arXiv subjects

Andrea Bressan

Publications and source records attributed to Andrea Bressan.

15 recordsLinked to original sources

arXiv2026

Sparse-grids-like surrogate models enhanced with gradient information

This work concerns surrogate modeling for quantities of interest (QoI) arising from parametric non-linear partial differential equations (PDEs). More specifically, we consider extending the sparse-grids surrogate modeling approach to incorporate derivatives of the QoI with respect to the PDE parameters. We discuss why this operation is not straightforward and propose a hybrid approach in which a sparse-grid scheme provides the collocation points in the parameter domain and a suitable polynomial space, but the surrogate model is built with a least-squares approach. We showcase our approach on several numerical tests, and we discuss in particular how its performance crucially depends on the relative cost and accuracy of evaluating the derivatives of the QoI compared to evaluating the QoI itself.

math.NA↗

arXiv2025

New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance, and applications to the Stokes' equations

We construct new Crouzeix-Raviart (CR) spaces of even degree $p$ that are spanned by basis functions mimicking those for the odd degree case. Compared to the standard CR gospel, the present construction allows for the use of nested bases of increasing degree and is particularly suited to design variable order CR methods. We analyze a nonconforming discretization of a two dimensional Poisson problem, which requires a DG-type stabilization; the employed stabilization parameter is considerably smaller than that needed in DG methods. Numerical results are presented, which exhibit the expected convergence rates for the $h$-, $p$-, and $hp$-versions of the scheme. We further investigate numerically the behaviour of new even degree CR-type discretizations of the Stokes' equations.

math.NA↗

arXiv2025

Factorizations and fast diagonalization for the heat equation

This work investigates diagonalization-based methods for efficiently solving linear evolution problems, with a particular focus on the heat equation. The plain diagonalization of the differential operator, though effective for elliptic problems where fast diagonalization can be used, exhibits instability when applied to the heat equation. To address this difficulty, we examine three alternative approaches, based on LU factorization, a suitable arrowhead factorization, and a low-rank modification. These methods introduce more robust factorizations of the time derivative, ensuring both computational efficiency and stability.

math.NA↗

arXiv2024

An efficient slope stability algorithm with physically consistent parametrisation of slip surfaces

This paper presents an optimised algorithm implementing the method of slices for analysing the stability of slopes. The algorithm adopts an improved physically based parameterisation of slip lines according to their geometrical characteristics at the endpoints, which facilitates the identification of all viable failure mechanisms while excluding unrealistic ones. The minimisation routine combines a preliminary discrete calculation of the factor of safety over a coarse grid covering the above parameter space with a subsequent continuous exploration of the most promising region via the simplex optimisation. This reduces computational time up to about 92% compared to conventional approaches that rely on the discrete calculation of the factor of safety over a fine grid covering the entire search space. Significant savings of computational time are observed with respect to recently published heuristic algorithms, which enable a continuous exploration of the entire parametric space. These efficiency gains are particularly advantageous for numerically demanding applications like, for example, the statistical assessment of slopes with uncertain mechanical, hydraulic and geometrical properties. The novel physically based parametrisation of the slip geometry and the adoption of a continuous local search allow exploration of parameter combinations that are necessarily neglected by standard grid-based approaches, leading to an average improvement in accuracy of about 5%.

cs.CE↗

arXiv2024

Overlapping subspaces and singular systems with application to Isogeometric Analysis

We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint union of subspace bases. This leads to a potentially singular linear system, which is handled by a Krylov linear solver. The framework may offer computational advantages in dealing with spaces like Hierarchical B-splines, T-splines, and LR-splines.

math.NA↗

arXiv2024

Two Nitsche-based mixed finite element discretizations for the seepage problem in Richards' equation

This paper proposes two algorithms to impose seepage boundary conditions in the context of Richards' equation for groundwater flows in unsaturated media. Seepage conditions are non-linear boundary conditions, that can be formulated as a set of unilateral constraints on both the pressure head and the water flux at the ground surface, together with a complementarity condition: these conditions in practice require switching between Neumann and Dirichlet boundary conditions on unknown portions on the boundary. Upon realizing the similarities of these conditions with unilateral contact problems in mechanics, we take inspiration from that literature to propose two approaches: the first method relies on a strongly consistent penalization term, whereas the second one is obtained by an hybridization approach, in which the value of the pressure on the surface is treated as a separate set of unknowns. The flow problem is discretized in mixed form with div-conforming elements so that the water mass is preserved. Numerical experiments show the validity of the proposed strategy in handling the seepage boundary conditions on geometries with increasing complexity.

math.NA↗

arXiv2023

Space-time least squares approximation for Schrödinger equation and efficient solver

In this work we present a space-time least squares isogeometric discretization of the Schrödinger equation and propose a preconditioner for the arising linear system in the parametric domain. Exploiting the tensor product structure of the basis functions, the preconditioner is written as the sum of Kronecker products of matrices. Thanks to an extension to the classical Fast Diagonalization method, the application of the preconditioner is efficient and robust w.r.t. the polynomial degree of the spline space. The time required for the application is almost proportional to the number of degrees-of-freedom, for a serial execution.

