A fast directional algorithm for high-frequency electromagnetic scattering

This paper is concerned with the fast solution of high-frequency electromagnetic scattering problems using the boundary integral formulation. We extend the O(N log N) directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case. We also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm. When combined with a standard iterative method, this results in an almost linear complexity solver for the combined field integral equations. In addition, the butterfly algorithm is utilized to compute the far field pattern and radar cross section with O(N log N) complexity.     

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.     

Numerical modeling of transient two-dimensional viscoelastic waves

This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the relaxation parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this numerical modeling for dealing with challenging problems, such as multiple scattering configurations.     

Sixth moment optimization of multi-channel Bragg filters

The design of multichannel optical filter is studied theoretically. New efficient two-step method based on combination of 6-th moment minimization and straightforward numerical minimization is developed. It is applied to find a fiber Bragg grating profile with minimal refractive index variation for 5 ÷ 32 channels. Obtained results are closer to the theoretical limit than previously reported.     

Numerical analysis of the output power of the injection-locked cw Ti:sapphire lasers

The optimization analysis of the output power of the injection-locked cw Ti:sapphire lasers is presented based on the fact that the injection-locked and free-running lasers almost have the same maximum output power. With the modified Ti:sapphire laser model, the dependences of the threshold and slope efficiency on the ring cavity and crystal parameters are studied through the numerical calculations, which clarify the roles of various parameters in affecting the output power. Our calculated results are in good agreement with the reported experimental data for the laser at 756 nm. Therefore our numerically calculated results could be used as a guideline for designing and optimizing such kind of the lasers.     

Analysis of two stacked cylindrical dielectric resonators in a TE₁₀₂ microwave cavity for magnetic resonance spectroscopy

The frequency, field distributions and filling factors of a DR/TE??? probe, consisting of two cylindrical dielectric resonators (DR1 and DR2) in a rectangular TE??? cavity, are simulated and analyzed by finite element methods. The TE(+++) mode formed by the in-phase coupling of the TE??(δ)(DR1), TE??(δ)(DR2) and TE??? basic modes, is the most appropriate mode for X-band EPR experiments. The corresponding simulated B(+++) fields of the TE(+++) mode have significant amplitudes at DR1, DR2 and the cavity's iris resulting in efficient coupling between the DR/TE??? probe and the microwave bridge. At the experimental configuration, B(+++) in the vicinity of DR2 is much larger than that around DR1 indicating that DR1 mainly acts as a frequency tuner. In contrast to a simple microwave shield, the resonant cavity is an essential component of the probe that affects its frequency. The two dielectric resonators are always coupled and this is enhanced by the cavity. When DR1 and DR2 are close to the cavity walls, the TE(+++) frequency and B(+++) distribution are very similar to that of the empty TE??? cavity. When all the experimental details are taken into account, the agreement between the experimental and simulated TE(+++) frequencies is excellent. This confirms that the resonating mode of the spectrometer's DR/TE??? probe is the TE(+++) mode. Additional proof is obtained from B?(x), which is the calculated maximum x component of B(+++). It is predominantly due to DR2 and is approximately 4.4 G. The B?(x) maximum value of the DR/TE??? probe is found to be slightly larger than that for a single resonator in a cavity because DR1 further concentrates the cavity's magnetic field along its x axis. Even though DR1 slightly enhances the performance of the DR/TE??? probe its main benefit is to act as a frequency tuner. A waveguide iris can be used to over-couple the DR/TE??? probe and lower its Q to ≈150. Under these conditions, the probe has a short dead time and a large bandwidth. The DR/TE??? probe's calculated conversion factor is approximately three times that of a regular cavity making it a good candidate for pulsed EPR experiments.     

Neutrinoless double beta decay studied with configuration mixing methods

We study neutrinoless double beta decay of several isotopes with state-of-the-art beyond self-consistent mean field methods to compute the nuclear matrix elements (NME). The generating coordinate method with particle number and angular momentum projection (GCM +PNAMP) is used for finding mother and granddaughter states and evaluating transition operators between different nuclei. We analyze explicitly the role of the deformation, pairing and configuration mixing in the evaluation of the NME.     

3D ultrasound reconstruction algorithms from analog and digital data

Freehand 3D ultrasound is increasingly being introduced in the clinic for diagnostics and image-assisted interventions. Various algorithms exist for combining 2D images of regular ultrasound probes to 3D volumes, being either voxel-, pixel- or function-based. Previously, the most commonly used input to 3D ultrasound reconstruction has been digitized analog video. However, recent scanners that offer access to digital image frames exist, either as processed or unprocessed data. To our knowledge, no comparison has been performed to determine which data source gives the best reconstruction quality. In the present study we compared both reconstruction algorithms and data sources using novel comparison methods for detecting potential differences in image quality of the reconstructed volumes. The ultrasound scanner used in this study was the Sonix RP from Ultrasonix Medical Corp (Richmond, Canada), a scanner that allow third party access to unprocessed and processed digital data. The ultrasound probe used was the L14-5/38 linear probe. The assessment is based on a number of image criteria: detectability of wire targets, spatial resolution, detectability of small barely visible structures, subjective tissue image quality, and volume geometry. In addition we have also performed the more “traditional” comparison of reconstructed volumes by removing a percentage of the input data. By using these evaluation methods and data from the specific scanner, the results showed that the processed video performed better than the digital scan-line data, digital video being better than analog video. Furthermore, the results showed that the choice of video source was more important than the choice of tested reconstruction algorithms.     

三维不规则区域热传导问题无网格方法的数值模拟

配点型无网格法是纯无网格法,它不需要任何背景网格,效率高。本文用加权最小二乘配点方法(Weighted Least-Squares Collocation Method-WLSCM)计算不规则区域热传导问题,形函数采用径向基函数近似。通过二维具有分析解的实例表明WLSCM方法精度高,稳定性好且具有较高的计算效率。此外,将WLSCM方法应用于工程中常见的三维不规则区域热传导问题,结果表明:WLSCM方法的计算结果与FLUENT的计算结果符合很好。