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Fabio Credali

Publications and source records attributed to Fabio Credali.

14 recordsLinked to original sources
arXiv2026

A Comprehensive p-VEM Framework for Advanced Variable Stiffness Plates with Arbitrary Shapes

This paper presents a comprehensive, high-order (p-version) Virtual Element Method (VEM) framework for the structural analysis of innovative variable stiffness plates. VEM is particularly suited for complex configurations due to its ability to handle arbitrary polygonal meshes, including curved edges. However, its mathematical formulation may hinder its spread in the engineering community. This work illustrates a formulation with an accessible implementation using well-known FEM notation and integrating at the same time a set of new advanced capabilities. Specifically, both standard stabilized and advanced self-stabilized strategies are adopted. To further improve the robustness of VEM in the presence of variable coefficients, polynomial projections taking into account the coefficients are employed. This approach is referred to as Variable Coefficients-VEM approach (VC-VEM). This unified framework is applied to linear static, free-vibration, and buckling analyses, and validated against analytical solutions and numerical benchmarks. In particular, plates with cutouts and problems featuring high-gradient solutions are investigated, demonstrating that the proposed comprehensive approach provides a flexible and ready-to-implement tool for advanced structural design.

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arXiv2026

Avoiding stabilization terms in virtual elements for eigenvalue problems: The Reduced Basis Virtual Element Method

We present the novel Reduced Basis Virtual Element Method (rbVEM) for solving the Laplace eigenvalue problem. This approach is based on the lowest-order virtual element method and exploits the reduced basis technique to obtain an explicit representation of the virtual (non-polynomial) contribution to the discrete space. rbVEM yields a fully conforming discretization of the considered problem, so that stabilization terms are avoided. We prove that rbVEM provides the correct spectral approximation with optimal error estimates. Theoretical results are supplemented by an exhaustive numerical investigation.

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arXiv2025

The Reduced Basis Multigrid scheme for the Virtual Element Method

We present a non-nested W-cycle multigrid scheme for the lowest order Virtual Element Method on polygonal meshes. To avoid the implicit definition of the Virtual Element space, which poses several issues in the computation of intergrid operators that underpin multigrid methods, the proposed scheme uses a fully-conforming auxiliary space constructed by cheaply computing the virtual basis functions via the reduced basis method.

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arXiv2025

Benchmarking stabilized and self-stabilized p-virtual element methods with variable coefficients

Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely defined by the underlying variational formulation and is typically introduced in an ad hoc manner, potentially affecting the numerical response. Stabilization-free and self-stabilized formulations have been proposed to overcome this issue, although their theoretical analysis is still less mature. This paper provides an in-depth numerical investigation into different stabilized and self-stabilized formulations for the p-version of VEM. The results show that self-stabilized and stabilization-free formulations achieve optimal accuracy while suffering from worse conditioning. Moreover, a new projection operator, which explicitly accounts for variable coefficients, is introduced within the framework of standard virtual element spaces. Numerical results show that this new approach is more robust than the existing ones for large values of p.

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arXiv2025

Automatic computation of the glycemic index: data driven analysis of the glucose standard

The Glycemic Index (GI) is a tool for classifying carbohydrates based on their impact on postprandial glycemia, useful for diabetes prevention and management. This study applies a mathematical model for a data driven simulation of the glycemic response following glucose ingestion. The analysis is performed on a dataset of 35 healthy subjects undergone a standard 50 g oral glucose test. The results reveal a direct correlation between glucose response profiles and parameters describing glucose absorption, enabling the classification of subjects into three groups based on the timing of their glycemic peak: <30 min, 30-50 min, >50 min. These findings highlight the ability of a physiology-based mathematical model to capture inter-individual variability in postprandial glucose dynamics and represent a step toward simulation-based approaches for GI estimation.

