Bruno Degli Esposti

Bruno Degli Esposti

Postdoctoral researcher in numerical analysis at the University of Siena.

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publications

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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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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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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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 work, we generalize our moment-free approach to any linear functional, provided that two conditions are met…

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Bayesian estimation of convergence rates in numerical methods

Status: in preparation. Last update: May 2026

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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A parallel-in-time isogeometric BEM for the 3D wave equation using B-spline linear multistep methods

Status: in preparation. Last update: July 2026

Joint work with L. Desiderio, M. L. Sampoli, A. Sestini. In this work, we introduce a novel high-order parallel-in-time discretization for the 3D wave equation using linear multistep methods as Boundary Value Methods (BVM). Unlike Runge-Kutta CQ, which requires eigendecompositions at the timestep level, our BVM approach exhibits global diagonalizability, immediately yielding decoupled Helmholtz problems…

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Decoupling solution and quadrature nodes in meshless Nyström methods for second-kind Fredholm integral equations

Status: under review. Last update: August 2026

Preprint available on arXiv. Joint work with A. Sestini. We introduce a meshless Nyström method for Fredholm integral equations of the second kind with smooth kernels in which the solution and quadrature nodes are chosen independently. Meshless moment-free quadrature formulas discretize the integral operator on scattered nodes, while local reconstruction with polyharmonic spline radial basis functions transfers values from a coarser set of solution nodes to a finer set of quadrature nodes. This construction yields a high-order method applicable to complex domains and irregular node distributions…

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A neural approach to point membership classification using local boundary samples

Status: in preparation. Last update: September 2026

Joint work with G. A. D’Inverno, F. Pelosi, M. L. Sampoli. In this work, we explore the use of neural networks to solve the point membership classification problem. The network learn a suitable function and delivers a nearest-neighbor method whose accuracy on randomly sampled query points exceeds that of state-of-the-art nearest-neighbor methods, even on non-smooth domains. Since the neural networks only take as inputs local boundary samples, they are naturally domain-independent and very quick to evaluate…

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teaching

Co-advisor of master’s thesis

Master's thesis in physics, University of Florence, Department of Physics, 2022

Candidate: Mauro Giliberti. Advisors: Prof. Aldo Lorenzo Cotrone, Dr. Francesco Bigazzi. Title of the thesis: Numerical solution of bubble dynamics in holographic vacuum decay. The thesis is part of a collaboration between the department of physics and the department of mathematics of the university of Florence. I have introduced Mauro Giliberti to numerical tools such as quadrature formulas, spline curves, splines on triangulations, and nonlinear optimization methods. Final grade: 110/110 with honors.