bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical calculations of three‐dimensional turbulent vortex breakdown
Authors: Spall Robert E. , Gatski Thomas B.
Published: August 2005

Numerical solutions to the three‐dimensional, unsteady, incompressible Reynolds‐averaged Navier‐Stokes equations have been obtained for bubble‐type vortex breakdown. Two different turbulence models were employed: (1) standard K‐ε and (2) an explicit, regularized algebraic Reynolds stress model. Results are computed at a Reynolds number of 10,000. The algebraic Reynolds stress model produced a breakdown bubble with a larger length‐to‐diameter ratio than did the K‐ε model. Breakdown also occurred at lower levels of adverse pressure gradient for the algebraic stress model than for the K‐ε model. In each case single‐cell breakdown structures resulted. This is contrasted with numerical calculations for laminar breakdown which reveal the existence of complex multicell bubble breakdown structures.
Finite element modelling of the flow of chemically reactive polymeric liquids
Authors: Lefebvre L. , Keunings R.
Published: August 2005

We consider steady state and time‐dependent flows of chemically reactive polymeric systems in two‐dimensional geometries. A numerical simulation tool is proposed for predicting the evolution of the macroscopic velocity, temperature, stress and species concentration fields in such flows. We formulate a general mathematical model on the basis of the first principles of continuum mechanics, which includes a description of the non‐liner coupling between kinematics, heat transfer and chemical kinetics. The resulting set of non‐linear partial differential equations is solved numerically by means of appropriate finite element techniques. We have implemented the resulting numerical model in the general‐purpose POLYFLOWR software developed in Louvain‐la‐Neuve, Belgium. Simulation results for various steady state and time‐dependent reactive flows are reported.
A second order finite element method for the solution of the transonic Euler and Navier‐Stokes equations
Authors: Baruzzi G. S. , Habashi W. G. , Guevremont J. G. , Hafez M. M.
Published: August 2005

The numerical solution of the compressible Euler and Navier‐Stokes equations in primitive variables form requires the use of artificial viscosity or upwinding. Methods that are first‐order‐accurate are too dissipative and reduce the effective Reynolds number substantially unless a very fine grid is used. A first‐order finite element method for the solution of the Euler and Navier‐Stokes equations can be constructed by adding Laplacians of the primitive variables to the governing equations. Second‐order schemes may require a fourth‐order dissipation and higher‐order elements. A finite element approach is proposed in which the fourth‐order dissipation is recast as the difference of two Laplacian operators, allowing the use of bilinear elements. The Laplacians of the primitive variables of the first‐order scheme are thus balanced by additional terms obtained from the governing equations themselves, tensor identities or other forms of nodal averaging. To demonstrate formally the accuracy of this scheme, an exact solution is introduced which satisfies the continuity equation identically and the momentum equations through forcing functions. The solutions of several transonic and supersonic inviscid and laminar viscous test cases are also presented and compared to other available numerical data.
Numerical simulation and optimal shape for viscous flow by a fictitious domain method
Authors: Glowinski Roland , Pan Tsorng‐Whay , Kearsley Anthony J. , Periaux Jacques
Published: August 2005

In this article we discuss the fictitious domain solution of the Navier‐Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no‐slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regriding. The resulting methodology is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier‐Stokes equations and then to an optimal shape problem for Stokes and Navier‐Stokes flow.
Positive schemes and shock modelling for compressible flows
Authors: Jameson Antony
Published: August 2005

A unified theory of non‐oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presented which confirm the properties of these schemes.
On computatbility and error control in CFD
Authors: Johnson Class
Published: August 2005

We give an overview of some recent results concerning quantitative adaptive error control in CFD.
Parameter identification and optimal control of ground temperature
Authors: Kawahara Mutsuto , Sasaki Ken‐Ichi , Sano Yasuhiko
Published: August 2005

To avoid the use of pesticides on putting greens of golf courses, a temperature regulator system is strongly recommended nowadays in Japan. To maintain grass on the putting green without pesticide, the temperature of the ground should be controlled. This system consists of a cooling machine and buried pipes in the ground. The temperature of the water in the pipes cannot be regulated. In this paper, both identification and control problems are presented by the minimization technique and applied to a practical problem. To establish the system, it is important to obtain accurate parameters which are included in the governing equation. These parameters can be determined by parameter identification. The conjugate gradient method is used for the parameter identification procedure. The control problem aims to make the temperature at arbitrary points close to the objective temperature. The discrete‐time dynamic programming is used for the control procedure.
Turbulence models for unstructured finite element calculations
Authors: Marcum David L. , Weatherill Nigel P.
Published: August 2005

