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The barycentric forms of polynomial and rational interpolation have recently gained popularity, because they can be computed with simple, efficient, and numerically stable algorithms. In this paper, we show more generally that the evaluation of any function that can be expressed as$$r(x)=\sum _{i=0}^n a_i(x) f_i\big /\sum _{j=0}^m b_j(x)$$r(x)=∑i=0nai(x)fi/∑j=0mbj(x)in terms of data values$$f_i$$fiand some functions$$a_i$$aiand$$b_j$$bjfor$$i=0,\ldots ,n$$i=0,…,nand$$j=0,\dots ,m$$j=0,⋯,mwith a simple algorithm that first sums up the terms in the numerator and the denominator, followed by a final division, is forward and backward stable under certain assumptions. This result includes the two barycentric forms of rational interpolation as special cases. Our analysis further reveals that the stability of the second barycentric form depends on the Lebesgue constant associated with the interpolation nodes, which typically grows withn, whereas the stability of the first barycentric form depends on a similar, but different quantity, that can be bounded in terms of the mesh ratio, regardless ofn. We support our theoretical results with numerical experiments.

The Laplace transform inversion is a well-known ill-conditioned problem and many numerical schemes in literature have investigated how to solve it. In this paper, we revise the Gaver-Stehfest method by using polyharmonic splines augmented with polynomials to approximate the Laplace transform into the numerical inversion formula. Theoretical accuracy bounds for the fitting model are given. Discussions on the effectiveness of the inversion algorithm are produced and confirmed by numerical experiments about approximation errors and inversion results. Comparisons with an existing model are also presented.

Well hydraulics concerns the process of flow toward/from wells, which occurs because of a vertical extraction or injection in the aquifer. The paper shows preliminary tests performed on the high performance computing (HPC) ReCaS infrastructure to compute simulations on the fluctuation of the water table in heterogeneous porous formation based on a stochastic parametrization of the transmissivity field of the aquifer for the horizontal flow around the pumping well. From a computational point of view, the more expensive aspects concern the storage of the samples and the numerical solution of the related boundary value problem. The numerical simulations were carried out by using packages/libraries included in the SCoPE toolkit v.3 available at the HPC ReCaS infrastructure.

La concessione di contributi per la riparazione dei danni causati dal sisma del 06 Aprile 2009 in Abruzzo, nei centri storici del Comune dell’Aquila e degli altri Comuni del Cratere, nella fase conseguente alla cessazione dello stato di emergenza (agosto 2012), è disciplinata da un modello parametrico. Il contributo per la riparazione del danno ed il miglioramento sismico dell’edificato è basato su un’analisi preliminare del livello di danno e vulnerabilità riferito alla consistenza degli edifici, considerando anche la presenza di elementi di pregio storico-artistico, architettonico e paesaggistico. Il modello implementato dall’Ufficio Speciale per la Ricostruzione dei Comuni del Cratere (Modello Integrato per i Comuni del Cratere - MIC) prevede la compilazione online di una scheda che consente di definire il contributo parametrico concedibile per l’intervento di riparazione e miglioramento sismico e la contestuale consegna del progetto esecutivo dei lavori. Qualora l’importo dell’intervento rientri nei limiti del contributo concedibile definito su base parametrica il progetto è oggetto di un’istruttoria semplificata che permette di liquidare il contributo stesso in tempi ridotti. Il modello parametrico presenta peculiarità che lo differenziano dai modelli parametrici adottati nei terremoti passati e in parte anche dal modello parametrico adottato dal Comune dell’Aquila. Nella memoria sono illustrate sinteticamente le considerazioni alla base del modello stesso e le sue caratteristiche principali.

Gli interventi di riparazione dei danni causati dal sisma del 06 Aprile 2009 in Abruzzo nei centri storici dei comuni del cosiddetto “cratere” sono disciplinati dal Modello Integrato per i Comuni del Cratere (MIC), che prevede la consegna contestuale di una scheda parametrica e del progetto esecutivo dell’intervento. Il modello parametrico adottato contiene apposite linee guida per l’identificazione degli elementi di pregio e la progettazione degli interventi nei centri storici, volte a valorizzare e preservare il costruito storico, ponendo dei limiti all’esecuzione di interventi riconosciuti dalla letteratura scientifica come particolarmente invasivi se non addirittura dannosi. Sono state individuate a tal fine 12 categorie di incremento del contributo collegate ad altrettante tipologie di interventi, che guidano i progettisti nella scelta degli interventi più efficaci in relazione alle caratteristiche del costruito. Nella memoria è effettuata una prima disamina dei costi di intervento dei progetti presentati con il modello MIC oltre ad alcune considerazioni sull’efficacia degli incrementi concessi.

In recent years, some strategies (e.g., server consolidation by means of virtualisation techniques) helped the managers of large Information Technology (IT) infrastructures to limit, when possible, the use of hardware resources in order to provide reliable services and to reduce the Total Cost of Ownership (TCO) of such infrastructures. Moreover, with the advent of Cloud computing, a resource usage rationalisation can be pursued also for the users applications, if this is compatible with the Quality of Service (QoS) which must be guaranteed. In this perspective, modern datacenters are “elastic”, i.e., able to shrink or enlarge the number of local physical or virtual resources from private/public Clouds. Moreover, many of large computing environments are integrated in distributed computing environment as the grid and cloud infrastructures. In this document, we report some advances in the realisation of a utility, we named Adaptive Scheduling Controller (ASC) which, interacting with the datacenter resource manager, allows an effective and efficient usage of resources, also by means of users jobs classification. Here, we focus both on some data mining algorithms which allows to classify the users activity and on the mathematical formalisation of the functional used by ASC to find the most suitable configuration for the datacenter’s resource manager. The presented case study concerns the SCoPE infrastructure, which has a twofold role: local computing resources provider for the University of Naples Federico II and remote resources provider for both the Italian Grid Infrastructure (IGI) and the European Grid Infrastructure (EGI) Federated Cloud.

The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has a finite set of data and one wants to recover an estimate of the inverse Laplace function from that. We propose a fitting model of data. More precisely, given a finite set of measurements on the real axis, arising from an unknown Laplace transform function, we construct a dth degree generalized polynomial smoothing spline, where d = 2m − 1, such that internally to the data interval it is a dth degree polynomial complete smoothing spline minimizing a regularization functional, and outside the data interval, it mimics the Laplace transform asymptotic behavior, i.e. it is a rational or an exponential function (the end behavior model), and at the boundaries of the data set it joins with regularity up to order m − 1, with the end behavior model. We analyze in detail the generalized polynomial smoothing spline of degree d = 3. This choice was motivated by the (ill)conditioning of the numerical computation which strongly depends on the degree of the complete spline. We prove existence and uniqueness of this spline. We derive the approximation error and give a priori and computable bounds of it on the whole real axis. In such a way, the generalized polynomial smoothing spline may be used in any real inversion algorithm to compute an approximation of the inverse Laplace function. Experimental results concerning Laplace transform approximation, numerical inversion of the generalized polynomial smoothing spline and comparisons with the exponential smoothing spline conclude the work.