other order reduction schemes.

Stability of the FDTD scheme containing macromodels

Stability analysis of the finite difference time domain scheme containing macromodels is presented. It is shown that for a stable macromodel, the stability of the combined scheme depends on the field interpolation at the macromodel boundary. The maximal allowable time step is shown to be much larger than for subgridding.

Macromodels in the frequency domain analysis of microwave resonators

We present a new technique of incorporating macromodels into the frequency domain formulation of grid based methods. Unlike previous methods, the new scheme does not introduce any frequency dependent elements into the system matrix and thus can be used in the analysis of resonator problems. Numerical results show an increase in accuracy of computations in a wide frequency range while convergence properties of the underlying matrix eigenvalue solver are not affected.

A Review of Antennas for Indoor Positioning Systems

This paper provides a review of antennas applied for indoor positioning or localization systems. The desired requirements of those antennas when integrated in anchor nodes (reference nodes) are discussed, according to different localization techniques and their performance. The described antennas will be subdivided into the following sections according to the nature of measurements: received signal strength (RSS), time of flight (ToF), and direction of arrival (DoA). This paper intends to provide a useful guide for antenna designers who are interested in developing suitable antennas for indoor localization systems.

Single-Anchor Indoor Localization Using ESPAR Antenna

In this letter, a new single-anchor indoor localization concept employing electronically steerable parasitic array radiator (ESPAR) antenna has been proposed. The new concept uses a simple fingerprinting algorithm adopted to work with directional main beam and narrow minimum radiation patterns of ESPAR antenna that scans 360 ° area around the base station, while the signal strength received from a mobile terminal is being recorded for each configuration. The letter describes the antenna design and necessary fingerprinting algorithm expansion and shows measurements of the proof-of-concept prototype performed within the experimental setup. Localization results obtained from indoor measurements indicate that the proposed concept can provide better results than the similar approach based on a switched-beam antenna introduced by Giorgetti (IEEE Commun. Lett., vol. 13, no. 1, pp. 58-60, Jan. 2009).

Reciprocity Principle for Stable Subgridding in the Finite Difference Time Domain Method

In this paper we present a method to analyze stability of the Finite Difference Time Domain schemes containing locally refined meshes. The method relies on the reciprocity principle derived from the operator approach to stability analysis and is an alternative to popular stability tests that are either time-consuming or difficult to implement. The proposed approach is verified in numerical tests which prove that verification of stability of any subgridding algorithm can easily be performed using reciprocity principle.

Enhancing performance of switched parasitic antenna for localization in Wireless Sensor Networks

This paper presents an Electronically Steerable Parasitic Array Radiator (ESPAR) antenna with enhanced performance of estimating the Incoming signal direction. Designed antenna is dedicated for 2.4 GHz ISM applications with emphasis on Wireless Sensor Networks (WSN). The limitations of the existing design approach are illustrated, as well as perspectives and challenges of the proposed solution in relation to the localization in Wireless Sensor Networks.