An unstructured finite element method is presented for calculation of turbulent flow fields about aerospace configurations. Algebraic, one‐equation, and two‐equation turbulence models are implemented and compared. A new procedure for implementing an unstructured algebraic model without an auxiliary structured grid is presented. The overall procedure is applied to simulation of flow about launch vehicle configurations. The turbulence models are evaluated for calculation of flow fields about a forebody with shock induced separation. For this case. the one‐equation model gives better predictions. An inviscid flow field about a complete launch vehicle with multiple boosters is also evaluated to demonstrate the overall procedure.
A general algorithm for compressible and incompressible flow—Part II. tests on the explicit form
Authors: Zienkiewicz O. C. , Morgan K. , Sai B. V. K. Satya , Codina R. , Vasquez M.
Published: August 2005

The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance. Examples range from nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks. In most examples linear triangular elements are used in the finite element approximation, but some use of quadratic approximation, again in triangles, indicates satisfactory performance even in the case of severe shocks.
Optimum aerodynamic shape design including mesh adaptivity
Authors: Bugeda Gabriel , Oñate Eugenio
Published: August 2005

This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation of the sensitivities of the geometrical design parameters, the mesh, the flow variables and the error estimator to project the refinement parameters from one design to the next. This sensitivity analysis is described for the incompressible potential equations and the Euler equations. The efficiency of the proposed method is checked by means of two 2D inverse problems.
A split‐characteristic based finite element model for the shallow water equations
Authors: Zienkiewicz O. C. , Ortiz P.
Published: August 2005

A new algorithm for the solution of the shallow water equations is introduced. The formulation is founded on a suitable operator‐splitting procedure for which a characteristic‐based rational form of including balancing dissipation terms is achieved.

In the semi‐explicit form the method circumvents the requirement of a critical time step given in terms of the wave celerity, which is restrictive for the analysis of long‐wave propagation in shallow waters.

In this work the robustness of the algorithm is illustrated for transient shallow water problems and for some supercritical flows, where the choice of an algorithm with optimal diffusion properties is manifest.
In vitro evaluation of biocompatibility of beta‐tricalcium phosphate‐reinforced high‐density polyethylene; an orthopedic composite
Authors: Homaeigohar S. SH. , Shokrgozar M. A. , Sadi A. Yari , Khavandi A. , Javadpour J. , Hosseinalipour M.
Published: August 2005

Beta‐tricalcium phosphate‐reinforced high‐density polyethylene (β‐TCP/HDPE) is a new biomaterial which was made as a copy of bone composition with the aim of replacement of bony tissues. The composite samples were prepared using medical grade TCP powder and granular polyethylene. The raw materials were first compounded and the resulting composite preforms were compression molded into desired shape. The biocompatibility of composite samples with different volume fractions of TCP (20, 30, and 40 vol %) was assessed by proliferation, alkaline phosphatase (ALP), and cell adhesion assays using G‐292 osteoblast cells. Cell–material interaction on the surface of the composites was observed by scanning electron microscopy (SEM). The effect of β‐TCP/HDPE on the behavior of G‐292 cells was compared with those of a composite and a negative control samples. Results showed the composite samples had a higher proliferation rate of G‐292 cells in the presence of composite samples as compared to the composite control sample after 3, 7, and 14 days of incubation period. ALP production after incubation in the presence of composite samples was seen to peak on the day 7. The number of adhered cells on the composite samples was higher than the numbers adhered on composite and negative control samples after the above incubation periods. Morphology investigation of adhered cells by SEM indicated a normal morphology and also many of the cells were in the process of cell division. The above results indicate that β‐TCP/HDPE samples are biocompatible, nontoxic, and in some cases show an increase in the proliferation rate of the cells, ALP production, and cell adhesion as compared to the control counterparts. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2005
A discrete model of substitutional‐interstitial diffusion in the Czochralski growth of semiconductor crystals
Authors: Hearne M. T. , Rogers T. G. , Tuck B.
Published: August 2005

A discrete model is developed to describe the diffusion of dopant/impurity in a single semiconductor crystal during Czochralski growth. The basic diffusion mechanism is assumed to be substitutional‐interstitial interchange for the impurity, together with self‐diffusion of the host atoms. In particular, the model incorporates the complicated conditions that result from the simultaneous growth and diffusion taking place at the crystal/melt interface. The high temperature dependence of the process is also taken into account, together with possible vacancy production to counteract vacancy depletion. The numerical model is explicit in time, and conditions for convergence and stability are considered. Results are presented for chromium doping of growing gallium arsenide crystals, and compared with published experimental data.
New one‐ and two‐dimensional algorithms for the transient simulation of semiconductor devices
Authors: Towers M. S. , McCowen A.
Published: August 2005

