A PDE-constrained optimization formulation for discrete fracture network flows

We investigate a new numerical approach for the computation of the 3D flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex 3D systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. Independent meshing process within each fracture is a very important issue for practical large scale simulations making easier mesh generation. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures

Repositioning template for mandibular reconstruction with fibular free flap: an alternative technique to pre-plating and virtual surgical planning

Oral malignancies involving the mandibular bone require a complex reconstructive plan. Mandibular reconstruction with a fibular free flap is currently considered the best choice for functional and aesthetic rehabilitation after oncological surgery. This flap can be modelled with multiple osteotomies and can provide bone, muscle and skin for composite reconstruction. One of the most delicate aspects of mandibular reconstruction is the technique of bone modelling; the risk of prolonging the period of ischaemia and not restoring the correct maxillomandibular and occlusal relationships can ultimately lead to a higher rate of complications as well as poor aesthetic and functional results. Recently, there has been rising interest in virtual surgical planning and computer-assisted mandibular reconstruction in pre-operative planning; however, this is not always possible because of the costs involved and the set-up time for the entire procedure. In this paper, we present a simple and inexpensive technique for fibular free flap modelling and repositioning after segmental resection of the mandible; the technique entails the pre-operative preparation of a resin repositioning template on a stereolithographic model. This technique has been successfully applied in four cases: two cases underwent resection involving only the mandibular body, one case involving the mandibular body and symphysis and one case in which a ramus to ramus resection was performed. In this preliminary report, we show that the resin repositioning template is an easy, safe and useful tool for mandibular reconstruction with a fibular free flap

A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method

A new approach for solving flow in Discrete Fracture Networks (DFN) is developed in this work by means of the Virtual Element Method. Taking advantage of the features of the VEM, we obtain global conformity of all fracture meshes while preserving a fracture-independent meshing process. This new approach is based on a generalization of globally conforming Finite Elements for polygonal meshes that avoids complications arising from the meshing process. The approach is robust enough to treat many DFNs with a large number of fractures with arbitrary positions and orientations, as shown by the simulations. Higher order Virtual Element spaces are also included in the implementation with the corresponding convergence results and accuracy aspects

Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks

In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed by adding penalization terms in the loss function and properly choosing the corresponding scaling coefficients; however, in practice, this requires an expensive tuning phase. We show through several numerical tests that modifying the output of the neural network to exactly match the prescribed values leads to more efficient and accurate solvers. The best results are achieved by exactly enforcing the Dirichlet boundary conditions by means of an approximate distance function. We also show that variationally imposing the Dirichlet boundary conditions via Nitsche's method leads to suboptimal solvers.Comment: 22 pages, 45 figure

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 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

Anisotropic a posteriori error estimate for the virtual element method

We derive an anisotropic a posteriori error estimate for the adaptive conforming virtual element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes

Complicanze sinusali monolaterali da patologia o trattamenti dentali: quando la chirurgia endoscopica endonasale necessita un approccio intraorale?

L'utilizzo diffuso degli impianti dentali e delle procedure ricostruttive per il loro posizionamento ha portato un aumento delle complicanze sinusali da patologia o trattamenti dentali (SCDDT). La diagnosi richiede una valutazione dentale e rinologica accurata, compresa la tomografia computerizzata (TC). Lo scopo di questo studio è stato quello di considerare un approccio multidisciplinare per il trattamento delle SCDDT, combinando la chirurgia endoscopica endonasale (EES) e l'approccio intraorale sulla base di un sistema di classificazione preliminare già proposto da altri autori. Inoltre, gli autori hanno analizzato la percentuale di sinusite mascellare a eziologica odontogena che si estende a interessare i seni etmoidali anteriori come anche i batteri coinvolti nella patogenesi delle SCDDT. Tra il gennaio 2012 e agosto 2015, nella nostra casistica di 31 pazienti, 16/31 pazienti (51,6%) sono stati trattati con approccio EES, 3/31 pazienti (9,7%) con approccio intraorale, e 12/31 pazienti (38,7%) con approccio combinato. Tutti i pazienti hanno riferito un miglioramento dei sintomi della rinosinusite, confermato attraverso i risultati degli esami clinici e della TC di controllo. Non è stata osservata nessuna complicanza significativa, né si è ricorsi a una revisione chirurgica. Infine, i risultati di questo studio preliminare suggeriscono che un approccio multidisciplinare delle SCDDT dalla diagnosi alla terapia permette una diagnosi più precisa e una terapia più esauriente, così da ottenere un rapido recupero, riducendo al minimo il rischio di recidiva