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A mathematical dashboard for the analysis of Italian COVID-19 epidemic data

Nicola Parolini, Alfio Quarteroni

An analysis of the COVID-19 epidemic is proposed on the basis of the epiMOX dashboard (publicly accessible at ) that deals with data of the epidemic trends and outbreaks in Italy from late February 2020. Our analysis provides an immediate appreciation of the past epidemic development, together with its current trends by fostering a deeper interpretation of available data through several critical epidemic indicators. In addition, we complement the epiMOX dashboard with a predictive tool based on an epidemiological compartmental model, named SUIHTER, for the forecast on the near future epidemic evolution.

WILEY2021

Reduced Basis Approximation And A Posteriori Error Estimates For Parametrized Elliptic Eigenvalue Problems

Andrea Manzoni, Nicola Parolini

We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the parameters, the error between the high-fidelity finite element approximation of the first eigenpair and the corresponding reduced basis approximation. The proposed error estimators are exploited not only to certify the RB approximation with respect to the high-fidelity one, but also to set up a greedy algorithm for the offline construction of a reduced basis space. Several numerical experiments show the overall validity of the proposed RB approach.

Edp Sciences S A2016

An explicit dynamics GPU structural solver for thin shell finite elements

Andrea Bartezzaghi, Nicola Parolini

With the availability of user oriented software tools, dedicated architectures, such as the parallel computing platform and programming model CUDA (Compute Unified Device Architecture) released by NVIDIA, one of the main producers of graphics cards, and of improved, highly performing GPU (Graphics Processing Unit) boards, GPGPU (General Purpose programming on GPU) is attracting increasing interest in the engineering community, for the development of analysis tools suitable to be used in validation/verification and virtual reality applications. For their inherent explicit and decoupled structure, explicit dynamics finite element formulations appear to be particularly attractive for implementations on hybrid CPU/GPU or pure GPU architectures. The issue of an optimized, double-precision finite element GPU implementation of an explicit dynamics finite element solver for elastic shell problems in small strains and large displacements and rotations, using unstructured meshes, is here addressed. The conceptual difference between a GPU implementation directly adapted from a standard CPU approach and a new optimized formulation, specifically conceived for GPUs, is discussed and comparatively assessed. It is shown that a speedup factor of about 5 can be achieved by an optimized algorithm reformulation and careful memory management. A speedup of more than 40 is achieved with respect of state-of-the art commercial codes running on CPU, obtaining real-time simulations in some cases, on commodity hardware. When a last generation GPU board is used, it is shown that a problem with more than 16 millions degrees of freedom can be solved in just few hours of computing time, opening the way to virtualization approaches for real large scale engineering problems. (C) 2015 Elsevier Ltd. All rights reserved.

Elsevier2015