One‐ and two‐dimensional algorithms for the transient simulation of semiconductor devices are presented which incorporate a solenoidal total current. The paper includes results from one‐dimensional simulation of a p‐n junction, including forward‐to‐reverse bias switching and also switching and also switch‐on into high injection in an asymmetric structure. A discretization scheme for the two‐dimensional formulation is described with details on handling voltage driven terminals and the associated boundary conditions.
High‐frequency propagation on nonuniform multiconductor transmission lines in uniform media
Authors: Baum Carl E.
Published: August 2005

The asymptotic form, for high frequencies, of the equations of propagation on a nonuniform N‐conductor transmission line is considered. Under the assumption of perfect conditions in uniform, isotropic media, all N propagation velocities are the same, but the characteristic impedance matrix is allowed to vary with position along the line. Closed‐form solutions are obtained for some cases of interest.
Drift–diffusion versus energy model for millimetre‐wave impatt diodes modelling
Authors: Dalle C. , Rolland P. A.
Published: August 2005

A new P–N junction device model is presented. It consists of two numerical unidimensional macroscopic models. The first is a drift–diffusion model. The second is an energy model accounting for the carrier energy relaxation effects. Because device optimization requires systematic investigations, the computing time is of paramount importance and, so an accurate comparison between these two models was undertaken under both static steady‐state and dynamic 94 GHz conditions in order to point out the relative interest of the energy model. This study is mainly devoted to silicon millimetre‐wave IMPATTs. This comparison has highlighted the superiority of the energy model for the description of low field transport phenomena. But as IMPATT RF properties are mainly governed by high field transport, the RF power levels predicted by the two models have been found to be similar. Moreover it has shown that the energy model tends to underestimate both the efficiency and the diode terminal negative resistance level. This parasitic effect is inherent to the description of the carrier generation process by impact ionization which in this model is assumed to be governed by the carrier energy.
An application of dyadics to the analysis of power transformers
Authors: Davies A. E. , Farrier D. R. , German D. M.
Published: August 2005

A simulation of power transformers following switching operations is presented in which each core section is represented by a non‐linear inductance, the differential inductance being determined from the flux density in that section of the core. In analysing the resultant circuit model for the transformer it is shown that the circuit equations have dyadic properties which can be used to give a more efficient numerical solution.
Investigation on the power‐handling capacity of a class of E‐plane millimetre‐wave filters using finite element modelling
Authors: Ney Michel M. , Chénier Mario , Costache George I.
Published: August 2005

An approach, based on the finite element method (FEM), is used for evaluating the electromagnetic field distribution in a class of E‐plane metal insert filters, operating in the Ka‐band. Artificial boundary conditions are inserted directly in a functional, enabling a solution of the scalar wave equation by finite element method.

The scattering parameters of the filter, the electromagnetic field and, therefore, the current distributions on the thin metal inserts are computed. Then, the power dissipated in the metallic septa, which is one of the major limitations for the maximum CW‐power that can be handled by these types of filter, is evaluated using a perturbational approach. Finally, the maximum field intensity is determined, allowing an estimate of the maximum peak power that these structures can handle.
Multigrid TLM for diffusion problems
Authors: Wong Chi Chung , Wong Wing Sun
Published: August 2005

The multigrid technique, which is mainly used in the finite difference method, is applied to the TLM (transmission‐line matrix or modeling) procedure. In the multigrid TLM, the field region is covered with sets of regular transmission‐line matrices of different mesh sizes. The finer grid pattern, which overlaps the coarser grid, fills the region with high field gradients. Data obtained in the coarser grid are transferred to the finer grid through an interpolation process and used as boundary conditions for the latter. The finer grid data are then transferred back to the coarser one, thus improving the coarse grid values. The method is applied to several diffusion problems and significant improvements in accuracy and efficiency are shown.
The modelling of EM leakage into advanced composite enclosures using the TLM technique
Authors: Mallik A. , Loller C. P.
Published: August 2005

The TLM technique has been enhanced to allow the accurate modelling of EM diffusion through advanced composite material shells. This is a significant development owing to the rapidly increasing use of conducting composite materials in aerospace vehicle design. The accurate EM modelling of this class of materials is important for correct design of vehicles with regard to electromagnetic compatibility (EMC).

