Variational Convergence of IP-DGFEM

In this paper, we develop the theory required to perform a variational convergence analysis for discontinuous Galerkin nite element methods when applied to minimization problems. For Sobolev indices in $\left[1;\infty\right)$, we prove generalizations of many techniques of classical analysis in Sobolev spaces and apply them to a typical energy minimization problem for which we prove convergence of a variational interior penalty discontinuous Galerkin nite element method (VIPDGFEM). Our main tool in this analysis is a theorem which allows the extraction of a "weakly" converging subsequence of a family of discrete solutions and which shows that any "weak limit" is a Sobolev function

Strategic Insider Trading with Imperfect Information: A Trading Volume Analysis

A model of insider trading is used to analyze the behaviour of trading volume in financial markets characterized by asymmetric information. This model extends the one in Bhattacharya and Nicodano (2001) by introducing competition among informed traders and imperfection of their private information. Contrary to the broad implications of adverse selection models and according to some empirical studies, this paper shows that trading volume is higher when the insiders are active in the market. A higher level of outsiders’ risky investment, due to an improved “risk sharing†among them, leads to a higher level of trading.

A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis

In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree $p$ and $p-2$ for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method

Isogeometric Analysis on V-reps: first results

Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parametrization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justify our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffusion and linear elasticity.Comment: 36 pages, 44 figures. Reviewed versio

On the Choice of Tool Material in Friction Stir Welding of Titanium Alloys

Friction Stir Welding (FSW) is a solid state welding process patented in 1991 by TWI; initially adopted to weld aluminum alloys, is now being successfully used also for magnesium alloys, copper and steels. The wide diffusion the process is having is due to the possibility to weld both materials traditionally considered difficult to be welded or "unweldable" by traditional fusion welding processes due to peculiar thermal and chemical material properties, and complex geometries as sandwich structures and straightening panels. Recently, research is focusing on titanium alloys thanks to the high interest that such materials are getting from the industry due to the extremely high strength-weight ratio together with good corrosion resistance properties. At the moment, the main limit to the industrial applicability of FSW to titanium alloys is the tool life, as ultra wear and deformation resistant materials must be used. In this paper a, experimental study of the tool life in FSW of titanium alloys sheets at the varying of the main process parameters is performed. Numerical simulation provided important information for the fixture design and analysis of results. Tungsten and Rhenium alloy W25Re tools are found to be the most reliable among the ones considered

BPX-Preconditioning for isogeometric analysis

We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or Nurbs mapping which we assume to be regular. The numerical solution of the PDE is computed by means of tensor product B-splines mapped onto the physical domain. We construct additive multilevel preconditioners and show that they are asymptotically optimal, i.e., the spectral condition number of the resulting preconditioned stiffness matrix is independent of $h$. Together with a nested iteration scheme, this enables an iterative solution scheme of optimal linear complexity. The theoretical results are substantiated by numerical examples in two and three space dimensions