arXiv subjects

Francesco Casella

Publications and source records attributed to Francesco Casella.

6 recordsLinked to original sources

arXiv2024

Steady-State Initialization of Object-Oriented Advanced Thermal Power Generation System Models with Application to the Case of the SOS-CO2 Cycle

The forthcoming energy transition calls for a new generation of thermal power generation systems with low- or zero-emission and highly flexible operation. Dynamic modelling and simulation is a key enabling factor in this field, as controlling such plants is a difficult task for which there is no previous experience and very short design times are expected. The steady-state initialization of those dynamic models is an essential step in the design process, but is unfortunately a difficult task which involves the numerical solution of large systems of nonlinear equations with iterative Newton methods, which is often prone to numerical failures. In this work, several strategies and methodologies are discussed to successfully achieve steady-state initialization of first-principles equation-based, object-oriented models of advanced thermal power generation systems. These are presented in the context of the Modelica modelling language, but could be applied to other equation-based, object-oriented modelling and simulation environments. Finally, the successful application of such strategies and methodologies to the SOS-CO2 advanced power generation system is presented.

eess.SY↗

arXiv2024

Multi-rate Runge-Kutta methods: stability analysis and applications

We present an approach for the efficient implementation of self-adjusting multi-rate Runge-Kutta methods and we introduce a novel stability analysis, that covers the multi-rate extensions of all standard Runge-Kutta methods and allows to assess the impact of different interpolation methods for the latent variables and of the use of an arbitrary number of sub-steps for the active variables. The stability analysis applies successfully to the model problem typically used in the literature for multi-rate methods. Furthermore,} we also propose a physically motivated model problem that can be used to assess stability to problems with purely imaginary eigenvalues and in situations closer to those arising in applications. Finally, we present an efficient implementation of multi-rate Runge-Kutta methods in the framework of the OpenModelica open-source modelling and simulation software. Results of several numerical experiments, performed with this implementation of the proposed methods, demonstrate the efficiency gains deriving from the use of the proposed multi-rate approach for physical modelling problems with multiple time scales.

math.NA↗

arXiv2022

Array-Aware Matching: Taming the Complexity of Large-Scale Simulation Models

Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays' problems, however, well assessed model translation techniques exhibit scalability issues, that are particularly severe when models contain very large arrays. In fact, such models can be made very compact by enclosing equations into looping constructs, but reflecting the same compactness into the translated imperative code is not trivial. In this paper, we face this issue by concentrating on a key step of equations-to-code translation, the equation/variable matching. We first show that an efficient translation of models with (large) arrays needs awareness of their presence, by defining a figure of merit to measure how much the looping constructs are preserved along the translation. We then show that the said figure of merit allows to define an optimal array-aware matching, and as our main result, that the so stated optimal array-aware matching problem is NP-complete. As an additional result, we propose a heuristic algorithm capable of performing array-aware matching in polynomial time. The proposed algorithm can be proficiently used by model translator developers in the implementation of efficient tools for large-scale system simulation.

cs.PL↗

arXiv2021

On the choice of initial guesses for the Newton-Raphson algorithm

The initialization of equation-based differential-algebraic system models, and more in general the solution of many engineering and scientific problems, require the solution of systems of nonlinear equations. Newton-Raphson's method is widely used for this purpose; it is very efficient in the computation of the solution if the initial guess is close enough to it, but it can fail otherwise. In this paper, several criteria are introduced to analyze the influence of the initial guess on the evolution of Newton-Raphson's algorithm and to identify which initial guesses need to be improved in case of convergence failure. In particular, indicators based on first and second derivatives of the residual function are introduced, whose values allow to assess how much the initial guess of each variable can be responsible for the convergence failure. The use of such criteria, which are based on rigorously proven results, is successfully demonstrated in three exemplary test cases.

math.NA↗

arXiv2020

Can the COVID-19 epidemic be controlled on the basis of daily test reports?

This paper studies if and to which extent COVID-19 epidemics can be controlled by authorities taking decisions on public health measures on the basis of daily reports of swab test results, active cases and total cases. A suitably simplified process model is derived to support the controllability analysis, highlighting the presence of very significant time delay; the model is validated with data from several outbreaks. The analysis shows that suppression strategies can be effective if strong enough and enacted early on. It also shows how mitigation strategies can fail because of the combination of delay, unstable dynamics, and uncertainty in the feedback loop; approximate conditions based on the theory of limitation of linear control are given for feedback control to be feasible.

physics.soc-ph↗

arXiv2018

A self adjusting multirate algorithm based on the TR-BDF2 method

We propose a self adjusting multirate method based on the TR-BDF2 solver. The potential advantages of using TR-BDF2 as the key component of a multirate framework are highlighted. A linear stability analysis of the resulting approach is presented and the stability features of the resulting algorithm are analysed. The analysis framework is completely general and allows to study along the same lines the stability of self adjusting multirate methods based on a generic one step solver. A number of numerical experiments demonstrate the efficiency and accuracy of the resulting approach also the time discretization of hyperbolic partial differential equations.

math.NA↗