Existing 3‐D time‐domain TLM models a non‐perfectly conducting shell using a resistive sheet (or sheets) to simulate the surface. The results from this model are shown to be slightly inaccurate and require lengthy computer solution times. A separate 1‐D, frequency‐domain transmission‐line model has been developed elsewhere to better analyse the diffusion properties of composite materials. The incorporation of the results from this frequency domain code into the 3‐D time‐domain TLM algorithm is outlined.
Transmission‐line modelling of semiconductor lasers: The transmission‐line laser model
Authors: Lowery Arthur James
Published: August 2005

The application of the transmission‐line modelling technique to the design of semiconductor lasers and optical systems is reviewed. Generalized scattering matrices are developed to allow the technique to be applied to novel devices and systems.
Planar analysis of radial‐line power dividers
Authors: Bartolucci G. , Giannini F. , Paoloni C.
Published: August 2005

The resonant mode field expansion technique presented in previous papers to analyse one‐ or two‐port microstrip structures of different geometrical shapes is now applied to multiport radial lines. In particular, a radial‐linen‐way power divider is considered. This device allows, under certain hypotheses, an equiphase and equiamplitude splitting of an input signal. TheZmatrix formulation has been derived and utilized to obtain the scattering parameters for the circuit. The numerical results are in good agreement with both experimental and theoretical data presented in the literature. The low number of resonant modes required to obtain satisfactory numerical convergence allows a substantial reduction of the computing time with respect to other more complicated approaches.
Non‐linear diffusion in process modelling
Authors: Baines M. J. , Birkett N. R. C. , Sweby P. K.
Published: August 2005

The non‐linear diffusion mechanism arising in process modelling is analysed via a model problem. Using a scaling of the dopant concentration and an adaptive finite element method, high resolution is obtained in a particularly economical way.
Estimation of parameters in numerical modelling of non‐linear diffusion in semiconductors
Authors: Meere M. G. , King J. R. , Rogers T. G.
Published: August 2005

A procedure is described for estimating various parameters governing the diffusion of impurities in semiconductors; these parameters are required for a number of explicit numerical models of non‐linear diffusion in III‐V crystals. The method is based on an analytical solution of the continuum equivalent of a discrete numerical model due to Zahari and Tuck and provides a systematic procedure for analysing experimental data to yield predictions for the coefficient of diffusion of the impurity, the coefficient of self‐diffusion of the host material, the bulk equilibrium vacancy concentration and, under conditions of “dissociation” pressure, the surface vacancy concentration. Application of the procedure to two sets of independent experimental data provided reasonably consistent values of the parameters.
The modelling of surface evolution during growth and erosion
Authors: Katardjiev I. V. , Carter G. , Nobes M. J.
Published: August 2005

When the erosion or growth of a surface that occurs in semiconductor device processing can be considered as everywhere continuous in space and time, the equations of motion of the surface may be specified and determined numerically using a kinetic model of surface evolution. In this review the fundamental concepts of the kinematic model of surface evolution are discussed. Detailed consideration of the theory of characteristics reveals its limitations which are overcome by recent theoretical development based on the Huygens principle of wavefront reconstruction. Correct interpretation of the nature of the basic wavelet, coupled with contemporary ideas of surface and edge propagation, form the essence of a new numerical algorithm. Numerical analysis and consequent numerical procedures derived from the generalized kinematic model are presented. Examples of surface evolution, with particular reference to ion beam induced erosion are given to show the advantages and potential of the method as opposed to existing models and theoretical prediction.

When evolution processes are discontinuous and localized, other approaches, particularly those that use numerical modelling, are required. Such approaches are also reviewed here.
A model for atomic mixing
Authors: Wadsworth M. , Armour D. G. , Badheka R. , Collins R.
Published: August 2005

This paper is concerned with the theoretical determination of the amount of atomic mixing which accompanies the erosion of a solid surface exposed to an energetic ion beam. The work is relevant to sputter depth profiling where such mixing complicates the deduction of the initial depth distributions from the measured ion yields.

A mathematical model, which considers the effects of incident ion accumulation, ballistic relocation and diffusion is described. The governing integro‐differential equations are solved numerically.

Results for a GaAs‐AlGaAs multi‐layer structure bombarded with O ions are compared with results obtained experimentally.
A hybrid moment‐ray‐mode method for wave scattering from an aperture coupled system
Authors: Lu I‐Tai , Ma Bai‐Lin
Published: August 2005

Wave scattering from an aperture coupled system is studied using a new method which combines the hybrid ray‐mode method and method of moments. The latter is used to formulate the coupling process and the former to provide the Green's function of a parallel plate waveguide. Following standard procedures of the method of moments, we first formulate a system equation for field distributions across the aperture. By expressing these unknown distributions in terms of appropriate basis functions and choosing appropriate weighting functions, the system equation is then reduced to a matrix equation which is solved numerically. In the system of equations, one needs to compute the Green's function of the waveguide for various arrangements of locations of source and receiver. The hybrid ray‐mode formulation is best suited for this purpose because it combines rays and modes self‐consistently to optimize the advantages of each. The efficiency of the ray‐mode Green's function makes use of the moment method practical in waveguides, and the flexibility of the moment method permits application of the Green's function considered to arbitrarily shaped and placed apertures. Numerical implementation illustrates these aspects.
Functional relaxations and spectral techniques in Computer‐Aided circuit analysis
Authors: Guarini Marcello W. , Palusinski Olgierd A.
Published: August 2005