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arXiv2025

On the stability and conditioning of a fictitious domain formulation for fluid-structure interaction problems

We consider a distributed Lagrange multiplier formulation for fluid-structure interaction problems in the spirit of the fictitious domain approach. This is an unfitted method, which does not require the construction of meshes conforming to the interface. We focus on the stationary problem arising from the time discretization and we analyze the behavior of the condition number with respect to mesh refinement. At the numerical level, the computation of the term coupling the fluid and the solid mesh requires the knowledge of the intersection between fluid and mapped solid elements and it might happen that a portion of the intersected elements is very small. We show that our formulation is stable independently of such intersections and that the conditioning is not affected by the interface position.

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arXiv2025

Advances on the finite element discretization of fluid-structure interaction problems

We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical findings concerning well-posedness, stability, and convergence of the numerical schemes, and discuss the related computational challenges. In the case of elliptic interface problems, we also present a posteriori error estimates.

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arXiv2025

The MINI mixed virtual element for the Stokes equation

We present and discuss a generalization of the popular MINI mixed finite element for the 2D Stokes equation by means of conforming virtual elements on polygonal meshes. We prove optimal error estimates for both velocity and pressure. Theoretical results are confirmed by several numerical tests performed with different choices of polynomial accuracy and meshes.

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arXiv2024

Quadrature error estimates on non-matching grids in a fictitious domain framework for fluid-structure interaction problems

We consider a fictitious domain formulation for fluid-structure interaction problems based on a distributed Lagrange multiplier to couple the fluid and solid behaviors. How to deal with the coupling term is crucial since the construction of the associated finite element matrix requires the integration of functions defined over non-matching grids: the exact computation can be performed by intersecting the involved meshes, whereas an approximate coupling matrix can be evaluated on the original meshes by introducing a quadrature error. The purpose of this paper is twofold: we prove that the discrete problem is well-posed also when the coupling term is constructed in approximate way and we discuss quadrature error estimates over non-matching grids.

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arXiv2023

Finite element discretization of a biological network formation system: a preliminary study

A finite element discretization is developed for the Cai-Hu model, describing the formation of biological networks. The model consists of a non linear elliptic equation for the pressure $p$ and a non linear reaction-diffusion equation for the conductivity tensor $\mathbb{C}$. The problem requires high resolution due to the presence of multiple scales, the stiffness in all its components and the non linearities. We propose a low order finite element discretization in space coupled with a semi-implicit time advancing scheme. The code is {verified} with several numerical tests performed with various choices for the parameters involved in the system. In absence of the exact solution, we apply Richardson extrapolation technique to estimate the order of the method.

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arXiv2023

A parallel solver for FSI problems with fictitious domain approach

We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier-Stokes equations, while the solid evolution is represented by the elasticity equations. The parallel implementation is based on the PETSc library and the solver has been tested in terms of robustness with respect to mesh refinement and weak scalability by running simulations on a Linux cluster.

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arXiv2022

A parallel solver for fluid structure interaction problems with Lagrange multiplier

The aim of this work is to present a parallel solver for a formulation of fluid-structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem, consisting of the non-stationary Stokes equations, is discretized in space by $\mathcal{Q}_2$-$\mathcal{P}_1$ finite elements, whereas the structure subproblem, consisting of the linear or finite incompressible elasticity equations, is discretized in space by $\mathcal{Q}_1$ finite elements. A first order semi-implicit finite difference scheme is employed for time discretization. The resulting linear system at each time step is solved by a parallel GMRES solver, accelerated by block diagonal or triangular preconditioners. The parallel implementation is based on the PETSc library. Several numerical tests have been performed on Linux clusters to investigate the effectiveness of the proposed FSI solver.

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arXiv2022

On the interface matrix for fluid-structure interaction problems with fictitious domain approach

We study a recent formulation for fluid-structure interaction problems based on the use of a distributed Lagrange multiplier in the spirit of the fictitious domain approach. In this paper, we focus our attention on a crucial computational aspect regarding the interface matrix for the finite element discretization: it involves integration of functions supported on two different meshes. Several numerical tests show that accurate computation of the interface matrix has to be performed in order to ensure the optimal convergence of the method.

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