Complete Radiation Boundary Conditions for Maxwell’s Equations

We describe the construction, analysis, and implementation of arbitrary-order local radiation boundary condition sequences for Maxwell’s equations. In particular we use the complete radiation boundary conditions which implicitly apply uniformly accurate exponentially convergent rational approximants to the exact radiation boundary conditions. Numerical experiments for waveguide and free space problems using high- order discontinuous Galerkin spatial discretizations are presented.

Quiet-Sun hydrogen Lyman-α line profile derived from SOHO/SUMER solar-disk observations

Context. The solar radiation in the Lyman-α spectral line of hydrogen plays a significant role in the illumination of chromospheric and coronal structures, such as prominences, spicules, chromospheric fibrils, cores of coronal mass ejections, and solar wind. Moreover, it is important for the investigation of the heliosphere, Earth’s ionosphere, and the atmospheres of planets, moons, and comets. Aims. We derive a reference quiet-Sun Lyman-α spectral profile that is representative of the Lyman-α radiation from the solar disk during a minimum of solar activity. This profile can serve as an incident radiation boundary condition for the radiative transfer modelling of chromospheric and coronal structures. Because the solar radiation in the Lyman lines is not constant over time but varies significantly with the solar cycle, we provide a method for the adaptation of the incident radiation Lyman line profiles (Lyman-α and higher lines) to a specific date. Moreover, we analyse how the change in the incident radiation influences the synthetic spectra produced by the radiative transfer modelling. Methods. We used SOHO/SUMER Lyman-α raster scans obtained without the use of the attenuator in various quiet-Sun regions on the solar disk. The observations were performed on three consecutive days (June 24, 25, and 26, 2008) during a period of minimum solar activity. The reference Lyman-α profile was obtained as a spatial average over eight available raster scans. To take into account the Lyman-α variation with the solar cycle, we used the LISIRD composite Lyman-α index. To estimate the influence of the change in the incident radiation in the Lyman lines on the results of radiative transfer models, we used a 2D prominence fine structure model. Results. We present the reference quiet-Sun Lyman-α profile and a table of coefficients describing the variation of the Lyman lines with the solar cycle throughout the lifetime of SOHO. The analysis of the influence of the change in the incident radiation shows that the synthetic spectra are strongly affected by the modification of the incident radiation boundary condition. The most pronounced impact is on the central and integrated intensities of the Lyman lines. There, the change in the synthetic spectra can often have the same amplitude as the change in the incident radiation itself. The impact on the specific intensities in the peaks of reversed Lyman-line profiles is smaller but still significant. The hydrogen Hα line can also be considerably affected, despite the fact that the Hα radiation from the solar disk does not vary with the solar cycle.

Temperature Field Boundary Conditions and Lateral Temperature Gradient Effect on a PC Box-Girder Bridge Based on Real-Time Solar Radiation and Spatial Temperature Monitoring

Climate change could impose great influence on infrastructures. Previous studies have shown that solar radiation is one of the most important factors causing the change in temperature distribution in bridges. The current temperature distribution models developed in the past are mainly based on the meteorological data from the nearest weather station, empirical formulas, or the testing data from model tests. In this study, a five-span continuous Prestressed-concrete box-girder bridge was instrumented with pyranometers, anemometers, strain gauges, displacement gauges, and temperature sensors on the top and bottom slabs and webs to measure the solar radiation, wind speeds, strain, displacement, and surface temperatures, respectively. The continuously monitoring data between May 2019 and May 2020 was used to study the temperature distributions caused by solar radiation. A maximum positive lateral temperature gradient prediction model has been developed based on the solar radiation data analysis. Then, the solar radiation boundary condition obtained from the monitoring data and the lateral temperature gradient prediction model were utilized to compute the tensile stresses in the longitudinal and transverse directions. It was demonstrated in this study that the tensile stress caused by the lateral temperature gradient was so significant that it cannot be ignored in structural design.

Sparsified discrete wave problem involving a radiation condition on a prolate spheroidal surface

We develop and analyse a high-order outgoing radiation boundary condition for solving three-dimensional scattering problems by elongated obstacles. This Dirichlet-to-Neumann condition is constructed using the classical method of separation of variables that allows one to define the scattered field in a truncated domain. It reads as an infinite series that is truncated for numerical purposes. The radiation condition is implemented in a finite element framework represented by a large dense matrix. Fortunately, the dense matrix can be decomposed into a full block matrix that involves the degrees of freedom on the exterior boundary and a sparse finite element matrix. The inversion of the full block is avoided by using a Sherman–Morrison algorithm that reduces the memory usage drastically. Despite being of high order, this method has only a low memory cost.