Analysis of transients in integrated circuits is performed with the use of highly specialized computer programs. The transient responses are computed using time‐marching integration methods and require a substantial amount of computer time. A new method based on spectral analysis and waveform relaxation is proposed. The method results in a substantial saving in computing time without compromising the accuracy. A basic algorithm utilizing the spectral technique in a relaxation framework is described. A prototype simulator based on the algorithm was developed and used to simulate certain types of CMOS circuits. The results showed a significant time savings in comparison with the widely used circuit simulator ‘SPICE’. Example circuits and relevant results are provided.
Numerical solution of inhomogeneous and non‐linear ordinary differential equations using the TLM multicompartment model
Authors: Saleh A. H. M. , De Cogan D.
Published: August 2005

The paper presents a simple algorithm for solving a system of inhomogeneous high order differential equations with variable coefficients. The method also provides a numerical solution to non‐linear ordinary differential equations. The technique is based on reducing the high order equations into a system of first order rate equations. Through a simple translation process, the variables in the reduced set of equations are solved simultaneously by an iterative scheme using the TLM multicompartment model. The numerical technique is demonstrated by solving well‐known second order differential equations. The numerical solutions are compared with the analytical solutions to the differential equations.
Comparison between different formulations of the transverse resonance field‐matching technique for the three‐dimensional analysis of metal‐finned waveguide resonators
Authors: Bornemann Jens
Published: August 2005

Two different formulations of the transverse resonance field‐matching technique are applied to evaluate the modal spectrum of metal‐finned waveguide structures. In the theoretical treatment, Method 1 uses boundary conditions prior to interface relations and allows the number of expansion terms to be selected according to the dimensions of the cross‐section subregions. Method 2 imposes boundary and interface conditions in reversed order but requires the same number of expansion terms to be used in various subregions. The two procedures are then compared with respect to their influence on the modal scattering matrix computation of metal‐finned waveguide resonators. Method 2 shows excellent agreement with measurements, but it is restricted to configurations with relatively thin fins and moderate slot widths. Although Method 1 may be applied to more general structures, this procedure requires a higher computational effort and leads to slightly different results. However, it constitutes a powerful PC‐operational alternative whenever an extended precision compiler, as required for Method 2, is not available.
Numerical modelling of microwave detectors at high signal level
Authors: Wolski Mark R. , Ishii T. Koryu
Published: August 2005

The relationship between microwave power absorbed by a detector diode and the resulting detected voltage at high signal level is investigated. Experimental data is obtained from a zero‐biased diode mounted in a rectangular waveguide system operating at 9.5 GHz. The Alpa Industries Inc. 4561, 6724 and 6725 Schottky diodes and the M/A‐COM 1N23 Point Contact diode with 1 kω and 106 kω loads are examined. The P–V relationships are analysed by solving a system of non‐linear differential equations based on a lumped parameter model of the microwave system and diode.
Numerical modelling of hot electron transport in A graded heterojunction diode
Authors: Hjelmgren Hans , Snowden Christopher M.
Published: August 2005

A detailed one‐dimensional energy transport model for unipolar GaAs/AlGaAs heterojunction structures is implemented, by extending the basic transport equations to include the energy balance equation for electrons. A non‐uniform grid‐mesh is used to obtain short simulation times, while the grid‐distance at the N–n++ interface is small, which is essential to obtain a low reverse current.
Hydrodynamic simulation of electron heating in conventional and lightly‐doped‐drain MOSFETs with application to substrate current calculation
Authors: Chai Kam‐Wing , Mawby P. A. , McCowen A.
Published: August 2005

This paper reviews the state of the art in hydrodynamic simulation of hot‐carrier transport in semiconductor devices with application to MOSFET substrate current calculation. Hydrodynamic equations for semiconductors and derived and discretized expressions of these equations for device simulation are presented. Special attention has been given to the discretization of the input power term that appears in the energy conservation equation. A new discretization method for the input power term, based on power generation consideration, is proposed. Energy‐based physical models for mobility and impact ionization are described for use in hydrodynamic simulation. Simulation results for both conventional and lightly‐doped‐drain MOSFETs are presented.
A space‐domain preconditioned spectral method for non‐linear boundary value problems
Authors: Axelrad V.
Published: August 2005

A novel spectral procedure for the numerical solution of non‐linear boundary value problems is presented. The discrete spectral equations are solved by an iterative algorithm using space‐domain preconditioning. The preconditioning operator is obtained by spatial weighting (or windowing) of the exact differential operator.