math.NA↗

arXiv2023

Energy conservative isogeometric techniques for the wave equation

We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is replaced by a strong form, written in terms of a projection operator. The system of equations is discretized with B-splines forming a De Rham complex along with suitable commutative projectors for the approximation of the second equation. The discrete scheme is energy conservative when discretized in time with a conservative method such as Crank-Nicolson. We propose a convergence analysis of the method to study the dependence with respect to the mesh size $h$, with focus on the consistency error. Numerical results show optimal convergence of the error in energy norm, and a relative error in energy conservation for long-time simulations of the order of machine precision.

math.NA↗

arXiv2023

Characterization of LAPPD timing at CERN PS testbeam

Large Area Picosecond PhotoDetectors (LAPPDs) are photosensors based on microchannel plate technology with about 400 cm$^2$ sensitive area. The external readout plane of a capacitively coupled LAPPD can be segmented into pads providing a spatial resolution down to 1 mm scale. The LAPPD signals have about 0.5 ns risetime followed by a slightly longer falltime and their amplitude reaches a few dozens of mV per single photoelectron. In this article, we report on the measurement of the time resolution of an LAPPD prototype in a test beam exercise at CERN PS. Most of the previous measurements of LAPPD time resolution had been performed with laser sources. In this article we report time resolution measurements obtained through the detection of Cherenkov radiation emitted by high energy hadrons. Our approach has been demonstrated capable of measuring time resolutions as fine as 25-30 ps. The available prototype had performance limitations, which prevented us from applying the optimal high voltage setting. The measured time resolution for single photoelectrons is about 80 ps r.m.s.

physics.ins-det↗

arXiv2021

CFNS Ad-Hoc meeting on Radiative Corrections Whitepaper

Current precision scattering experiments and even more so many experiments planed for the Electron Ion Collider will be limited by systematics. From the theory side, a fundamental source of systematic uncertainty is the correct treatment of radiative effects. To gauge the current state of technique and knowledge, help the cross-pollination between different direction of nuclear physics, and to give input to the yellow report process, the community met in an ad-hoc workshop hosted by the Center for Frontiers in Nuclear Science, Stony Brook University. This whitepaper is a collection of contributions to this workshop.

nucl-th↗

arXiv2020

On best constants in $L^2$ approximation

In this paper we provide explicit upper and lower bounds on certain $L^2$ $n$-widths, i.e., best constants in $L^2$ approximation. We further describe a numerical method to compute these $n$-widths approximately, and prove that this method is superconvergent. Based on our numerical results we formulate a conjecture on the asymptotic behaviour of the $n$-widths. Finally we describe how the numerical method can be used to compute the breakpoints of the optimal spline spaces of Melkman and Micchelli, which have recently received renewed attention in the field of Isogeometric Analysis.

math.NA↗

arXiv2019

Approximation in FEM, DG and IGA: A Theoretical Comparison

In this paper we compare approximation properties of degree $p$ spline spaces with different numbers of continuous derivatives. We prove that, for a given space dimension, $\smooth {p-1}$ splines provide better a priori error bounds for the approximation of functions in $H^{p+1}(0,1)$. Our result holds for all practically interesting cases when comparing $\smooth {p-1}$ splines with $\smooth {-1}$ (discontinuous) splines. When comparing $\smooth {p-1}$ splines with $\smooth 0$ splines our proof covers almost all cases for $p\ge 3$, but we can not conclude anything for $p=2$. The results are generalized to the approximation of functions in $H^{q+1}(0,1)$ for $q<p$, to broken Sobolev spaces and to tensor product spaces.

math.NA↗

arXiv2018

Local approximation operators on box meshes

This paper analyzes the approximation properties of spaces of piece-wise tensor product polynomials over box meshes with a focus on application to IsoGeometric Analysis (IGA). The errors are measured in Lebesgue norms. Estimates of different types are considered: local and global, with full or reduced Sobolev seminorms. Attention is also paid to the dependence on the degree and exponential convergence is proved for the approximation of analytic functions.

math.NA↗

arXiv2009

COMPASS Results on Collins and Sivers Asymmetries

In the list of the main items studied by the CERN COMPASS experiment there are the transverse spin and momentum effects visible in the azimuthal distributions of hadrons produced in the deep inelastic scattering. In the years 2002-2004 COMPASS has collected data with a 6LiD target with the polarization oriented transversely with respect to the muon beam direction for about 20% of the running time; in 2007, COMPASS has used for the first time a proton NH_3 target with the data taking time equally shared between longitudinal and transverse polarization of the target. After reviewing the results obtained with the deuteron, the new results for the Collins and Sivers asymmetries of the proton will be presented.

hep-ex↗

arXiv2009

Azimuthal asymmetries in SIDIS off unpolarized targets at COMPASS

Azimuthal asymmetries measured in unpolarized semi-inclusive deep inelastic scattering bring important information on the inner structure of the nucleons, and can be used both to estimate the average quark transverse momentum k_T and to access the so-far unmeasured Boer-Mulders functions. COMPASS results using part of the 2004 data collected with a 6LiD target and a 160 GeV positive muon beam are presented separately for positive and negative hadrons.

hep-ex↗