[BOG][B] Generalized locally Toeplitz sequences: theory and applications

C Garoni, S Serra-Capizzano - 2017 - Springer
Sequences of matrices with increasing size naturally arise in several contexts and especially
in the discretization of continuous problems, such as integral and differential equations. The …

Symbol-based analysis of finite element and isogeometric B-spline discretizations of eigenvalue problems: exposition and review

C Garoni, H Speleers, SE Ekström, A Reali… - … Methods in Engineering, 2019 - Springer
We present an example-based exposition and review of recent advances in symbol-based
spectral analysis. We consider constant-and variable-coefficient, second-order eigenvalue …

The GLT class as a generalized Fourier analysis and applications

S Serra-Capizzano - Linear Algebra and its Applications, 2006 - Elsevier
Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced
as a generalization both of classical Toeplitz sequences and of variable coefficient …

Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case

G Barbarino, C Garoni… - Electronic Transactions on …, 2020 - ricerca.sns.it
In computational mathematics, when dealing with a large linear discrete problem (eg, a
linear system) arising from the numerical discretization of a partial differential equation …

[BOG][B] Block generalized locally Toeplitz sequences: theory and applications in the unidimensional case

G Barbarino, C Garoni, S Serra-Capizzano - 2019 - diva-portal.org
In computational mathematics, when dealing with a large linear discrete problem (eg, a
linear system) arising from the numerical discretization of a differential equation (DE), the …

Symbol-based multigrid methods for Galerkin B-spline isogeometric analysis

M Donatelli, C Garoni, C Manni… - SIAM Journal on …, 2017 - SIAM
We consider the stiffness matrices arising from the Galerkin B-spline isogeometric analysis
discretization of classical elliptic problems. By exploiting their specific spectral properties …

Non‐Hermitian perturbations of Hermitian matrix‐sequences and applications to the spectral analysis of the numerical approximation of partial differential equations

G Barbarino, S Serra‐Capizzano - Numerical Linear Algebra …, 2020 - Wiley Online Library
This article concerns the spectral analysis of matrix‐sequences which can be written as a
non‐Hermitian perturbation of a given Hermitian matrix‐sequence. The main result reads as …

U-splines: Splines over unstructured meshes

DC Thomas, L Engvall, SK Schmidt, K Tew… - Computer Methods in …, 2022 - Elsevier
U-splines are a novel approach to the construction of a spline basis for representing smooth
objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). A spline …

[HTML][HTML] Block generalized locally Toeplitz sequences: from the theory to the applications

C Garoni, M Mazza, S Serra-Capizzano - axioms, 2018 - mdpi.com
The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for
computing the asymptotic spectral distribution of matrices A n arising from virtually any kind …

Are the eigenvalues of the B‐spline isogeometric analysis approximation of −Δu = λu known in almost closed form?

SE Ekström, I Furci, C Garoni, C Manni… - … Linear Algebra with …, 2018 - Wiley Online Library
We consider the B‐spline isogeometric analysis approximation of the Laplacian eigenvalue
problem− Δ u= λ u over the d‐dimensional hypercube (0, 1) d. By using tensor‐product …