Alessandro Russo

Alejandro Ortiz-Bernardin, Catalina Alvarez, Nancy Hitschfeld-Kahler et al.

This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in two dimensions have been chosen as the starting stage for the development of this library. The theory of the VEM, upon which Veamy is built, is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis. Several examples are provided to demonstrate the usage of Veamy, and in particular, one of them features the interaction between Veamy and the polygonal mesh generator PolyMesher. A computational performance comparison between VEM and FEM is also conducted. Veamy is free and open source software.

Lourenco Beirao da Veiga, Carlo Lovadina, Alessandro Russo

We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to the parent element diameter), can be dealt with. Our general approach applies to different choices of the stability form, including, for example, the "classical" one introduced in [L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013), no. 1, 199-214], and a recent one presented in [Wriggers, P., Rust, W.T., and Reddy, B.D., A virtual element method for contact, submitted for publication]. Finally, we show that the stabilization term can be simplified by dropping the contribution of the internal-to-the-element degrees of freedom. The resulting stabilization form, involving only the boundary degrees of freedom, can be used in the VEM scheme without affecting the stability and convergence properties. The numerical tests are in accordance with the theoretical predictions.

Lorenzo Mascotto, Lourenço Beirão da Veiga, Alexey Chernov et al.

In the present work, we analyze the $hp$ version of Virtual Element methods for the 2D Poisson problem. We prove exponential convergence of the energy error employing sequences of polygonal meshes geometrically refined, thus extending the classical choices for the decomposition in the $hp$ Finite Element framework to very general decomposition of the domain. A new stabilization for the discrete bilinear form with explicit bounds in $h$ and $p$ is introduced. Numerical experiments validate the theoretical results. We also exhibit a numerical comparison between $hp$ Virtual Elements and $hp$ Finite Elements.

Lourenco Beirao da Veiga, Franco Brezzi, Franco Dassi et al.

We numerically validate the Virtual Element Method of order k for general second order elliptic problems with variable coefficients in three dimensions. Moreover, we investigate numerically also the Serendipity version of the VEM (in three dimensions) and the associated computational gain in terms of degrees of freedom.

Miguel Ceriani, Fiorela Ciroku, Alessandro Russo et al.

Climate change impacts a broad spectrum of human resources and activities, necessitating the use of climate models to project long-term effects and inform mitigation and adaptation strategies. These models generate multiple datasets by running simulations across various scenarios and configurations, thereby covering a range of potential future outcomes. Currently, researchers rely on traditional search interfaces and APIs to retrieve such datasets, often piecing together information from metadata and community vocabularies. The Climate Change Knowledge Graph is designed to address these challenges by integrating diverse data sources related to climate simulations into a coherent and interoperable knowledge graph. This innovative resource allows for executing complex queries involving climate models, simulations, variables, spatio-temporal domains, and granularities. Developed with input from domain experts, the knowledge graph and its underlying ontology are published with open access license and provide a comprehensive framework that enhances the exploration of climate data, facilitating more informed decision-making in addressing climate change issues.

Alessandro Russo, Stefano Serra Capizzano, Cristina Tablino Possio

The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a Finite Element approximation to diffusion-dominated convection-diffusion equations. We consider a model setting in which the structured finite element partition is made by equi-lateral triangles. Under such assumptions, if the problem is coercive, and the diffusive and convective coefficients are regular enough, then the proposed preconditioned matrix sequences exhibit a strong clustering at unity, the preconditioning matrix sequence and the original matrix sequence are spectrally equivalent, and the eigenvector matrices have a mild conditioning. The obtained results allow to show the optimality of the related preconditioned Krylov methods. %It is important to stress that The interest of such a study relies on the observation that automatic grid generators tend to construct equi-lateral triangles when the mesh is fine enough. Numerical tests, both on the model setting and in the non-structured case, show the effectiveness of the proposal and the correctness of the theoretical findings.

Stefano De Giorgis, Aldo Gangemi, Alessandro Russo

The development of artificial intelligence systems capable of understanding and reasoning about complex real-world scenarios is a significant challenge. In this work we present a novel approach to enhance and exploit LLM reactive capability to address complex problems and interpret deeply contextual real-world meaning. We introduce a method and a tool for creating a multimodal, knowledge-augmented formal representation of meaning that combines the strengths of large language models with structured semantic representations. Our method begins with an image input, utilizing state-of-the-art large language models to generate a natural language description. This description is then transformed into an Abstract Meaning Representation (AMR) graph, which is formalized and enriched with logical design patterns, and layered semantics derived from linguistic and factual knowledge bases. The resulting graph is then fed back into the LLM to be extended with implicit knowledge activated by complex heuristic learning, including semantic implicatures, moral values, embodied cognition, and metaphorical representations. By bridging the gap between unstructured language models and formal semantic structures, our method opens new avenues for tackling intricate problems in natural language understanding and reasoning.

Luigi Asprino, Paolo Ciancarini, Andrea Giovanni Nuzzolese et al.

Social Robotics poses tough challenges to software designers who are required to take care of difficult architectural drivers like acceptability, trust of robots as well as to guarantee that robots establish a personalised interaction with their users. Moreover, in this context recurrent software design issues such as ensuring interoperability, improving reusability and customizability of software components also arise. Designing and implementing social robotic software architectures is a time-intensive activity requiring multi-disciplinary expertise: this makes difficult to rapidly develop, customise, and personalise robotic solutions. These challenges may be mitigated at design time by choosing certain architectural styles, implementing specific architectural patterns and using particular technologies. Leveraging on our experience in the MARIO project, in this paper we propose a series of principles that social robots may benefit from. These principles lay also the foundations for the design of a reference software architecture for Social Robots. The ultimate goal of this work is to establish a common ground based on a reference software architecture to allow to easily reuse robotic software components in order to rapidly develop, implement, and personalise Social Robots.

Alessandro Russo, Cristina Tablino Possio

A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The theoretical spectral analysis focuses on the case of matrix sequences related to FE approximations on uniform structured meshes, by referring to spectral tools derived from Toeplitz theory. In such a setting, if the problem is coercive, and the diffusive and convective coefficients are regular enough, then the proposed preconditioned matrix sequence shows a strong clustering at unity, i.e., a superlinear preconditioning sequence is obtained. Under the same assumptions, the optimality of the PHSS method is proved and some numerical experiments confirm the theoretical results. Tests on unstructured meshes are also presented, showing the some convergence behavior.