Convergence behaviour of the iterative solution is investigated using an eigenvalue analysis. Theoretical estimates for the convergence rate and accuracy are compared with that achieved in a numerical application—a non‐linear boundary value problem from semiconductor device modelling.

The method combines the infinite‐order exponential accuracy of spectral discretizations with the sparse structure of finite difference equations. This offers numerical advantages in comparison to previously developed Fourier–Galerkin algorithms, particularly important for physically ill‐conditioned and strongly non‐linear problems. The tradeoff of achievable accuracy versus computer time is easily controlled, thus making essential speed‐ups possible for moderate accuracy requirements.
Discrete modelling of transport processes in two spatial dimensions
Authors: Enders Peter , de Cogan Donard
Published: August 2005

A random flight model of linear transport processes in two spatial dimensions is considered and solved exactly in closed algebraic form. Its one‐dimensional version had been proposed by Taitel as a means to overcome the paradox of infinite speed of propagation within classical heat diffusion theory. The connection with hyperbolic diffusion theory is complemented here by deriving the discrete fluxes and their relaxation term. Moreover, such an approach circumvents the discretization of a continuum model for an intrinsically discrete process, when diffusion processes are to be solved numerically. Finite samples are treated by means of the reflection method. Some applications of these general results are mentioned.
An error parameter in TLM diffusion modelling
Authors: Gui Xiang , Webb Paul W. , de Cogan Donard
Published: August 2005

This paper reports the results of a study of an error parameter, m, which has been proposed as a measure for determining the effects on accuracy of the basic assumptions upon which TLM modelling of diffusion and heat flow has been founded. The nature of the m parameter is studied in detail by using a two‐dimensional thermal diffusion problem. The use of m in the implementation of automatic timestepping is discussed in a practical three‐dimensional engineering problem.
Finite difference time‐domain simulation of electromagnetic fields and microwave circuits
Authors: Wolff Ingo
Published: August 2005

An overview is given on the application of finite difference time‐domain analysis techniques to the simulation of electromagnetic wave phenomena and the design of planar microwave integrated circuits. In particular the application to the analysis of three‐dimensional discontinuities in coplanar microwave circuits is described and numerical and experimental results are presented. Finally the design of planar microwave circuits containing non‐linear active components using the finite difference time‐domain method in combination with a harmonic balance technique is demonstrated using an example of a LUFET circuit.
Multidimensional wave digital filters for discrete‐time modelling of Maxwell's equations
Authors: Fettweis Alfred
Published: August 2005

An approach for numerically integrating the partial differential equations describing passive physical systems consists in modelling the continuous‐domain physical system by means of a passive discrete‐domain system. As has recently been shown, this can be achieved, in particular also for Maxwell's equations, by means of the same principles as known from multidimensional wave digital filters, which offers a number of important advantages. The present paper deals specifically with the application of the approach to Maxwell's equations and supplements corresponding results previously published.
Body fitted grid generation with moving boundary and its application for dielectric waveguides
Authors: Kuroda Shigeaki , Kuroda Michiko
Published: August 2005

The stress birefringence and mode coupling effects in polarization‐preserving fibres are most important problems which need to be improved. For a realization of some optical devices, the dielectric waveguide with sinusoidally varying circular cross‐section has been investigated. It becomes very important to analyse the electromagnetic field distribution in a dielectric waveguide with a time‐dependent moving boundary. This paper shows that numerical methods can simulate the effect of the external disturbance on the dielectric waveguide from time to time. The author has discussed body fitted grid generation with moving boundary for the Poisson and Laplace equations.1,2 We have extended this technique for Maxwell's equation. The technique employs a kind of an expanded numerical grid generation. As the author adds the time component to grid generation, the time dependent co‐ordinate system which coincides with a contour of moving boundary can be transformed into a fixed rectangular co‐ordinate system. We could show the electric distribution in the waveguide time by time to verify the possibility of an application for an optical fibre. This technique makes it possible not only to analyse the effect of the external disturbance in a coherent optical communication system but also to fabricate optical devices.
An E‐plane sectoral horn fitted with side‐lobe suppression devices
Authors: Ata O. W. , Benson T. M. , Marincic A.
Published: August 2005

A finite difference method is used to design a new type of sectoral horn antenna with corner channel inserts which produces a tapered aperture amplitude distribution in the E‐plane. The channel inserts, which present a simple modification to the horn aperture geometry, act as effective side‐lobe suppression devices. The efficiency of the suppression technique was successfully tested on an experimental horn whose performance is compared to that of a horn with similar geometrical dimensions but with no channel sections.
A comparative study of two TLM networks for the modelling of diffusion processes
Authors: Gui Xiang , Webb Paul W.
Published: August 2005

