764 research outputs found
Serendipity Face and Edge VEM Spaces
We extend the basic idea of Serendipity Virtual Elements from the previous
case (by the same authors) of nodal (-conforming) elements, to a more
general framework. Then we apply the general strategy to the case of
and conforming Virtual Element Methods, in two and three dimensions
Serendipity Nodal VEM spaces
We introduce a new variant of Nodal Virtual Element spaces that mimics the
"Serendipity Finite Element Methods" (whose most popular example is the 8-node
quadrilateral) and allows to reduce (often in a significant way) the number of
internal degrees of freedom. When applied to the faces of a three-dimensional
decomposition, this allows a reduction in the number of face degrees of
freedom: an improvement that cannot be achieved by a simple static
condensation. On triangular and tetrahedral decompositions the new elements
(contrary to the original VEMs) reduce exactly to the classical Lagrange FEM.
On quadrilaterals and hexahedra the new elements are quite similar (and have
the same amount of degrees of freedom) to the Serendipity Finite Elements, but
are much more robust with respect to element distortions. On more general
polytopes the Serendipity VEMs are the natural (and simple) generalization of
the simplicial case
Lowest order Virtual Element approximation of magnetostatic problems
We give here a simplified presentation of the lowest order Serendipity
Virtual Element method, and show its use for the numerical solution of linear
magneto-static problems in three dimensions. The method can be applied to very
general decompositions of the computational domain (as is natural for Virtual
Element Methods) and uses as unknowns the (constant) tangential component of
the magnetic field on each edge, and the vertex values of the
Lagrange multiplier (used to enforce the solenoidality of the magnetic
induction ). In this respect the method can be seen
as the natural generalization of the lowest order Edge Finite Element Method
(the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost
arbitrary shape, and as we show on some numerical examples it exhibits very
good accuracy (for being a lowest order element) and excellent robustness with
respect to distortions
Applications of nonvariational finite element methods to Monge--Amp\`ere type equations
The goal of this work is to illustrate the application of the nonvariational
finite element method to a specific Monge--Amp\`ere type nonlinear partial
differential equation. The equation we consider is that of prescribed Gauss
curvature.Comment: 7 pages, 3 figures, tech repor
Spaces of finite element differential forms
We discuss the construction of finite element spaces of differential forms
which satisfy the crucial assumptions of the finite element exterior calculus,
namely that they can be assembled into subcomplexes of the de Rham complex
which admit commuting projections. We present two families of spaces in the
case of simplicial meshes, and two other families in the case of cubical
meshes. We make use of the exterior calculus and the Koszul complex to define
and understand the spaces. These tools allow us to treat a wide variety of
situations, which are often treated separately, in a unified fashion.Comment: To appear in: Analysis and Numerics of Partial Differential
Equations, U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, eds.,
Springer 2013. v2: a few minor typos corrected. v3: a few more typo
correction
Innovative passive reinforcements for the gradual stabilization of a landslide according with the observational method
A large number of landslides occur in North-Eastern Italy during every rainy period due to the particular hydrogeological conditions of this area. Even if there are no casualties, the economic losses are often significant, and municipalities frequently do not have sufficient financial resources to repair the damage and stabilize all the unstable slopes. In this regard, the research for more economically sustainable solutions is a crucial challenge. Floating composite anchors are an innovative and low-cost technique set up for slope stabilization: it consists in the use of passive sub-horizontal reinforcements, obtained by coupling a traditional self-drilling bar with some tendons cemented inside it. This work concerns the application of this technique according to the observational method described within the Italian and European technical codes and mainly recommended for the design of geotechnical works, especially when performed in highly uncertain site conditions. The observational method prescribes designing an intervention and, at the same time, using a monitoring system in order to correct and adapt the project during realization of the works on the basis of new data acquired while on site. The case study is the landslide of Cischele, a medium landslide which occurred in 2010 after an exceptional heavy rainy period. In 2015, some floating composite anchors were installed to slow down the movement, even if, due to a limited budget, they were not enough to ensure the complete stabilization of the slope. Thanks to a monitoring system installed in the meantime, it is now possible to have a comparison between the site conditions before and after the intervention. This allows the evaluation of benefits achieved with the reinforcements and, at the same time, the assessment of additional improvements. Two stabilization scenarios are studied through an FE model: the first includes the stabilization system built in 2015, while the second evaluates a new solution proposed to further increase the slope stability
Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems
This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives.PostprintPeer reviewe
Multiphysics simulation of corona discharge induced ionic wind
Ionic wind devices or electrostatic fluid accelerators are becoming of
increasing interest as tools for thermal management, in particular for
semiconductor devices. In this work, we present a numerical model for
predicting the performance of such devices, whose main benefit is the ability
to accurately predict the amount of charge injected at the corona electrode.
Our multiphysics numerical model consists of a highly nonlinear strongly
coupled set of PDEs including the Navier-Stokes equations for fluid flow,
Poisson's equation for electrostatic potential, charge continuity and heat
transfer equations. To solve this system we employ a staggered solution
algorithm that generalizes Gummel's algorithm for charge transport in
semiconductors. Predictions of our simulations are validated by comparison with
experimental measurements and are shown to closely match. Finally, our
simulation tool is used to estimate the effectiveness of the design of an
electrohydrodynamic cooling apparatus for power electronics applications.Comment: 24 pages, 17 figure
Stabilization of high-order solutions of the cubic Nonlinear Schrodinger Equation
In this paper we consider the stabilization of non-fundamental unstable
stationary solutions of the cubic nonlinear Schrodinger equation. Specifically
we study the stabilization of radially symmetric solutions with nodes and
asymmetric complex stationary solutions. For the first ones we find partial
stabilization similar to that recently found for vortex solutions while for the
later ones stabilization does not seem possible
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