Product algebras for Galerkin discretisations of boundary integral operators and their applications

Operator products occur naturally in a range of regularised boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems

Product algebras for Galerkin discretisations of boundary integral operators and their applications

Operator products occur naturally in a range of regularized boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp we have implemented a complete operator algebra that depends on knowledge of the domain, range and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible while hiding the complexities of Galerkin discretisations. In this paper, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems

Solving Boundary Integral Problems with BEM++

Many important partial differential equation problems in homogeneous media, such as those of acoustic or electromagnetic wave propagation, can be represented in the form of integral equations on the boundary of the domain of interest. In order to solve such problems, the boundary element method (BEM) can be applied. The advantage compared to domain-discretisation-based methods such as finite element methods is that only a discretisation of the boundary is necessary, which significantly reduces the number of unknowns. Yet, BEM formulations are much more difficult to implement than finite element methods. In this paper we present BEM++, a novel open-source library for the solution of boundary integral equation for Laplace and Helmholtz problems in three space dimensions. BEM++ is a C++ library with Python bindings for all important features, making it possible to integrate the library into other C++ projects or to use it directly via Python scripts. The internal structure and design decisions for BEM++ are discussed. Several examples are presented to demonstrate the performance of the library for larger problems

Early Diagnosis of Vegetation Health From High-Resolution Hyperspectral and Thermal Imagery: Lessons Learned From Empirical Relationships and Radiative Transfer Modelling

[Purpose of Review] We provide a comprehensive review of the empirical and modelling approaches used to quantify the radiation–vegetation interactions related to vegetation temperature, leaf optical properties linked to pigment absorption and chlorophyll fluorescence emission, and of their capability to monitor vegetation health. Part 1 provides an overview of the main physiological indicators (PIs) applied in remote sensing to detect alterations in plant functioning linked to vegetation diseases and decline processes. Part 2 reviews the recent advances in the development of quantitative methods to assess PI through hyperspectral and thermal images.[Recent Findings] In recent years, the availability of high-resolution hyperspectral and thermal images has increased due to the extraordinary progress made in sensor technology, including the miniaturization of advanced cameras designed for unmanned aerial vehicle (UAV) systems and lightweight aircrafts. This technological revolution has contributed to the wider use of hyperspectral imaging sensors by the scientific community and industry; it has led to better modelling and understanding of the sensitivity of different ranges of the electromagnetic spectrum to detect biophysical alterations used as early warning indicators of vegetation health.[Summary] The review deals with the capability of PIs such as vegetation temperature, chlorophyll fluorescence, photosynthetic energy downregulation and photosynthetic pigments detected through remote sensing to monitor the early responses of plants to different stressors. Various methods for the detection of PI alterations have recently been proposed and validated to monitor vegetation health. The greatest challenges for the remote sensing community today are (i) the availability of high spatial, spectral and temporal resolution image data; (ii) the empirical validation of radiation–vegetation interactions; (iii) the upscaling of physiological alterations from the leaf to the canopy, mainly in complex heterogeneous vegetation landscapes; and (iv) the temporal dynamics of the PIs and the interaction between physiological changes.The authors received funding provided by the FluorFLIGHT (GGR801) Marie Curie Fellowship, the QUERCUSAT and ESPECTRAMED projects (Spanish Ministry of Economy and Competitiveness), the Academy of Finland (grants 266152, 317387) and the European Research Council Synergy grant ERC-2013-SyG-610028 IMBALANCE-P.Peer reviewe

RIVER MORPHOLOGY MONITORING of A SMALL-SCALE ALPINE RIVERBED USING DRONE PHOTOGRAMMETRY and LIDAR

An efficient alternative to labour-intensive terrestrial and costly airborne surveys is the use of small, inexpensive Unmanned Aerial Vehicles (UAVs) or Remotely Piloted Aerial Systems (RPAS). These low-altitude remote sensing platforms, commonly known as drones, can carry lightweight optical and LiDAR sensors. Even though UAV systems still have limited endurance, they can provide a flexible and relatively inexpensive monitoring solution for a limited area of interest. This study investigated the applicability of monitoring the morphology of a frequently changing glacial stream using high-resolution topographic surface models derived from low-altitude UAV-based photogrammetry and LiDAR. An understanding of river-channel morphology and its response to anthropogenic and natural disturbances is imperative for effective watershed management and conservation. We focus on the data acquisition, processing workflow and highlight identified challenges and shortcomings. Additionally, we demonstrate how LiDAR data acquisition simulations can help decide which laser scanning approach to use and help optimise data collection to ensure full coverage with desired level of detail. Lastly, we showcase a case study of 3D surface change analysis in an alpine stream environment with UAV-based photogrammetry. The datasets used in this study were collected as part of the ISPRS Summer School of Alpine Research, which will continue to add new data layers on a biyearly basis. This growing data repository is freely available for research

Factors influencing temperature measurements from miniaturized thermal infrared (Tir) cameras: A laboratory-based approach

The workflow for estimating the temperature in agricultural fields from multiple sensors needs to be optimized upon testing each type of sensor’s actual user performance. In this sense, readily available miniaturized UAV-based thermal infrared (TIR) cameras can be combined with proximal sensors in measuring the surface temperature. Before the two types of cameras can be operationally used in the field, laboratory experiments are needed to fully understand their capabilities and all the influencing factors. We present the measurement results of laboratory experiments of UAV-borne WIRIS 2nd GEN and handheld FLIR E8-XT cameras. For these uncooled sensors, it took 30 to 60 min for the measured signal to stabilize and the sensor temperature drifted continuously. The drifting sensor temperature was strongly correlated to the measured signal. Specifically for WIRIS, the automated non-uniformity correction (NUC) contributed to extra uncertainty in measurements. Another problem was the temperature measurement dependency on various ambient environmental parameters. An increase in the measuring distance resulted in the underestimation of surface temperature, though the degree of change may also come from reflected radiation from neighboring objects, water vapor absorption, and the object size in the field of view (FOV). Wind and radiation tests suggested that these factors can contribute to the uncertainty of several Celsius degrees in measured results. Based on these indoor experiment results, we provide a list of suggestions on the potential practices for deriving accurate temperature data from radiometric miniaturized TIR cameras in actual field practices for (agro-)environmental research