SUMMARYGmsh is an open-source 3-D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents the overall philosophy, the main design choices and some of the original algorithms implemented in Gmsh.

International audienceIn multiscale analysis of components, there is usually a need to solve microstructures with complex geometries. In this paper, we use the extended finite element method (X-FEM) to solve scales involving complex geometries. The X-FEM allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach. For material interfaces, this is achieved by introducing a new enrichment strategy. Although the mesh does not need to conform to the physical surfaces, it needs to be fine enough to capture the geometry of these surfaces. A simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement. Numerical experiments on the periodic homogenization of two-phase complex cells demonstrate the accuracy and simplicity of the X-FEM

Abstract. The purpose of this study was to relate regional variation in litter mass-loss rates (first year) in pine forests to climate across a large, continental-scale area. The variation in mass-loss rate was analyzed using 39 experimental sites spanning climatic regions from the subarctic to subtropical and Mediterranean: the latitudinal gradient ranged from 31 N to 70 N and may represent the the largest geographical area that has ever been sampled and observed for the purpose of studying biogeochemical processes. Because of unified site design and uniform laboratory procedures, data from all sites were directly comparable and permitted a determination of the relative influence of climate versus substrate quality viewed from the perspective of broad regional scales.Simple correlation applied to the entire data set indicated that annual actual evapotranspiration (AET) should be the leading climatic constraint on mass-loss rates (R2d = 128 0.496). The combination of AET, average July temp. and average annual temp. could explain about 70% of the sites' variability on litter mass-loss. In an analysis of 23 Scots pine sites north of the Alps and Carpatians AET alone could account for about 65% of the variation and the addition of a substrate-quality variable was sufficiently significant to be used in a model.The influence of litter quality was introduced into a model, using data from 11 sites at which litter of different quality had been incubated. These sites are found in Germany, the Netherlands, Sweden and Finland. At any one site most (> 90%/6) of the variation in mass-loss rates could be explained by one of the litter-quality variables giving concentration of nitrogen, phosphorus or water solubles. However, even when these models included nitrogen or phosphorus even small changes in potential evapotranspiration resulted in large changes in early-phase decay rates.Further regional subdivision of the data set, resulted in a range of strength in the relationship between loss rate and climatic variables, from very weak in Central Europe to strong for the Scandinavian and Atlantic coast sites (Rdj = 0.912; AET versus litter mass loss). Much of the variation in observed loss rates could be related to continental versus marine/Atlantic influences. Inland locations had mass-loss rates lower than should be expected on the basis of for example AET alone. Attempts to include seasonality variables were not successful. It is clear that either unknown errors and biases, or, unknown variables are causing these regional differences in response to climatic variables. Nevertheless these results show the powerful influence of climate as a control of the broad-scale geography of mass-loss rates and substrate quality at the stand level.Some of these relationships between mass-loss rate and climatic variables are among the highest ever reported, probably because of the care taken to select uniform sites and experimental methods. This suggest that superior, base line maps of predicted mass-loss rates could be produced using climatic...

We describe a strategy for detecting discontinuities and for limiting spurious oscillations near such discontinuities when solving hyperbolic systems of conservation laws by high-order discontinuous Galerkin methods. The approach is based on a strong superconvergence at the outflow boundary of each element in smooth regions of the flow. By detecting discontinuities in such variables as density or entropy, limiting may be applied only in these regions; thereby, preserving a high order of accuracy in regions where solutions are smooth. Several one-and two-dimensional flow problems illustrate the performance of these approaches.