arXiv subjects

L. Bergamaschi

Publications and source records attributed to L. Bergamaschi.

3 recordsLinked to original sources

arXiv2025

Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices

We develop eigenvalue bounds for symmetric, block tridiagonal multiple saddle-point linear systems, preconditioned with block diagonal matrices. We extend known results for $3 \times 3$ block systems [Bradley and Greif, IMA J.\ Numer. Anal. 43 (2023)] and for $4 \times 4$ systems [Pearson and Potschka, IMA J. Numer. Anal. 44 (2024)] to an arbitrary number of blocks. Moreover, our results generalize the bounds in [Sogn and Zulehner, IMA J. Numer. Anal. 39 (2018)], developed for an arbitrary number of blocks with null diagonal blocks. Extension to the bounds when the Schur complements are approximated is also provided, using perturbation arguments. Practical bounds are also obtained for the double saddle-point linear system. Numerical experiments validate our findings.

math.NA↗

arXiv2022

Parallel Matrix-free polynomial preconditioners with application to flow simulations in discrete fracture networks

We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling parameter aimed at avoiding unwanted clustering of eigenvalues of the preconditioned matrices at the extrema of the spectrum. We use this preconditioned framework to solve a $3 \times 3$ block system arising in the simulation of fluid flow in large-size discrete fractured networks. We apply our polynomial preconditioner to a suitable Schur complement related with this system, which can not be explicitly computed because of its size and density. Numerical results confirm the excellent properties of the proposed preconditioner up to very high polynomial degrees. The parallel implementation achieves satisfactory scalability by taking advantage from the reduced number of scalar products and hence of global communications.

math.NA↗

arXiv2013

Instrumental neutron activation analysis of an enriched 28Si single-crystal

The determination of the Avogadro constant plays a key role in the redefinition of the kilogram in terms of a fundamental constant. The present experiment makes use of a silicon single-crystal highly enriched in 28Si that must have a total impurity mass fraction smaller than a few parts in 109. To verify this requirement, we previously developed a relative analytical method based on neutron activation for the elemental characterization of a sample of the precursor natural silicon crystal WASO 04. The method is now extended to fifty-nine elements and applied to a monoisotopic 28Si single-crystal that was grown to test the achievable enrichment. Since this crystal was likely contaminated, this measurement tested also the detection capabilities of the analysis. The results quantified contaminations by Ge, Ga, As, Tm, Lu, Ta, W and Ir and, for a number of the detectable elements, demonstrated that we can already reach the targeted 1 ng/g detection limit.

physics.chem-ph↗