Overresolving in the Laplace domain for convolution quadrature methods

Convolution quadrature (CQ) methods have enjoyed tremendous interest in recent years as an efficient tool for solving time-domain wave problems in unbounded domains via boundary integral equation techniques. In this paper we consider CQ type formulations for the parallel space-time evaluation of multistep or stiffly accurate Runge--Kutta rules for the wave equation. In particular, we decouple the number of Laplace domain solves from the number of time steps. This allows us to overresolve in the Laplace domain by computing more Laplace domain solutions than there are time steps. We use techniques from complex approximation theory to analyze the error of the CQ approximation of the underlying time-stepping rule when overresolving in the Laplace domain and show that the performance is intimately linked to the location of the poles of the solution operator. Several examples using boundary integral equation formulations in the Laplace domain are presented to illustrate the main results. Read More: http://epubs.siam.org/doi/10.1137/16M106474

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

On the attenuation coefficient of monomode periodic waveguides

It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation-rate coefficient alpha = -/L. In this letter, we evidence that the exponential-damping law is not valid in general for periodic monomode waveguides, especially as the group velocity decreases. This result that contradicts common beliefs and experimental practices aiming at measuring alpha is supported by a theoretical study of light transport in the limit of very small imperfections, and by numerical results obtained for two waveguide geometries that offer contrasted damping behaviours

Image-based software solutions for advanced materials processing and characterization

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordNew image-based solutions are being developed for advanced materials processing and characterization, which involve working with and creating high-quality models from scan data (such as MRI, CT, micro-CT…). Techniques involving the reconstruction and analysis of 3D materials data can accurately reconstruct internal structures, even to the nano level, and generate high-quality meshes suitable for design and simulation applications. By looking at key techniques and their applications, it is possible to better understand the wider impact and benefits of image-based modelling for industry when working with advanced materials

Solution of time-domain problems using Convolution Quadrature methods and BEM++

Convolution Quadrature methods are efficient techniques for the solution of time-domain wave prob- lems in unbounded domains via Boundary Element Methods. In this proceeding we use the Convolution Quadrature approach to decouple the time-domain problems into a series of independent frequency-domain problems that can be solved efficiently in parallel. In contrast to previous approaches we solve many more frequency-domain problems than there are time steps. We demonstrate numerically that this approach ap- proximates the underlying time-stepping scheme with exponential accuracy as the number of frequency problems is increased. The implementation of the method is done using BEM++, a modern C++ based boundary element library with an easy to use Python interface

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

The benefits and negative impacts of citizen science applications to water as experienced by participants and communities

Citizen science is proliferating in the water sciences with increasing public involvement in monitoring water resources, climate variables, water quality, and in mapping and modeling exercises. In addition to the well-reported scientific benefits of such projects, in particular solving data scarcity issues, it is common to extol the benefits for participants, for example, increased knowledge and empowerment. We reviewed 549 publications concerning citizen science applications in the water sciences to examine personal benefits and motivations, and wider community benefits. The potential benefits of involvement were often simply listed without explanation or investigation. Studies that investigated whether or not participants and communities actually benefitted from involvement, or experienced negative impacts, were uncommon, especially in the Global South. Assuming certain benefits will be experienced can be fallacious as in some cases the intended benefits were either not achieved or in fact had negative impacts. Identified benefits are described and we reveal that more consideration should be given to how these benefits interrelate and how they build community capitals to foster their realization in citizen science water projects. Additionally, we describe identified negative impacts showing they were seldom considered though they may not be uncommon and should be borne in mind when implementing citizen science. Given the time and effort commitment made by citizen scientists for the benefit of research, there is a need for further study of participants and communities involved in citizen science applications to water, particularly in low-income regions, to ensure both researchers and communities are benefitting. This article is categorized under: Human Water > Human Water