Stefan Benkler

A new 3-D conformal PEC FDTD scheme with user-defined geometric precision and derived stability criterion

A new conformal finite-difference time-domain (CFDTD) updating scheme for metallic surfaces nonaligned in the grid is presented in this paper. In contrast to existing conformal models, the new model can be formulated with the original Yee FDTD update equation. Therefore, the proposed scheme can be easily added in standard FDTD codes even if the codes are already parallelized or hardware-accelerated. In addition, based on the commonly used conventional stability criterion, a derivation of the stability is presented and based on the conformal geometric information, a time step reduction formula is presented. The time step reduction is used as a user-defined parameter to tradeoff speed versus accuracy. The achievable geometric precision is optimized to a given time step. Therefore, even with the conventional time step (no reduction) the presented scheme profits from the conformal discretization. To show the performance and the robustness of the proposed scheme canonical validations and two real world applications were investigated. A broadband low profile (circular) antenna was successfully simulated showing the benefit of the conformal FDTD method compared to the conventional scheme. Furthermore, a CAD based mobile phone was conformally discretized and successfully simulated showing that the proposed scheme is highly suited for the simulation of advanced engineering problems.

Analysis of human brain exposure to low‐frequency magnetic fields: A numerical assessment of spatially averaged electric fields and exposure limits

Compliance with the established exposure limits for the electric field (E-field) induced in the human brain due to low-frequency magnetic field (B-field) induction is demonstrated by numerical dosimetry. The objective of this study is to investigate the dependency of dosimetric compliance assessments on the applied methodology and segmentations. The dependency of the discretization uncertainty (i.e., staircasing and field singularity) on the spatially averaged peak E-field values is first determined using canonical and anatomical models. Because spatial averaging with a grid size of 0.5 mm or smaller sufficiently reduces the impact of artifacts regardless of tissue size, it is a superior approach to other proposed methods such as the 99th percentile or smearing of conductivity contrast. Through a canonical model, it is demonstrated that under the same uniform B-field exposure condition, the peak spatially averaged E-fields in a heterogeneous model can be significantly underestimated by a homogeneous model. The frequency scaling technique is found to introduce substantial error if the relative change in tissue conductivity is significant in the investigated frequency range. Lastly, the peak induced E-fields in the brain tissues of five high-resolution anatomically realistic models exposed to a uniform B-field at ICNIRP and IEEE reference levels in the frequency range of 10 Hz to 100 kHz show that the reference levels are not always compliant with the basic restrictions. Based on the results of this study, a revision is recommended for the guidelines/standards to achieve technically sound exposure limits that can be applied without ambiguity.

Estimation Formulas for the Specific Absorption Rate in Humans Exposed to Base-Station Antennas

The demonstration of compliance with guidelines for human exposure to base-station antennas can be a time consuming process or often results in overly conservative estimates. To alleviate this burden and reduce the overestimation, approximation formulas for the whole-body average specific absorption rate (SAR) and the peak spatial SAR of human bodies using readily available basic antenna parameters have been developed and validated in this study. The formulas can be used for adults standing in the radiating near field of base-station antennas operating between 300 MHz and 5 GHz, at distances larger than 200 mm. It is shown that the 95th-percentile absorption for the human population can be well approximated by the absorption mechanism and statistical data of weight, height, and body-mass index of the human population. The validation was performed numerically using three anatomical human models (Duke, Ella, and Thelonious) exposed to 12 generic base-station antennas in the frequency range 300 MHz to 5 GHz at six distances between 10 mm and 3 m. From the 432 evaluated configurations, the estimation formulas for adult models are proven to be conservative in predicting the SAR exposure values of the two adults, but as expected not of the child.

Analysis of the accuracy of the numerical reflection coefficient of the finite-difference time-domain method at planar material interfaces

This paper presents a rigorous analysis of the numerical error of the reflection coefficient of the finite-difference time-domain (FDTD) algorithm at planar material boundaries. The derived expressions show that the numerical reflection depends on a large number of parameters, such as the grid resolution and the time step, the frequency, the angle, and the polarization of the incident wave. In conclusion, the FDTD algorithm does not accurately fulfil the boundary conditions for the continuity of the fields. The theoretical findings enable the detailed characterization of the field behavior in the grid at material interfaces. The numerical total reflection and the Brewster angle are studied as well as the discretization influences on the specific absorption rate (SAR).

