Using cubic B-spline interpolation for efficient ray-tracing-based ultrawideband propagation modeling

Polarization ray tracing, which consist of several extensions to geometrical ray tracing, calculates the evolution of polarization states along ray paths and determines the intrinsic polarization properties, such as diattenuation and retardance, associated with ray paths. This paper compares the suitability of the Jones, Mueller, and a three-dimensional polarization ray tracing calculi, examining the issues of local versus global coordinates, amplitude versus phase representations, inclusion of the wavefront aberration function, partially polarized light, measurements of images by polarimeters, and diffraction image formation by low and high numerical aperture beams.

Ray tracing is a method that allows the creation of stunning photo‐realistic images on a computer. Most ray tracing programs can model any three‐dimensional object which can be described by mathematical formulae. Looking closely at ray tracing many situations can be found where this technique can be useful. In this article a widely available shareware ray tracing program, PovRay, is described. Some ideas how PovRay can be used in teaching and 3D geometry, physics, and other high school and university subjects.

Electromagnetic field and potential computations on elements with curved contours in boundary element and volume integral methods require evaluation of a number of Jacobian complete and/or incomplete elliptic integrals of all three kinds for the same modulus but different angles, depending on the arc length and the angle coordinate of the field point. Up to now, they have been evaluated individually, repeating the same algorithms a number of times. To reduce such redundant computations, a compact algorithm based on a modified Landen transformation is developed for elliptic integrals with an extended integration range - pi <or= alpha /sub i/<or= pi . Computational accuracy and time saving are discussed.<<ETX>>

Ray tracing has been traditionally used with applications for media and entertainment (3D animation, rendering), product development (CAD/CAM/CAE), life sciences (medical, molecular), energy, and other operations. The ray-tracing programs are used by engineers and artist proposing a project concept or new product design, by designers who bring the first renditions of the project or product for evaluation, by manufacturing people who build and test the project, or product virtually in the computer. And then when everything is proven and acceptable, marketing people use ray tracing to create images to sell the product. Ray tracing is used in all four stages from project concept to fulfillment. The concept of virtual prototyping and in the film industry pre-viz has been embraced by most industries and has saved millions of dollars by eliminating redos and expensive after-sales repairs.

End-to-end modeling of the photometric performance of LCD projection system using Monte Carlo geometrical ray tracing methods is an accurate and precise tool for predicting and improving the performance of these deices before, during and after product development. However, an accurate simulation first requires considering which physical properties contribute most to the system's photometric performance. Second, these properties must be characterized by physical measurements and translated into the tangible modeling parameters of a ray tracing program. Third, the implications of using a Monte Carlo ray tracing algorithm, and in general any other optical transformation algorithm, on radiometric accuracy must be well understood. These considerations as well as a generalized approach to the characterization and simulation of an LCD projector are described. A commercially available ray tracing program, the Advanced Systems Analysis Program, is used to demonstrate this approach. The irradiance uniformity, CIE color performance and screen brightness of an arc source LCD projector system are computed as an example.

This special issue of BIT contains articles related to the Workshop on Computational Electromagnetics andAcoustics, held at theMathematisches Forschungsinstitut Oberwolfach, Germany, in January 2013. This workshop was organized by R. Hiptmair (ETH Zurich, Switzerland), R. H.W. Hoppe (Univ. Augsburg, Germany and Houston, Texas), P. Joly (INRIA, Paris, France), and U. Langer (Univ. Linz, Austria). It was attended by 52 invited researchers in the field and had its focus on recent developments of mathematical theory and algorithms. A total of 26 presentations were given at the workshop, their topics covering major current developments in the field of Computational Electromagnetics and Acoustics. Extended abstracts of all contributions have been collected in the Oberwolfach Report 03/2013 (http://www.ems-ph.org/journals/ show_issue.php?issn=1660-8933&vol=10&iss=1, doi:10.4171/OWR/2013/03). Now, several participants of theworkshop, all leaders in their fields, have heeded the organizers’ call for papers for this special issue of the journal BIT. Their manuscripts provide a glimpse of current progress in the mathematical and numerical analysis of problems arising in acoustics or electromagnetics. The contribution P. Monk and J. Chen is in the very topical area of time-domain boundary integral equation methods, and contains deep numerical analysis of a convolution quadrature based scheme for transient electromagnetics. The article by X. Claeys, E. Spindler and myself proposes and analyses a novel boundary integral formulation for scattering transmission problems, whose Galerkin boundary discretization will always yield well conditioned linear systems In their paper M. Dauge, R. A. Norton, and R. Scheichl study the regularity of Bloch modes in photonic crystals, which arise as solutions of eigenvalue problems. They obtain new results in elliptic regularity theory, which are important for designing good approximation spaces for numerical methods.

We develop a new formulation of the integral equation (IE) method for three-dimensional (3D) electromagnetic (EM) field computation in large-scale models with multiple inhomogeneous domains. This problem arises in many practical appli- cations including modeling the EM fields within the complex geoelectrical structures in geophysical exploration. In geophysical applications, it is difficult to describe an earth structure using the horizontally layered background conductivity model, which is required for the efficient implementation of the conventional IE approach. As a re- sult, a large domain of interest with anomalous conductivity distribution needs to be discretized, which complicates the computations. The new method allows us to con- sider multiple inhomogeneous domains, where the conductivity distribution is differ- ent from that of the background, and to use independent discretizations for different domains. This reduces dramatically the computational resources required for large- scale modeling. In addition, using this method, we can analyze the response of each domain separately without an inappropriate use of the superposition principle for the EM field calculations. The method was carefully tested for the modeling the marine controlled-source electromagnetic (MCSEM) fields for complex geoelectric structures with multiple inhomogeneous domains, such as a seafloor with the rough bathymetry, salt domes, and reservoirs. We have also used this technique to investigate the return induction effects from regional geoelectrical structures, e.g., seafloor bathymetry and salt domes, which can distort the EM response from the geophysical exploration target.

