Enabling Radiative Transfer on AMR grids in CRASH

We introduce CRASH-AMR, a new version of the cosmological Radiative Transfer (RT) code CRASH, enabled to use refined grids. This new feature allows us to attain higher resolution in our RT simulations and thus to describe more accurately ionisation and temperature patterns in high density regions. We have tested CRASH-AMR by simulating the evolution of an ionised region produced by a single source embedded in gas at constant density, as well as by a more realistic configuration of multiple sources in an inhomogeneous density field. While we find an excellent agreement with the previous version of CRASH when the AMR feature is disabled, showing that no numerical artifact has been introduced in CRASH-AMR, when additional refinement levels are used the code can simulate more accurately the physics of ionised gas in high density regions. This result has been attained at no computational loss, as RT simulations on AMR grids with maximum resolution equivalent to that of a uniform cartesian grid can be run with a gain of up to 60% in computational time.Comment: 19 pages, 17 figures. MNRAS, in pres

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings

What Do the First 597 Global Fungal Red List Assessments Tell Us about the Threat Status of Fungi?

Fungal species are not immune to the threats facing animals and plants and are thus also prone to extinction. Yet, until 2015, fungi were nearly absent on the IUCN Red List. Recent efforts to identify fungal species under threat have significantly increased the number of published fungal assessments. The 597 species of fungi published in the 2022-1 IUCN Red List update (21 July 2022) are the basis for the first global review of the extinction risk of fungi and the threats they face. Nearly 50% of the assessed species are threatened, with 10% NT and 9% DD. For regions with a larger number of assessments (i.e., Europe, North America, and South America), subanalyses are provided. Data for lichenized and nonlichenized fungi are also summarized separately. Habitat loss/degradation followed by climate change, invasive species, and pollution are the primary identified threats. Bias in the data is discussed along with knowledge gaps. Suggested actions to address these gaps are provided along with a discussion of the use of assessments to facilitate on-the-ground conservation efforts. A research agenda for conservation mycology to assist in the assessment process and implementation of effective species/habitat management is presented

What Do the First 597 Global Fungal Red List Assessments Tell Us about the Threat Status of Fungi?

Fungal species are not immune to the threats facing animals and plants and are thus also prone to extinction. Yet, until 2015, fungi were nearly absent on the IUCN Red List. Recent efforts to identify fungal species under threat have significantly increased the number of published fungal assessments. The 597 species of fungi published in the 2022-1 IUCN Red List update (21 July 2022) are the basis for the first global review of the extinction risk of fungi and the threats they face. Nearly 50% of the assessed species are threatened, with 10% NT and 9% DD. For regions with a larger number of assessments (i.e., Europe, North America, and South America), subanalyses are provided. Data for lichenized and nonlichenized fungi are also summarized separately. Habitat loss/degradation followed by climate change, invasive species, and pollution are the primary identified threats. Bias in the data is discussed along with knowledge gaps. Suggested actions to address these gaps are provided along with a discussion of the use of assessments to facilitate on-the-ground conservation efforts. A research agenda for conservation mycology to assist in the assessment process and implementation of effective species/habitat management is presented