Solver algorithm for stabilized space-time formulation of advection-dominated diffusion problem

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using higher-order continuous B-spline basis functions in its spatial and temporal dimensions. This problem is very difficult to solve numerically using the standard Galerkin finite element method due to artificial oscillations present when the advection term dominates the diffusion term. However, a first-order constraint least-square formulation allows us to obtain numerical solutions avoiding oscillations. The advantages of space-time formulations are the use of high-order methods and the feasibility of developing space-time mesh adaptive techniques on well-defined discrete problems. We develop a solver for a least-square formulation to obtain a stabilized and symmetric problem on finite element meshes. The computational cost of our solver is bounded by the cost of the inversion of the space-time mass and stiffness (with one value fixed at a point) matrices and the cost of the GMRES solver applied for the symmetric and positive definite problem. We illustrate our findings on an advection-dominated diffusion space-time model problem and present two numerical examples: one with isogeometric analysis discretizations and the second one with an adaptive space-time finite element method.Comment: 24 pages, 7 figures, 2 table

A global metagenomic map of urban microbiomes and antimicrobial resistance

We present a global atlas of 4,728 metagenomic samples from mass-transit systems in 60 cities over 3 years, representing the first systematic, worldwide catalog of the urban microbial ecosystem. This atlas provides an annotated, geospatial profile of microbial strains, functional characteristics, antimicrobial resistance (AMR) markers, and genetic elements, including 10,928 viruses, 1,302 bacteria, 2 archaea, and 838,532 CRISPR arrays not found in reference databases. We identified 4,246 known species of urban microorganisms and a consistent set of 31 species found in 97% of samples that were distinct from human commensal organisms. Profiles of AMR genes varied widely in type and density across cities. Cities showed distinct microbial taxonomic signatures that were driven by climate and geographic differences. These results constitute a high-resolution global metagenomic atlas that enables discovery of organisms and genes, highlights potential public health and forensic applications, and provides a culture-independent view of AMR burden in cities.Funding: the Tri-I Program in Computational Biology and Medicine (CBM) funded by NIH grant 1T32GM083937; GitHub; Philip Blood and the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF grant number ACI-1548562 and NSF award number ACI-1445606; NASA (NNX14AH50G, NNX17AB26G), the NIH (R01AI151059, R25EB020393, R21AI129851, R35GM138152, U01DA053941); STARR Foundation (I13- 0052); LLS (MCL7001-18, LLS 9238-16, LLS-MCL7001-18); the NSF (1840275); the Bill and Melinda Gates Foundation (OPP1151054); the Alfred P. Sloan Foundation (G-2015-13964); Swiss National Science Foundation grant number 407540_167331; NIH award number UL1TR000457; the US Department of Energy Joint Genome Institute under contract number DE-AC02-05CH11231; the National Energy Research Scientific Computing Center, supported by the Office of Science of the US Department of Energy; Stockholm Health Authority grant SLL 20160933; the Institut Pasteur Korea; an NRF Korea grant (NRF-2014K1A4A7A01074645, 2017M3A9G6068246); the CONICYT Fondecyt Iniciación grants 11140666 and 11160905; Keio University Funds for Individual Research; funds from the Yamagata prefectural government and the city of Tsuruoka; JSPS KAKENHI grant number 20K10436; the bilateral AT-UA collaboration fund (WTZ:UA 02/2019; Ministry of Education and Science of Ukraine, UA:M/84-2019, M/126-2020); Kyiv Academic Univeristy; Ministry of Education and Science of Ukraine project numbers 0118U100290 and 0120U101734; Centro de Excelencia Severo Ochoa 2013–2017; the CERCA Programme / Generalitat de Catalunya; the CRG-Novartis-Africa mobility program 2016; research funds from National Cheng Kung University and the Ministry of Science and Technology; Taiwan (MOST grant number 106-2321-B-006-016); we thank all the volunteers who made sampling NYC possible, Minciencias (project no. 639677758300), CNPq (EDN - 309973/2015-5), the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science – MOE, ECNU, the Research Grants Council of Hong Kong through project 11215017, National Key RD Project of China (2018YFE0201603), and Shanghai Municipal Science and Technology Major Project (2017SHZDZX01) (L.S.