Bruno Degli Esposti

Bruno Degli Esposti

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

Posts by Collection

portfolio

High-order isogemetric boundary element methods for acoustic and elastodynamic problems on complex 3D domains

My research goal is to advance numerical schemes for the simulation of 3D acoustic and elastic wave propagation phenomena by designing an efficient, high-order Isogeometric Boundary Element Method (IgA-BEM) framework based on convolution quadrature. Novel strategies for the accurate computation of collocation BEM integrals will be investigated in the case of piecewise smooth multi-patch CAD geometries, possibly with trimming.

Purely meshless boundary methods on 3D CAD geometries using moment-free quadrature

My research goal is to develop a purely meshless pipeline for the numerical solution of partial differential equations on 3D CAD geometries based on the original combination of the following techniques: meshless boundary methods, possibly coupled with volume methods such as RBF-FD, my own C++ library NodeGenLib for the generation of variable-density unstructured nodes on the surface of 3D CAD domains given in B-Rep format, the moment-free meshless quadrature formulas introduced in my doctoral dissertation, and methods such as quadrature by expansion that allow singular integrals to be evaluated in terms of regular integrals.

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 talk, 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: 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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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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talks

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.