A comparative study of two alternative networks for TLM modelling of diffusion processes has been undertaken. Some of their inherent advantages and disadvantages are analysed according to the ratio between the impedance of the lossless transmission lines and the lumped resistance. Their relative accuracy and utility in controlling the timestep automatically are examined.
An extended frequency‐domain prony's method for transfer function parameter estimation
Authors: Chakrabarti Swapan , Demarest Kenneth R. , Miller Edmund K.
Published: August 2005

The estimation of transfer‐function parameters, such as poles and zeros, is useful for characterizing and identifying electromagnetic scatterers. The conventional frequency‐domain Prony's technique can estimate these parameters from sampled, frequency‐domain data. However, it fails to estimate the true parameters when the sampled data contains contributions from out‐of‐band poles. In this paper, an extended frequency‐domain Prony's technique is developed that circumvents this problem by adding polynomial terms to the standard, Prony pole series. This new technique is shown to be very effective for estimating the poles of transfer functions over very wide bandwidths, without the need for large numbers of simultaneous equations, even when the data are corrupted by noise.
Finite deffernce time‐domain approximation of Maxwell's equations with non‐orthogonal condensed TLM mesh
Authors: Hein Steffen
Published: August 2005

A convex hexahedral TLM mesh of arbitrary shape is presented and the transmission‐line matrix method extended to any non‐orthogonal configuration. The novel mesh constitutes a natural generalization of Johns' condensed node. The associated TLM process is analysed and reconstructed as a genuine finite difference time‐domain algorithm. Nodal S‐parameters are derived from discretized Maxwell's equations and canonical stability criteria yield the TLM timestep. Unitarity is discussed and energy conservation confirmed in the non‐conductive case.

A given block‐diagonal representation of the S‐matrix restrains processing time per node and iteration within the range of traditional methods. The shortcomings of the rigid classical grid, as the need for inaccurate staircasing approximations, are, however, ruled out.

Our analysis takes advantage of the recently developed propagator integral approach.
Transverse tranśmission theory for multilayer planar microwave circuits
Authors: Wu Ke , Tong Cheuk‐Yu Edward , Saguet Pierre
Published: August 2005

Transverse transmission concepts in the Fourier transmission domain for multilayer planar transmission medium are presented. This complete transverse transmission theory (TTT) is found to be a superset of different Fourier‐transform‐based numerical techniques widely used in guided wave analysis, namely the modematching method and the spectral‐domain approach. The features of the theory are: the expansion of field quantities in longitudinal section (LSE/LSM) modes, the concept of rotation of the transverse field vectors, and a comprehnsive algorithm using recursive matrix standard form. It is shown that the mode‐matching method and spectral‐domain approach are generally equivalent except for the last step of imposing the final boundary conditions, and can therefore be summarized in a unified theory within the framework of TTT. In addition, a new parameter, the polarization coefficient, has been introduced to describe the field polarization of the guided wave in a quantitative manner. It is believed that the present theory will help us to gain more insight into hybrid mode propagation in multilayer planar circuits.
Symbolic approach to inverse problems in method of moments
Authors: Analoui Morteza , Fujimoto Masayoshi , Kagawa Yukio
Published: August 2005

Symbolic computational systems introduce some unique features in computational engineering. There have been several papers published on the solution of differential equations under given boundary conditions by symbolic systems. The finite element formalism has received prime attention in the course of development of symbolic computation in engineering. The main idea has been to develop a symbolic FEM package to reduce the burden of manual algebra, eliminate errors introduced by numerical quadrature, and improve the efficiency of element generation.

This work discusses a symbolic solution to electromagnetic linear antenna problems. The solution is a method of moments that transforms Pocklington's integral equation to a matrix equation. The symbolic system is used to produce (1) analytical integration, (2) the parametric expression for the input impedance and (3) computational code for forward and reverse problem of the input impedance.
Discrete Green's functions and hybrid modelling of thermal and particle diffusion
Authors: De Cogan D. , Enders P.
Published: August 2005

This paper provides details of a widely applicable technique of hybrid modelling of thermal and particle diffusion which can help to reduce computational load in explicit formulation. The undesirable effects of artificial boundaries, which are introduced when a simulation is truncated or when an expanding mesh is used, can be eliminated by the use of discrete Green's functions. The technique can also be applied to problems involving infinite or near‐infinite domains or problems where a complex thermal region is embedded within a larger, more simply described domain.
A Laplace domain finite element method (LDFEM) applied to diffusion and propagation problems in electrical engineering
Authors: Cai X.‐D. , Costache G. I.
Published: August 2005