Indoor wireless systems will be used in a large variety of office, factory and residential environments. Thus, adequate guidelines for radio port placement are needed to ensure satisfactory performance at the lowest cost. These guidelines must be derived from a large body of site-specific propagation data. However, collecting a statistically significant database through measurements is a daunting task. Alternatively, this database can be generated by using propagation models, validated by measurements. Several models exist for the statistical characterization of microwave propagation within buildings, However, statistical models do not provide site-specific information. We propose a hybrid model in which ray tracing is used to predict, at any given location, the local mean of the received power and the delay profile. Variations about the mean values can then be captured via a statistical description matched to the local environment. We describe an efficient 3-D ray tracing algorithm which accounts for all (transmitted as well as reflected) rays reaching the receiver location after an arbitrary number of reflections. We include the effects of the angle of incidence, the material dielectric constant and the antenna patterns. The predicted values for the local means of the received power are then compared against measurements to establish the accuracy of this approach.

The act of performing a sequential trigonometric ray trace through an optical system is as simple as applying Snell's Laws of refraction and reflection, along with some form of the grating equation, to the geometric description of the lenses and mirrors which can comprise that system. The orderly incorporation of these physical laws into an algorithm, which at the same time incorporates all possible geometries which may occur in this optical system, will be the result of this paper. The ray/surface equations and other useful numerical techniques will be spelled out in detail so that this paper can be used as a starting point for their own ray tracing program when commercial optical design codes are either not available or inappropriate.

The Whitney elements, discrete spaces based on differential forms, have proven their efficiency in electromagnetic field computation. However, they are built only in first order. This paper gives a general description of high order p-form (nodal, edge, facet and volume) elements. Their function spaces and the assignment of degrees of freedom on the simplexes are analyzed. General expressions of the basis functions are given. A comparison of several 2nd order elements is carried out. A procedure for the generation of the hierarchical basis of p-form elements is provided.

Computational method of modeling using COMSOL Multiphysics has been conducted to evaluate the performance of novel interdigital sensors. Based on the electromagnetic field analysis the optimum structure of interdigital sensor has been derived. The uniformity of electric field intensity in the sensing region resulted in the largest sensitivity of measurement. Three different structures of interdigital sensor were designed and fabricated. Experiments using raw seafood contaminated with peptide derivates and biotoxins were conducted.

Evaluation of electromagnetic fields may be performed in a systematic, general and efficient way by following the computational architecture outlined in [1, 2, 3] which suggests several types of hybrid methods. In this contribution we introduce the external and internal hybridization schemes: in the former, a volume of space is subdivided into subregions where different numerical methods are used, while in the latter, different numerical methods are combined together in the frame of the same subregion. p] Examples of internal and combinations of both are provided, showing their characters and usefulness in practical cases.

To improve the current density distribution and electromagnetic performance of air-core inductors, a structural optimization method combining back-propagation(BP) neural network and genetic algorithm(GA) is proposed for the study of axial and radial spiral multi-winding inductors. The Monte Carlo method was used to extract the structural size samples of the inductors, and the training dataset was obtained through the finite element calculation of electromagnetic fields. Based on BP neural networks, nonlinear mapping models between the inductance value, volumetric inductance density, current distribution non-uniformity coefficient, and inductor structural parameters were constructed. A sensitivity analysis of the inductor inductance value affected by the structural parameters was conducted using the Sobol index calculation. Using the current distribution non-uniformity coefficient as the fitness function and the volumetric inductance density as the constraint condition, a genetic algorithm was applied to globally optimize the structural parameters of the inductor. The optimization results were verified through a finite element comparison. The results show that, under the requirement of satisfying the volumetric inductance density, the current distribution non-uniformity coefficient of the Axial Helical Inductor (AHI)-type inductor was reduced by 4.57% compared with the best sample in the sampling, while that of the Radial Helical Inductor (RHI)-type inductor was reduced by 5.33%, demonstrating the practicality of the BP-GA joint algorithm in the structural optimization design of inductors.

Theoretical Research for Unmanned Aircraft Electromagnetic Survey: Electromagnetic Field Calculation and Analysis by Arbitrary Shaped Transmitter-Loop

The theory for calculating the intensity of sound in a refracting medium after reflection from a sloping bottom was first formulated by Einstein and Eby [L. T. Einstein and E. S. Eby, USL Tech. Memo. No. 1210-103-60 (1960)]. However, they did not pursue their development to the point of evaluating certain angle derivatives which are necessary to obtain quantitative results. The present paper describes such a computation for the particular case of up- and down-slope reflection from a flat inclined bottom bounding a medium in which the sound speed gradient is constant. The results have an important bearing on the sound intensities obtained with most ray tracing programs, since these usually trace rays from receiver to source, and a correction must be applied to obtain the intensity for the reverse path. For the flat bottom or for RSR or refracted transmission, this correction factor is the well-known ratio Cs2/Cr2, where Cs and Cr are the sound speeds at the source and receiver, respectively. This factor is not modified in the presence of reflection from a sloping bottom. [This work was supported by the U. S. Navy Electronic Systems Command.]