The last few years have witnessed a surge in the development and usage of discretization methods supporting general meshes in geoscience applications. The need for general polyhedral meshes in this context can arise in several situations, including the modelling of petroleum reservoirs and basins, CO2 and nuclear storage sites, etc. In the above and other situations, classical discretization methods are either not viable or require ad hoc modifications that add to the implementation complexity. Discretization methods able to operate on polyhedral meshes and possibly delivering arbitrary-order approximations constitute in this context a veritable technological jump. The goal of this monograph is to establish a state-of-the-art reference on polyhedral methods for geoscience applications by gathering contributions from top-level research groups working on this topic. This book is addressed to graduate students and researchers wishing to deepen their knowledge of advanced numerical methods with a focus on geoscience applications, as well as practitioners of the field.

The last few years have witnessed a surge in the development and usage of discretization methods supporting general meshes in geoscience applications. The need for general polyhedral meshes in this context can arise in several situations, including the modelling of petroleum reservoirs and basins, CO2 and nuclear storage sites, etc. In the above and other situations, classical discretization methods are either not viable or require ad hoc modifications that add to the implementation complexity. Discretization methods able to operate on polyhedral meshes and possibly delivering arbitrary-order approximations constitute in this context a veritable technological jump. The goal of this monograph is to establish a state-of-the-art reference on polyhedral methods for geoscience applications by gathering contributions from top-level research groups working on this topic. This book is addressed to graduate students and researchers wishing to deepen their knowledge of advanced numerical methods with a focus on geoscience applications, as well as practitioners of the field.

This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion - possibly heterogeneous and anisotropic - and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.

This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion - possibly heterogeneous and anisotropic - and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

Infectious fungal diseases continue to take their toll in terms of human suffering and enormous economic losses. Invasive infections by opportunistic fungal pathogens are a major cause of morbidity and mortality in immuno-compromised individuals. At the same time, plant pathogenic fungi have devastating effects on crop production and human health. New strategies for antifungal control are required to meet the challenges posed by these agents, and such approaches can only be developed through the identification of novel biochemical and molecular targets. However, in contrast to bacterial pathogens, fungi display a wealth of lifestyles and modes of infection. This diversity makes it extremely difficult to identify individual, evolutionarily conserved virulence determinants and represents a major stumbling block in the search for common antifungal targets. In order to activate the infection programme, all fungal pathogens must undergo appropriate developmental transitions that involve cellular differentiation and the introduction of a new morphogenetic programme. How growth, cell cycle progression and morphogenesis are co-ordinately regulated during development has been an active area of research in fungal model systems such as budding and fission yeast. By contrast, we have only limited knowledge of how these developmental processes shape fungal pathogenicity, or of the role of the cell cycle and morphogenesis regulators as true virulence factors. This book combines state-of-the-art expertise from diverse pathogen model systems to update our current understanding of the regulation of fungal morphogenesis as a key determinant of pathogenicity in fungi.

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Infectious fungal diseases continue to take their toll in terms of human suffering and enormous economic losses. Invasive infections by opportunistic fungal pathogens are a major cause of morbidity and mortality in immuno-compromised individuals. At the same time, plant pathogenic fungi have devastating effects on crop production and human health. New strategies for antifungal control are required to meet the challenges posed by these agents, and such approaches can only be developed through the identification of novel biochemical and molecular targets. However, in contrast to bacterial pathogens, fungi display a wealth of lifestyles and modes of infection. This diversity makes it extremely difficult to identify individual, evolutionarily conserved virulence determinants and represents a major stumbling block in the search for common antifungal targets. In order to activate the infection programme, all fungal pathogens must undergo appropriate developmental transitions that involve cellular differentiation and the introduction of a new morphogenetic programme. How growth, cell cycle progression and morphogenesis are co-ordinately regulated during development has been an active area of research in fungal model systems such as budding and fission yeast. By contrast, we have only limited knowledge of how these developmental processes shape fungal pathogenicity, or of the role of the cell cycle and morphogenesis regulators as true virulence factors. This book combines state-of-the-art expertise from diverse pathogen model systems to update our current understanding of the regulation of fungal morphogenesis as a key determinant of pathogenicity in fungi.

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This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.