Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is prove

On affine scaling inexact dogleg methods for bound-constrained nonlinear systems

Within the framework of affine scaling trust-region methods for bound constrained problems, we discuss the use of a inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Focusing on bound-constrained systems of nonlinear equations, an inexact affine scaling method for large scale problems, employing the inexact dogleg procedure, is described. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given

Towards effective flow simulations in realistic Discrete Fracture Networks

We focus on the simulation of underground flow in fractured media, modeled by means of Discrete Fracture Networks. Focusing on a new recent numerical approach proposed by the authors for tackling the problem avoiding mesh generation problems, we further improve the new family of methods making a step further towards effective simulations of large, multi-scale, heterogeneous networks. Namely, we tackle the imposition of Dirichlet boundary conditions in weak form, in such a way that geometrical complexity of the DFN is not an issue; we effectively solve DFN problems with fracture transmissivities spanning many orders of magnitude and approaching zero; furthermore, we address several numerical issues for improving the numerical solution also in quite challenging networks

On simulations of discrete fracture network flows with an optimization-based extended finite element method

Following the approach introduced in [Berrone,Pieraccini,Scialò,2013], we consider the formulation of the problem of fluid flow in a system of fractures as a PDE constrained optimization problem, with discretization performed using suitable extended finite elements; the method allows independent meshes on each fracture, thus completely circumventing meshing problems usually related to the DFN approach. The application of the method to discrete fracture networks of medium complexity is fully analyzed here, accounting for several issues related to viable and reliable implementations of the method in complex problems

A three-field based optimization formulation for flow simulations in networks of fractures on non-conforming meshes

A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field domain decomposition framework, in which independent variables are introduced at the interfaces generated in the process of decoupling the original problem on the whole network into a set of fracture-local problems. A PDE-constrained formulation is then used to enforce compatibility conditions at the interfaces. The combination of the three-field domain decomposition and of the optimization based coupling strategy results in a novel method which can handle non-conforming meshes, independently built on each geometrical object of the computational domain, and ensures local mass conservation property at fracture intersections, which is of paramount importance for hydro-geological applications. An iterative solver is devised for the method, suitable for parallel implementation on parallel computing architectures

A hybrid mortar virtual element method for discrete fracture network simulations

The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN), is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in handling polygonal meshes in order to easily construct meshes conforming to the traces on each fracture, and we resort to the mortar approach in order to ``weakly'' impose continuity of the solution on intersecting fractures. The resulting method replaces the need for matching grids between fractures, so that the meshing process can be performed independently for each fracture. Numerical results show optimal convergence and robustness in handling very complex geometries

Coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies

The aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios, in order to define the impact on air quality of different strategies for the reduction of traffic emissions. To this aim, we complement a well assessed traffic model on networks (Garavello, Piccoli, 2006) with a strategy for estimating data needed from the model and we couple it with the urban dispersion model Sirane (Soulhac, 2000)

A valence bond description of the bromine halogen bond

A theoretical investigation on the nature of the halogen bond through a valence-bond approach has been carried out with two main goals: (a) finding further confirmations of already existing explanations on the physical origins of the halogen bond and (b) possibly enriching the current models with new details. To achieve these goals we have exploited the spin-coupled method and we have performed computations on RBr efNH3 dimers characterized by a different electron withdrawing power of substituent \uf8ffR to the bromine atom. The analysis of typical spin-coupled descriptors (eg, shapes and overlaps of the spin-coupled orbitals, weights of the spin-coupled structures) in the different cases and in function of the distance between the monomers allowed us to draw qualitative conclusions about the formation and the strength of the halogen bonds. In particular, the investigation not only confirmed the validity of already existing models (ie, \u3c3-hole and lump-hole models) but also highlighted interesting new features, such as the fact that the depletion of electron density around the bromine atom does not extend only toward the acceptor of the halogen bond, but also in the opposite direction (toward the substituent of the halogen), thus forming a sort of \u3c3-tunnel, rather than a simple \u3c3-hole

Halogen bonding in the framework of classical force fields: The case of chlorine

Halogen bonding is nowadays a consolidated tool in chemistry. Only recently, the importance of halogen bonding has been demonstrated also in biological systems, owing to the presence of halogens in drugs. This interaction is due to the anisotropy of the electron density around the halogen that leads to the formation of the \u2018\u3c3-hole\u2019, which is responsible for the interaction with a nucleophile site. Unfortunately, classical force fields used in the study of ligand-receptor systems are not able to describe the \u2018\u3c3-hole\u2019. Here, we propose a pseudo-atom based methodology able to correctly describe halogen bonding involving chlorine using classical force field

Comprehensive Review on the Dynamic and Seismic Behavior of Flat-Bottom Cylindrical Silos Filled With Granular Material

The seismic design of industrial flat-bottom ground-supported silos filled with granular material still presents several challenges to be addressed. They are related to the main aspects which differentiate silo structures containing granular material from other civil structural typologies: 1) the relatively low silo structure mass as compared to the ensiled content mass; 2) the granular nature of the ensiled material. Indeed, the internal actions in the structural members are governed by the complex dynamic interactions along the interfaces between granular content and silo wall or base, or even the internal interaction between particles. More in detail, even though the scientific interest in such complex interactions dates back to the middle of the 19th century, several issues are still unclear such as the dependency of the fundamental dynamic properties (period of vibration and damping ratio) on the characteristics of the dynamic excitation (intensity, frequency content, duration) or the amount of ensiled material mass activated during a seismic excitation and provoking extra pressures on the wall (effective mass). Therefore, most of current seismic code provisions for silos are grounded on rather approximate and simplified assumptions leading to often over-conservative evaluations. The present paper intends to provide a comprehensive summary of the mainly acknowledged experimental and theoretical advances in the dynamic and seismic behavior of silos, supporting the potential researcher in the field to understand the real differences between the code assumptions and recommendations and the actual conditions, as well as illustrating the open issues to be still further investigated