M.J. White

Development of a multigrid FDTD code for three-dimensional applications

Numerical modeling of realistic engineering problems using the finite-difference time-domain (FDTD) technique often requires more detail than is possible when using a uniform-grid FDTD code. We describe the development of a three-dimensional (3-D) multigrid FDTD code that focuses a large number of cells of small dimensions in the region of interest. The detailed solution procedure is described and some test geometries are solved using both a uniform-grid and the developed multigrid FDTD code to validate the results and check the accuracy of the solution. Results from these comparisons as well as comparisons between the new FDTD code and another available multigrid code are presented. In addition, results from the simulation of realistic microwave-sintering experiments in large multimode microwave cavities are given to illustrate the application of the developed method in modeling electrically large geometries. The obtained results show improved resolution in critical sites inside the 3-D multimode sintering cavity while keeping the required computational resources manageable. It is shown that it is possible to simulate the sintering of ceramic samples of 0.318-cm wall thickness in a cylindrical multimode microwave cavity with a diameter of 74 cm and a length of 112 cm using 2.24/spl times/10/sup 6/ total FDTD cells. For comparison, a total of 102/spl times/10/sup 6/ cells would have been required if a uniform-grid code with the same resolution had been used.

A new 3D FDTD multigrid technique with dielectric traverse capabilities

The finite-difference time-domain (FDTD) technique has become increasingly popular and is being used to model extremely complex and electrically large structures. These simulations are computationally demanding and often exceed available limits on computer resources. In this paper, we present an FDTD sub-gridding technique that allows for increased resolution in regions of interest without increasing the overall computational requirements beyond the available resources. Furthermore, the formulation presented here allows for traversing dielectric boundaries using any integer refinement factor and the maximum Courant number. By allowing the coarse-/fine-grid boundary to traverse dielectric boundaries, numerical simulations that were previously either extremely difficult or impossible to perform are now possible. The technique presented here uses a weighted current value from the coarse region at the boundary between the fine- and coarse-grid regions to update the fine-region tangential fields on that boundary. The weighting function depends on the material properties and the relative position of the fine-region electric field within the current contour at the boundary. The complete formulation of this new technique is described and some results of simulation cases are presented to validate the accuracy and stability of the newly developed FDTD code. Simulations include simple cases where the analytical solution exists and more complex cases, which were impossible to model using a uniform-grid FDTD code. In some simulation examples, computer memory savings as high as 70 times what would have been necessary with a uniform-grid code were achieved. It is shown that errors of less than 2% are achievable with ratios of coarse-to-fine grid sizes exceeding ten. The new technique is expected to be used in simulating many electrically large and complex structures in the biomedical microwave processing of materials and the wireless communications areas.

A new 3D FDTD multi-grid technique with dielectric-traverse capabilities

The finite-difference time-domain technique (FDTD) has become increasingly popular and is being used to model extremely complex and electrically large structures. These simulations are computationally demanding and often exceed available limits of computer resources. In this paper we present a FDTD sub-gridding technique that allows for increased resolution in regions of interest without increasing the overall computational requirements beyond the available resources. Furthermore, the formulation presented here is the first to allow for traversing dielectric boundaries using any integer refinement factor and the maximum Courant number. The technique presented here uses a weighted current value from the coarse region at the boundary between the fine- and coarse-grid regions to update the fine-region tangential fields on that boundary. The weighting function depends on the material properties and the relative position of the fine-region electric field within the current contour at the boundary. The complete formulation of this new technique is described and some results of simulation cases are presented to validate the accuracy and stability of the developed FDTD code. In some simulation examples, computer memory savings as high as 70 times what would have been necessary with a uniform-grid code were achieved. It is shown that errors less than 2 percent are achievable with coarse-to-fine-grid ratios exceeding 10. The new technique is expected to be used in simulating many electrically large and complex structures in the biomedical, microwave processing of materials, and cellular-communications areas.

Finite-Difference Time-Domain Simulation of Microwave Sintering in A Variable-Frequency Multimode Cavity

There have been recent indications that variable-frequency microwave sintering of ceramics provides several advantages over single-frequency sintering, including more uniform heating, particularly for larger samples. The Finite-Difference Time-Domain (FDTD) code at the University of Utah was modified and used to simulate microwave sintering using variable frequencies and was coupled with a heat-transfer code to provide a dynamic simulation of this new microwave sintering process. This paper summarizes results from the FDTD simulations of sintering in a variable-frequency cavity. FDTD simulations were run in 100-MHz steps to account for the frequency variation in the electromagnetic fields in the multimode cavity. It is shown that a variable-frequency system does improve the heating uniformity when the proper frequency range is chosen. Specifically, for a single ceramic sample (4 × 4 × 6 cm 3 ), and for a variable-frequency range from f = 2.5 GHz to f = 3.2 GHz, the temperature distribution pattern was much more uniform than the heating pattern achieved when using a single-frequency sintering system at f = 2.45 GHz.

