Bruno Degli Esposti

Bruno Degli Esposti

Postdoc in numerical analysis at the department of mathematics and computer science of the University of Florence

Publications

You can also find my articles on my ORCID page, or my Google Scholar profile.

Journal Articles

Meshless moment-free quadrature formulas arising from numerical differentiation

Published in Computer Methods in Applied Mechanics and Engineering, July 2025

Joint work with O. Davydov. We suggest a method for simultaneously generating high order quadrature weights for integrals over Lipschitz domains and their boundaries that requires neither meshing nor moment computation. The weights are computed on pre-defined scattered nodes as a minimum norm solution of a sparse underdetermined linear system arising from a discretization of a suitable boundary value problem by either collocation or meshless finite differences…

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IgA-BEM for 3D Helmholtz problems using conforming and non-conforming multi-patch discretizations and B-spline tailored numerical integration

Published in Computers & Mathematics with Applications, August 2023

Joint work with A. Falini, T. Kanduč, M. L. Sampoli, A. Sestini. An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth multi-patch representation of their finite boundary surface. The discretization spaces are formed by \(C^0\) inter-patch continuous functional spaces whose restriction to a patch simplifies to the span of tensor product B-splines composed with the given patch NURBS parameterization. Both conforming and non-conforming spaces are allowed, so that local refinement is possible at the patch level…

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Work in Progress

A decoupled meshless Nyström scheme for 2D Fredholm integral equations of the second kind with smooth kernels

Status: in preparation. Last update: October 2025

Joint work with A. Sestini. The Nyström method for the numerical solution of Fredholm integral equations of the second kind is generalized by decoupling the set of solution nodes from the set of quadrature nodes. The accuracy and efficiency of the new method is investigated for smooth kernels and complex 2D domains using recently developed moment-free meshless quadrature formulas on scattered nodes. Compared to the classical Nyström method, our variant has a clear performance advantage, especially for narrow kernels…

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Bayesian estimation of convergence rates in numerical methods

Status: in preparation. Last update: September 2025

Joint work with D. Fabbrico. In numerical analysis, it is common to estimate the convergence rate of numerical methods by plotting absolute or relative errors against a discretization parameter \(h\) on a log-log scale. The rate is then typically judged by visually comparing the data to reference lines with known slopes, which correspond to integer powers of \(h\). This approach is quite different from standard scientific practice, where experimental data are analyzed with statistical methods. The main reason for this difference is that simple visual approaches are often enough, especially when theory already predicts the expected decay rate. However, these methods are not effective when errors are noisy, for example in stochastic algorithms, or even in deterministic methods affected by random choices such as mesh generation…

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Moment-free approximation of linear functionals

Status: in preparation. Last update: September 2025

Joint work with O. Davydov. In previous work, we have introduced a way to overcome the moment computation problem in the context of numerical integration. Our approach only requires a single non-zero moment to be known, and in many cases leads to an effectively moment-free numerical scheme. In this talk, we generalize our moment-free approach to any linear functional, provided that two conditions are met…

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Doctoral Dissertation

Domain discretization and moment-free quadrature for meshless methods

Defended in Florence, March 2025

This dissertation addresses two fundamental challenges in meshless numerical methods: robust node generation for real-world 3D domains, including CAD geometries, and high-order numerical integration on scattered nodes. The results in Chapters 4 and 5 have been expanded and published. The results in the other chapters are being split into two papers, and will be submitted to peer-reviewed journals in the upcoming months.

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