Trapezoid-Grid Finite-Difference Time-Domain Method for 3D Seismic Wavefield Modeling Using CPML Absorbing Boundary Condition

The large computational memory requirement is an important issue in 3D large-scale wave modeling, especially for GPU calculation. Based on the observation that wave propagation velocity tends to gradually increase with depth, we propose a 3D trapezoid-grid finite-difference time-domain (FDTD) method to achieve the reduction of memory usage without a significant increase of computational time or a decrease of modeling accuracy. It adopts the size-increasing trapezoid-grid mesh to fit the increasing trend of seismic wave velocity in depth, which can significantly reduce the oversampling in the high-velocity region. The trapezoid coordinate transformation is used to alleviate the difficulty of processing ununiform grids. We derive the 3D acoustic equation in the new trapezoid coordinate system and adopt the corresponding trapezoid-grid convolutional perfectly matched layer (CPML) absorbing boundary condition to eliminate the artificial boundary reflection. Stability analysis is given to generate stable modeling results. Numerical tests on the 3D homogenous model verify the effectiveness of our method and the trapezoid-grid CPML absorbing boundary condition, while numerical tests on the SEG/EAGE overthrust model indicate that for comparable computational time and accuracy, our method can achieve about 50% reduction on memory usage compared with those on the uniform-grid FDTD method.

From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

Оптические свойства кремниевых нанопилларов со встроенным вертикальным p-n-переходом

Resonance reflection of light from the ordered arrays of silicon nanopillars (Si NP) was investigated. The height of Si NP was 450 nm. The effect of Si NP oxidation in concentrated nitric acid on the position of resonances in reflection spectra was studied. A weak influence of the additional polymeric coating on the characteristics of reflection from the structures was proven. It is established on the basis of the results of experimental investigation and direct numerical modeling by means of three-dimensional finite difference time domain algorithm (3D FDTD) that the dependence of the resonant wavelength for Si NP on the diameter of Si NP is a linear function with nonzero displacement depending on the pitch.

A Novel Dual-Band Implantable Antenna for Pancreas Telemetry Sensor Applications

In this study, a novel implantable dual-band planar inverted F-antenna (PIFA) is proposed and designed for wireless biotelemetry. The developed antenna is intended to operate on the surface of the pancreas within the Medical Device Radiocommunications Service (MedRadio 401–406 MHz) and the industrial scientific and medical band (ISM, 2.4–2.5 GHz). The design analysis was carried out in two steps, initially inside a canonical model representing the pancreas, based on a finite element method (FEM) numerical solver. The proposed antenna was further simulated inside the human body taking into account the corresponding dimensions of the tissues and the electrical properties at the frequencies of interest using a finite-difference time-domain (FDTD) numerical solver. Resonance, radiation performance, electrical field attenuation, total radiated power, and specific absorption rate (SAR), which determines the safety of the patient and the maximum permissible input power and other electromagnetic parameters, are presented and evaluated.

Optical Vortices Sharp Focusing by Silicon Ring Gratings Using High-Performance Computer Systems

The diffraction of vortex laser beams with circular polarization (with different direction of polarization rotation) by silicon ring gratings was investigated in this paper. The silicon diffractive axicons with different numerical apertures (NA) were considered as such ring gratings. The considered diffractive axicons are compared with single silicon circular protrusion (cylinder). The finite difference time domain method was used for Light propagation (3D) through the proposed silicon ring gratings and silicon cylinder. The possibility of subwavelength focusing by varying the height of the elements is demonstrated. In particular, it is numerically shown that a silicon cylinder forms a light spot with the minimum size (intensity) of the longitudinal component of the electric field FWHM is 0.32λ.

A Numerical Method for Pulse Propagation in Nonlinear Dispersive Optical Media

In this work, the pulse propagation in a nonlinear dispersive optical medium is numerically investigated. The finite difference time-domain scheme of third order and periodic boundary conditions are used to solve generalized nonlinear Schr¨odinger equation governing the propagation of the pulse. As a result a discrete system of ordinary differerential equations is obtained and solved numerically by fourth order Runge-Kutta algorithm. Varied input ultrashort laser pulses are used. Accurate results of the solutions are obtained and the comparison with other results is excellent.