192 research outputs found
Lowest order stabilization free Virtual Element Method for the Poisson equation
We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E^2VEM) for the Poisson problem. The method has the interesting property of allowing the definition of bilinear forms that do not require a stabilization term. We provide a proof of well-posedness and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the theoretical convergence rates
SUPG-stabilized stabilization-free VEM: a numerical investigation
We numerically investigate the possibility of defining stabilization-free
Virtual Element (VEM) discretizations of advection-diffusion problems in the
advection-dominated regime. To this end, we consider a SUPG stabilized
formulation of the scheme. Numerical tests comparing the proposed method with
standard VEM show that the lack of an additional arbitrary stabilization term,
typical of VEM schemes, that adds artificial diffusion to the discrete
solution, allows to better approximate boundary layers, in particular in the
case of a low order scheme.Comment: 15 page
Lowest order stabilization free Virtual Element Method for the Poisson equation
We introduce and analyse the first order Enlarged Enhancement Virtual Element
Method (EVEM) for the Poisson problem. The method has the interesting
property of allowing the definition of bilinear forms that do not require a
stabilization term. We provide a proof of well-posedness and optimal order a
priori error estimates. Numerical tests on convex and non-convex polygonal
meshes confirm the theoretical convergence rates.Comment: 29 pages, 6 figure
Film inorganici per la protezione dell'acciaio inox
Deposizione di un coating di silice su substrati in acciaio inox attraverso una tecnica innovativa e caratterizzazione del film ottenutoope
Analysis of the relationships between wild ungulates and forest in the Northern Apennines, Italy
I explored some ecological aspects of the interaction between wild ungulates and forest environment. I reviewed the existent literature on the topic, and I found the relationship to be part of a extended ecological network, that includes several biotic and abiotic factors. The most advocated cause for elevated ungulate impact on forest is ungulate overabundance. Hence, I assessed the precision and applicability of three different census methods (drive census, pellet-group count, camera trapping method – REM) for roe deer in a mountainous forest. I found the R.E.M. method to be the best compromise, with intermediate precision and low demands. Moreover, I analyzed the browsing pressure of roe deer in several areas over a density gradient. I found the impact to be directly related to densities, and that the early-stage effects of browsing pressure will result in long-term differences in volume, between browsed and unbrowsed trees, even several years later the clear-cutting. Finally, to understand the effects of roe deer impact on the forest development, I used a forest development model (LANDIS-II) to simulate 200 years of forest development, considering harvesting and roe deer impact. I found that both disturbances influence species richness, abundance, and forest structure. Roe deer impact does not significantly affect harvesting yield, and the disturbances combined do not seem to represent an hazard for forest functionality
Model-aware Deep Learning Method for Raman Amplification in Few-Mode Fibers
One of the most promising solutions to overcome
the capacity limit of current optical fiber links is space-division
multiplexing, which allows the transmission on various cores of
multi-core fibers or modes of few-mode fibers. In order to realize
such systems, suitable optical fiber amplifiers must be designed.
In single mode fibers, Raman amplification has shown significant
advantages over doped fiber amplifiers due to its low-noise and
spectral flexibility. For these reasons, its use in next-generation
space-division multiplexing transmission systems is being studied
extensively. In this work, we propose a deep learning method that
uses automatic differentiation to embed a complete few-mode
Raman amplification model in the training process of a neural
network to identify the optimal pump wavelengths and power
allocation scheme to design both flat and tilted gain profiles.
Compared to other machine learning methods, the proposed
technique allows to train the neural network on ideal gain
profiles, removing the need to compute a dataset that accurately
covers the space of Raman gains we are interested in. The ability
to directly target a selected region of the space of possible gains
allows the method to be easily generalized to any type of Raman
gain profiles, while also being more robust when increasing the
number of pumps, modes, and the amplification bandwidth. This
approach is tested on a 70 km long 4-mode fiber transmitting
over the C+L band with various numbers of Raman pumps in
the counter-propagating scheme, targeting gain profiles with an
average gain in the interval from 5 dB to 15 dB and total tilt in
the interval from 1.425 dB to 1.425 dB. We achieve wavelengthand
mode-dependent gain fluctuations lower than 0.04 dB and
0.02 dB per dB of gain, respectively
A lowest order stabilization-free mixed Virtual Element Method
We initiate the design and the analysis of stabilization-free Virtual Element
Methods for the laplacian problem written in mixed form. A Virtual Element
version of the lowest order Raviart-Thomas Finite Element is considered. To
reduce the computational costs, a suitable projection on the gradients of
harmonic polynomials is employed. A complete theoretical analysis of stability
and convergence is developed in the case of quadrilateral meshes. Some
numerical tests highlighting the actual behaviour of the scheme are also
provided
Early and long-term impacts of browsing by roe deer in oak coppiced woods along a gradient of population density
Over the last few decades, wild ungulate populations have exhibited relevant geographic and demographic expansion in most European countries; roe deer is amongst the most widespread ungulate species. The increasing roe deer densities have led to strong impact on forest regeneration; the problem has been recently recognized in coppice woods, a silvicultural system which is widespread in Italy, where it amounts to about 56% of the total national forested area.In this study we investigated the effect of roe deer browsing on the vegetative regeneration of Turkey oak few years after coppicing, along a gradient of roe deer density. A browsing index revealed that browsing impact was high at any given roe deer density but increased at higher density, with the browsing rate ranging from 65% to 79%. We also analyzed the long-term impact of browsing six and eleven years after coppicing under a medium roe deer density. Results indicated the early impact are not ephemeral but produced prolonged impacts through time, with an average reduction in volume of -57% and -41% six and eleven years after coppicing, respectively. Based on these results we proposed integrating browsing monitoring with roe deer density estimation to allow identifying ungulate densities which are compatible with silvicultural and forest management objectives. The proposed browsing index can be regarded as an effective management tool, on account of its simplicity and cost-effectiveness, being therefore highly suitable for routine, large scale monitoring of browsing impact
SUPG-stabilized stabilization-free VEM: a numerical investigation
We numerically investigate the possibility of defining Stabilization-Free Virtual Element discretizations–i.e., Virtual Element Method discretizations without an additional non-polynomial non-operator-preserving stabilization term–of advection-diffusion problems in the advection-dominated regime, considering a Streamline Upwind Petrov-Galerkin stabilized formulation of the scheme. We present numerical tests that assess the robustness of the proposed scheme and compare it with a standard Virtual Element Method
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