Novel FDTD Huygens source enables highly complex simulation scenarios on ordinary PCs

This article demonstrated the effectiveness of a novel FDTD source called Huygens source. The source uses a generalized TFSF implementation and enables straightforward FDTD unidirectional subgridding with tremendous savings in DPU time and memory onsumption. Furthermore, the incident field can be provided by other numerical EM tools like MoM and the new FDTD Huygens sources acts as a powerful hybridization between the two methods.

Development and validation of a magneto-hydrodynamic solver for blood flow analysis

The objective of this study was to develop a numerical solver to calculate the magneto-hydrodynamic (MHD) signal produced by a moving conductive liquid, i.e. blood flow in the great vessels of the heart, in a static magnetic field. We believe that this MHD signal is able to non-invasively characterize cardiac blood flow in order to supplement the present non-invasive techniques for the assessment of heart failure conditions. The MHD signal can be recorded on the electrocardiogram (ECG) while the subject is exposed to a strong static magnetic field. The MHD signal can only be measured indirectly as a combination of the hearts electrical signal and the MHD signal. The MHD signal itself is caused by induced electrical currents in the blood due to the moving of the blood in the magnetic field. To characterize and eventually optimize MHD measurements, we developed a MHD solver based on a finite element code. This code was validated against literature, experimental and analytical data. The validation of the MHD solver shows good agreement with all three reference values. Future studies will include the calculation of the MHD signals for anatomical models. We will vary the orientation of the static magnetic field to determine an optimized location for the measurement of the MHD blood flow signal.

Low frequency electromagnetic field exposure study with posable human body model

This paper investigates the electric field and current density induced in a human body when exposed to low frequency electromagnetic fields. A numerical technique based on the Finite Element Method and electromagnetic quasistatic approximations is employed to compute both the fields generated by low frequency sources and the fields induced inside a human body due to exposure or contact. Case study is conducted to investigate exposure situations pertaining to the safety of human being in the vicinity of high intensity low frequency electromagnetic fields.

FDTD subcell models powering latest progress in computational antenna optimization

This article demonstrates the capability of using the finite-differences time-domain (FDTD) method as simulation tool for optimizing the design of an antenna. The FDTD simulation method is locally enhanced with subcell modeling techniques, which incorporates a-priori known field behavior in (1) curved material interfaces and (2) strong field gradients near sharp metal edges. Combining the FDTD subcell modeling technique with a FDTD simulation hardware acceleration card enables the efficient optimization of several parameters based on genetic algorithms. The ongoing work targets the improved optimization of commercial CAD based mobile phones.

Full human body exposure assessment in low frequency electromagnetic fields

This paper investigates the electric field and current density induced in a human body when exposed to low frequency electromagnetic fields. A numerical technique based on the Finite Element Method and electromagnetic quasistatic approximations is developed to compute both the fields generated by low frequency sources and the fields induced inside a human body due to direct or indirect exposure scenarios. A case study is conducted to investigate exposure situations pertaining to the safety of human beings in the vicinity of high intensity low frequency electromagnetic fields.

Development of a magneto-hydrodynamic solver for anatomical models

The developed MHD solver is able to calculate the induced current distribution and the equi-potentials in simple geometries. Preliminary validation of the MHD solver shows good agreement with values found in the literature [7] based on computational modeling. The implemented MHD solver is also able to calculate the induced fields in highly accurate models of the human anatomy. We will repeat the simulations in the future with an exact model of the geometry used in [7]. In addition we will perform an experimental validation to compare the MHD solver results with actual measurements. Future simulations will also include the calculation of the MHD signals for all four models of the Virtual Family. We will vary the orientation of the static magnetic field to maximize the MHD signal, and we will determine an optimized location for the measurement of the MHD signal. The optimal location for measuring the MHD signal is a location on the surface of the patient which maximizes the signal strength and optimizes the correlation of the MDH signal to the blood flow by minimizing the influence of the ECG signal. The volunteers based on which the Virtual Family models were developed (two adults and two children) will be used to measure the ECG signal and the combined ECG + MDH signal. The combined ECG + MDH will be measured inside a 3T MR scanner using an MR compatible ECG monitor. We will correlate the computational MHD results with the actual measurement. Based on this information we hope to develop a MHD based biomarker to non-invasively estimate the blood flow for the evaluation of heart failure.