This paper presents a new finite element formulation in the Laplace domain for both diffusion and wave equations with applications in the field of electrical engineering. With the aid of congruence transformation of matrices, the finite element equations in the Laplace domain are solved and time‐domain results can be obtained through the inverse Laplace transform. In a test problem, good agreement between the numerical results derived with the present method and the analytical solutions has been found. For applications in which only Dirichlet and Neumann boundary conditions are involved, this new finite element approach can be applied and provide both frequency‐domain and time‐domain results in one run without any timestepping scheme. The limitations of using the congruence transformation in solving propagation problems are also addressed in this paper.
Numerical analysis of discontinuities in a rectangular waveguide loaded with isotropic or anisotropic obstacles by means of the coupled‐mode method and the mode‐matching method
Authors: Solano Miguel A. , Vegas Angel , Prieto Andreés
Published: August 2005

A hybrid method obtained as a combination of the coupled‐mode method (CMM) and the mode‐matching method (MMM) is developed and applied in the analysis of multiple dielectric and magnetic discontinuities in rectangular waveguides. As both are moment methods, some kind of truncation has to be carried out in the computer implementation. It is shown that selection of a different number of modes in the two methods is not necessary, unless low‐permittivity meida inside the waveguide are considered. As a consequence, the procedure for slecting the number of basis functions is only done in one of the methods. Numerical examples are presented showing the behaviour of the method and the proofs of convergence. Examples are included illustrating the power of this hybrid technique, especially in relation to non‐reciprocal structures containing magnetized ferrites.
Use of the two‐dimensional TLM method in the electromagnetic simulation of thin semiconductor samples
Authors: Dindo Salam F. , Ney Michel M. , Harrison Robert G.
Published: August 2005

A two‐dimensional lossy shunt TLM node is incorporated into a TLM system and adapted to model for the first time the Maxwell field equations in thin semiconductor samples. Both the characteristics of the node and the TLM system itself are fully described. By considering a parallel‐plate structure containing a thin GaAs sample, driven by a voltage source, it is shown, with an example, that this TLM technique can simulate the response of non‐stationary electromagnetic fields in a semiconductor to applied excitations.
A survey of various computer architectures for solution of large matrix equations
Authors: Swaminathan Madhavan , Sarkar Tapan K.
Published: August 2005

In electromagnetics, a numerical technique that finds immense application is the method of moments. This method reduces the boundary value problem containing integro‐differential equations into the form AX = Y, where A is a full complex matrix, that is known and X is the unknown to be solved for the given excitation Y. In this paper, the matrix equation has been solved on various computers such as the VAX 3500, VAX 8530, Multimax 320, Alliant FX/80 and IBM 3090‐600E. Two of the established methods, viz. gaussian elimination and the conjugate gradient method have been used to solve the above matrix equations. A detailed timing analysis has been done to bring out the features of various computer architectures.
Parallel and distributed TLM computation with singal processing for electromagnetic field modelling
Authors: So P. P. M. , Eswarappa C. , Hoefer W. J. R.
Published: August 2005

This paper describes the implementation of transmission‐line matirix (TLM) method algorithms on a massively parallel computer (DECmpp 12000), the technique of distributed computing in the UNIX environment, and the combination of TLM analysis with Prony's method as well as with autoregressive moving average (ARMA) digital signal processing for electromagnetic field modelling. By combining these advanced computation techniques, typical electromagnetic field modelling of microwave structures by TLM analysis can be accelerated by a few orders of magnitude.
A connection machine (CM‐2) implementation of a three‐dimensional parallel finite difference time‐domain code for electromagnetic field simulation
Authors: Davidson David B. , Ziolkowski Richard W.
Published: August 2005

This paper describes a parallel three‐dimensional finite difference time‐domain (FDTD) code for electromagnetic field simulation that has been developed for the Connection Machine (CM‐2). The CM‐2 is briefly discussed. Then the FDTD method is reviewed using a one‐dimensional example, and the extensions required for the 3‐D case are outlined. The parallelization of the FDTD method is considered, and a simple analytical timing model is dervied. This model predicts the efficiency of the parallelized algorithm as a function of grain size. Some specific points relating to the implementation of the parallel FDTD algorithm in Fortrans‐90 on the CM‐2 are discussed. Timing data for the parallel 3‐D FDTD code measured on a CM‐2 is presented and compared qualitatively with the theoretical model. These results are then put into perspective for a particular computations electromagnetics problem, viz. the development of software tools for full‐wave modelling of 3‐D optical devices. Finally, we draw some conclusions about this work.
Parallel FDTD simulator for MIMD computers
Authors: Effing U. , Kümpel W. , Wolff I.
Published: August 2005

A parallel implementation of the finite difference time‐domain algorithm for the analysis of planar microwave circuits is presented in this paper. For this the FDTD mesh is divided in equal‐sized subspaces. Every processor of the parallel computer calculates the field in one subspace. Furthermore detailed efficiency investigations are made to predict the timing performance of the parallel FDTD simulator.