A three dimensional multi-grid FDTD code for modeling microwave sintering of materials

Computer modeling and simulation provide a valuable tool for characterizing complex electromagnetic (EM) devices and for developing fundamental understanding in the applications which involve complex electromagnetic interactions such as the biological effects of EM radiation and the microwave sintering of ceramics. In the area of microwave processing of materials, continued numerical modeling efforts are expected to aid in the scale-up and commercialization of this new technology. We describe the development of a three dimensional multi-grid FDTD code to help focus large number of cells around the desired region of interest. Solution procedures are described and some test geometries were solved using a uniform grid and the developed multi-grid codes to help validate the results from the developed code. Results from these comparisons, as well as the results of comparisons between the developed FDTD code and another available variable mesh code are presented. In addition, results from the simulation of realistic microwave sintering experiments showed improved resolution in critical sites inside the three dimensional sintering cavity. With the validation of the FDTD code, simulations for electrically large multimode microwave sintering cavities with multiple layers of samples were carried out to fully demonstrate the advantages of the developed multi-grid FDTD code.

Numerical simulation and experimental validation of RF drying

The Finite-Difference Time-Domain (FDTD) method has been used by the group to simulate a wide variety of Radio Frequency (RF) and induction-drying processes and realistic, microwave-sintering experiments. Many results were presented and some guidelines towards the effective use of the microwave and RF heating technologies of ceramic ware were developed. In this paper the authors describe an experimental effort which was used to validate the FDTD simulation results. Specifically an experimental RF dryer, Thermax Model No. T3GB operating at 25 MHz, was used to dry ceramic ware of various materials, sizes, and shapes and the temperature distribution pattern was monitored using six fiber-optic temperature probes. The measured heating patterns were then compared with the FDTD simulation results. Many of the guidelines developed using the numerical simulations were confirmed experimentally. Results from various comparisons between simulation and experimental data will be presented. Additional results from the simulation efforts illustrating possible procedures for improving the efficiency and the uniformity of RF drying will also be described.

Multigrid FDTD code for calculating microwave absorption pattern in human head radiated by hand-held antennas

Numerical modeling of realistic engineering problems using the finite-difference time-domain (FDTD) technique often requires more details than are possible when using a uniform-grid FDTD code. With the increasing interest in the FDTD method, and the desire to extend modeling to more complex structures. The use of the uniform-grid FDTD algorithm becomes prohibitive due to limited computer resources. We describe the application of a three-dimensional multigrid FDTD code in describing the microwave power absorption distribution in a realistic model of a human head exposed to radiation from a hand-held antenna. With the multigrid FDTD code it is possible to focus a large number of cells of small dimensions in the head region, and the rest of the body is modeled using coarse cells. The proposed procedure makes it possible for the first time to take into account the effect of the rest of the human body on the absorption characteristic in the head and the radiation pattern of the antenna. It is shown that this effect is particularly important when antennas are placed at a relatively larger distances from the body. Body shapes and dimensions also play an important role in determining the radiation characteristics of these antennas.

FDTD simulations and analysis of thin sample dielectric properties measurements using coaxial probes

A metallized ceramic probe has been designed for high temperature broadband dielectric properties measurements. The probe was fabricated out of an alumina tube and rod as the outer and inner conductors respectively. The alumina was metallized with a 3 mil layer of moly-manganese and then covered with a 0.5 mil protective layer of nickel plating. The probe has been used to make complex dielectric properties measurements over the complete frequency band from 500 MHz to 3 GHz, and for temperatures as high as 1,000 C. A 3D Finite-Difference Time-Domain (FDTD) code was used to help investigate the feasibility of this probe to measure the complex permittivity of thin samples. It is shown that by backing the material under test with a standard material of known dielectric constant, the complex permittivity of thin samples can be measured accurately using the developed FDTD algorithm. This FDTD procedure for making thin sample dielectric properties measurements will be described.

Broadband, high-temperature dielectric properties measurements of thin substrates using open-ended probes

A metallized-ceramic probe has been designed for high-temperature broadband dielectric properties measurements. The probe has been used to make complex dielectric properties measurements over the frequency band from 500 MHz to 3 GHz, and up to temperatures as high as 1000/spl deg/C. We present results illustrating the use of this probe for broadband, high-temperature, dielectric properties measurements of thin samples and substrates. It is shown that by backing the material under test with a standard material of known dielectric constant such as air or metal, the complex permittivity of thin samples can be accurately measured. A 2D cylindrical FDTD code utilizing the symmetry of the probe was used for these thin-sample measurements. Results for thin (0.6 mm) alumina and sapphire samples for temperatures up to 800/spl deg/C are presented. This measurement method has important applications in the on-line characterization of semiconductor wafers.

Numerical modeling and simulation of microwave heating process

The use of induction heating and RF drying in the processing and curing of materials has been in commercial use for over 20 years. New high-conductivity ceramics are being developed which require delicate drying and sintering processes. The authors use the finite-difference time-domain method (FDTD) to examine the feasibility of using induction heating in same delicate high-conductivity ceramic drying processes in which uniformity of the electromagnetic power deposition pattern in the sample is critical. Furthermore, FDTD was used to simulate the RF drying process in which a ceramic ware is placed on a conveyor belt moving between two capacitor electrodes. The finite-difference time-domain method, using the Yee cell, provides an effective way to analyze the effects of material properties, ware shape and dimensions, and the frequency of operation on the microwave drying processes. The FDTD method displays both the dynamic behavior and the steady-state behavior of the microwave heating process. FDTD results of the induction and RF drying processes are shown and guidelines to help optimize the performance of both drying processes are presented. Specifically, coil pitch, coil diameter, and frequency of operation are investigated, while for the RF drying process, the electrode spacing and sample shape, dimensions, and orientation are evaluated.<<ETX>>